Pressure measuring apparatus, flow sensor and methods

Abstract

A pressure measuring apparatus (10) comprising: a microfluidic chip (20) comprising at least one capillary measurement chamber and a fluid inlet fluidically coupled to the measurement chamber, wherein the measurement chamber and the fluid inlet are configured to permit a stable meniscus between a first fluid and a second fluid to be formed in the measurement chamber when supplying the second fluid via the fluid inlet to the measurement chamber; and a sensing system (90) configured to detect a position and a shape of the meniscus and to determine a pressure in the second fluid based on the position and the shape of the meniscus.

Description

[0001] Pressure Measuring Apparatus, Flow Sensor and Methods

[0002] DESCRIPTION

[0003] Embodiments of the present invention relate to a pressure measuring apparatus, i.e., a pressure sensor configured to measure pressure using a meniscus formed in a capillary measurement chamber, to methods for measuring pressure, and to flow sensors.

[0004] TECHNICAL BACKGROUND

[0005] Sensors for measuring the pressure or flow inside a (micro-)channel containing a fluid are used in a large number of applications, e.g., in medical devices, pharmaceutical, technological or chemical industries, laboratory automation as well as in industrial production to monitor and / or meter the transport and conditions of the fluid. Many of these applications require small amounts of fluids, e.g., medical applications of drug delivery, metering and dispensing of fluids for industrial production, biotechnology and microchemical synthesis, automated dosing of adhesives or underfill for electronic assemblies, etc. Most of these applications benefit from measuring or monitoring fluid pressure or flow of the working fluid inside the transport channel for precise dosage (metering), quality control or process monitoring. Since pressure of flow sensors typically have to be in direct contact with the flow to measure these quantities, hygienic issues, strong wear or clogging of the sensor may call for frequent cleaning or replacement of the sensor. However, according to the state of the art, such sensors are usually too expensive to be replaced frequently or even to be considered as a single use item (e.g. like mandatory in most medical applications). Currently, there is no cost efficient solution available that allows for single use of pressure or flow sensors at satisfactory performance, particularly at flow rates below several milliliters per minute (mL / min). Therefore, sensors usually have to be cleaned and re-used, which is costly and time-consuming or even prohibitive for hygienic reasons, e.g., in medical applications.

[0006] Today, state of the art pressure sensors are mainly based on piezoresistive or capacitive transduction principles, and devices are mostly fabricated in MEMS technology. One or more of such pressure sensors may be combined by applying the concepts of Pitot, Venturi or differential pressure sensing [1] to realize sensors for measuring the flow rate. Such pressure deduced flow measurements are a very common principle of flow sensing and many variations of it exist. Alternatively, flow rates may also be measured by thermal flow sensors or the Coriolis type flow sensors [2, 3], which are - apart from pressure deduced flow measurements - the prominent technologies for low flow rates, while for larger flow rates, often mechanical or ultra-sonic principles are used. Most of these sensor technologies usually require that the transducer element (e.g., a membrane, or a heater or a vibrating channel, etc.) are in direct contact with the fluid. Thus, the transducers are contaminated by the fluid and due to the small size and fragile nature, they are very difficult to clean when they are clogged or the fluid has to be changed. Physically separating the transducer from the fluid contaminated parts of the sensor (i.e., the measurement channel or chamber) is not a satisfactory solution, because this separation reduces the sensitivity and implies additional fabrication and packaging efforts to efficiently mate the transducer with the disposable, fluid contaminated measurement channel of the sensor. This increases the costs of the systems, while reducing the performance and making disposable use of the sensors still prohibitive.

[0007] Typical examples of such pressure and flow measurement sensors according to the state of the art that suffer from the mentioned problems are described in the following publications. US 4,384,578 A describes a flow sensor. Flow metering is effected by means of a thermal principle. JP 3149030 A describes pressure metering which is effected by a conventional MEMS pressure sensor. WO 94 / 04073 A1 describes a flow monitoring system. Flow metering is effected by means of an acoustic principle using Doppler shift. JP 2004117366 A describes a flow measuring machine. Flow metering is effected by a rotating disc that is read out by an optical sensor including a LED and a photodiode. WO 2006 / 060226 A1 describes a pressure sensor. The sensor measures a pressure change due to a change in the resonance frequency between a capacitance and an inductance. One of the electrodes has to be disposed with the fluid-contaminated part (i.e. membrane). EP 2901121 B1 describes a capacitive pressure sensor and its use for flow measurement where the electrodes of the capacitor are separated from the fluidic channel and not contaminated by the liquid. Therefore, the electronic part can be re-used, while the liquid contaminated measurement channel can be exchanged and disposed of at low cost. In practice, the capacitive measurement principle turns out to be unreliable and the inevitable walls of the deformable measurement channel reduce the sensitivity of the measurement. Chia-Chu Chiang et al., "An implantable capacitive pressure sensor for biomedical applications", Sensors and Actuators A, 134 (2007) pages 382-388, describe a capacitive pressure sensor. The pressure sensor is based on the deformation of a PDMS (polydimethylsiloxan) layer which is embedded between two electrodes. The electrodes are formed by gold layers, whereby the PDMS layer is a pressure-sensitive dielectric. In order to realize a "tube sensor", such a pressure sensor is wrapped around a silicone tube and jacketed with a PI (polyimide) tube. The distance between the two electrodes varies depending on the thickness of the PDMS layer, i.e. the measurement principle is based on the deformation of the dielectric material (PDMS) that leads to a change in the electrode distance. When a pressure is applied to the sensor, the gap between two sensing electrodes is reduced and the capacitance rises accordingly. R.E. Oosterbroek, et al., "A micromachined pressure / flow sensor", Sensors and Actuators 77, 1999, pages 167-177, describe a differential pressure flow sensor. The flow sensor comprises two capacitive or piezo-resistive pressure sensors. In the capacitive sensor, the distance between the plates will be reduced when the pressure rises. More examples of miniaturized flow sensors according to the state of the art are described in [1], [2], and [3] and the references therein.

[0008] Despite the larger variety of available approaches to measure pressure and flow by various methods, sensors with single-use application with good performance at relatively low cost can be hardly found on the market.

[0009] SUMMARY OF THE INVENTION

[0010] It is a well-known approach that pressure can be measured by the height of a fluid column, or even more precisely by the position of a meniscus in a transparent tube, like commonly applied to illustrate the Venturi principle. Usually, the height level h of a liquid column (e.g. water or mercury) over an equilibrium position is attributed to a hydrodynamic pressure p acting on the column, as given by the following equation:

[0011] (1) P = p - g - h , depending on the density p of the liquid column and the acceleration g by gravity. Thus, the height h of the liquid I gas interface, is a measure for the pressure p acting on the other end of the liquid column. It should be noted that in this “classical” approach for pressure measurement, the capillary pressure exerted by the meniscus is usually neglected, because its value is very small compared to the hydrostatic pressure exerted by the weight of the liquid column, given by equation (1). The classical measurement principle thus assumes equilibrium between the input pressure (referred to as p / „) and the hydrostatic pressure exerted by a liquid column (given by equation (1)), which is considered to be independent of surface tension (which is not strictly valid in general). The transduction principle of this classical pressure measurement is very simple and does not require either a membrane nor a transducer. The result can be readily read by the human eye on an attached scale.

[0012] The drawback of this differential pressure sensing approach is that it is not independent from gravity. Ultimately, the height of the column indicates by definition the “hydrostatic pressure” and by means of fluidic design of the apparatus, this hydrostatic pressure has to be equal to the pressure pm measured at the input port of the device, according to Pascal’s principle. The liquid column used for measurement therefore needs to be aligned well with the direction of gravity to prevent measurement errors, and any dynamic movement of the apparatus needs to be avoided, as any acceleration would also act on the liquid column and influence the final measurement result. In particular, the measurement principle would fail totally in microgravity conditions and in space, due to absence of gravity. Therefore, such pressure measuring devices based on the principle of hydrostatic liquid columns can only be operated in stable terrestrial environments and are today mainly used for educational purposes, only.

[0013] In some prior art publications the position of a liquid column in a micro channel was considered as indicator for pressure in the limit of negligible gravity and dominating capillary forces (i.e. at low Bond numbers) where the capillary forces work against a compressible gas volume enclosed by the liquid meniscus in a dead-end channel. In these prior art concepts only the position of the meniscus in the dead-end channel has been considered for determining the pressure, similarly like for the classical hydrostatic approach described above. Reference is made to

[0014] to

[0019] , for example. Taking the meniscus position as an indicator for the pressure inside the dead-end channel is a reasonable approximation, but not an exact solution, because the curvature of the meniscus is not considered. In prior art disclosures, the meniscus curvature is not determined explicitly by the sensor but it is either neglected or assumed to be constant or to be changing according to a known ideal relationship [4], These can be reasonable approximations in case the channel walls have homogenous, ideal and well-known properties everywhere, and both fluids are homogeneous with constant wetting angle and surface tension. In practice, however, the wetting properties (i.e. contact angle) of the channel walls are neither constant nor known with high accuracy. In microchannels made from polymer or glass the contact angle is often variable by +- 10° (or even more) and the variations can be different at different positions along the channel. Also, a drift over time in the contact angle can be observed quite often, associated with a contamination of the clean surface by exposure to the environment, as well as hysteresis effects due to differences in advancing or receding contact angles. In practice, the contact angle is hardly constant in time and at different locations, and with it the Laplace pressure exerted by the liquid meniscus. Finally, also the liquid surface energy might be different than assumed due to additives and contaminations of the liquid, or the liquid properties might be completely unknown. Thus, any approach using an analytical formula aiming to determine the pressure from the measured meniscus position h, assuming a constant Laplace pressure (corresponding to a certain constant meniscus curvature as a consequence of the assumed liquid and solid properties) and not having a- priori knowledge of the fluid properties, such as surface tension and the contact angle formed in the measurement chamber, will be lacking in accuracy and suffers from systematic errors in measuring pressure.

[0014] Therefore, there is a particular need for a pressure measuring apparatus using the principle of differential pressure sensing which can sense pressure with improved accuracy and reduce systematic errors in pressure measurements compared to the state of the art, can be fabricated at low cost, and is easily extendable and disposable to realize single use applications in a flexible manner. It is also advantageous that such a pressure measuring apparatus can be operated in microgravity conditions and in space (i.e. at low Bond numbers). There is also a particular need for a flow measuring apparatus using the principle of differential pressure based flow sensing.

[0015] Such needs are fulfilled, and multiple advantages are provided, by a pressure measuring apparatus according to claim 1 , a pressure measuring apparatus according to claim 34, a flow measuring apparatus according to 23, and methods for measuring pressure according to claims 25 and 39. Further, specific implementations of the present inventive concept are defined in the dependent claims.

[0016] According to an embodiment, a pressure measuring apparatus comprises a microfluidic chip comprising at least one capillary measurement chamber and a fluid inlet fluidically coupled to the measurement chamber. The measurement chamber and the fluid inlet are configured to permit a stable meniscus between a first fluid and a second fluid to be formed in the measurement chamber when supplying the second fluid (such as under pressure) via the fluid inlet to the measurement chamber. The pressure measuring apparatus further comprises a sensing system configured to detect a position and a shape of the meniscus and to determine a pressure in the second fluid based on the position and the shape of the meniscus. The transduction principle of the pressure measuring apparatus of the present concept relates to using an interface formed between the first fluid and the second fluid, such as the meniscus stably formed in the capillary measurement chamber, as a pressure transducing mechanism instead of a solid material membrane. Since less pressure is needed to produce a detectable deformation of the meniscus compared to silicon, metal or even rubber membranes in conventional pressure sensors, the pressure sensitive meniscus formed by fluids as the transducing membrane allows more sensitivity than conventional membranes formed by solid materials. Thus, the pressure measuring apparatus of the present concept using the free fluidic interface between the fluids in the measurement chamber provides pressure sensing with an increased sensitivity.

[0017] In the pressure measuring apparatus, pressure is transduced into the position and the shape of the meniscus in the measurement chamber. In other words, it was recognized that the pressure in the second fluid does not only have an effect on the position or the shape of the meniscus, but may influence both, the shape and the position. Both of which are essential to exactly determine the Laplace pressure across the free interface between the fluids. Thus, detecting both, the shape and the position of the meniscus permits determining the pressure in the second fluid more precisely when compared to state of the art pressure sensors which rely only on detecting the meniscus position.

[0018] It may be known to persons skilled in the art that the position, or the height, of the meniscus in capillary fall experiments may change discontinuously despite a continuous flow being supplied to the capillary [6], At times, the meniscus may ‘stick’ at certain positions within the capillary and suddenly ‘slip’ to a different position when the pressure may have exceeded a certain limit which enables the meniscus to overcome the ‘pinning’ situation. During the described ‘pinning’ of the meniscus, the shape of the meniscus may deform to equilibrate the pressure that may have been built up due to the outflow of the fluid. Thus, by observing changes in the meniscus such as changes in the shape of the meniscus, in addition to its position, corresponding changes in the pressure of the meniscus may be detected even when the meniscus may not be moving due to the ‘pinning’ situation.

[0019] The combined detection of the position and the shape, or curvature, of the meniscus by the sensing system allows the pressure measuring apparatus to determine and to compensate any global offsets that may be introduced through non-ideal surfaces of the measurement chamber, such as a contact angle being different than assumed, or changes in the surface tension of the liquid, such as due to different fluidic properties, temperature effects or surface active agents. The present inventive concept may reduce systematic errors arising due to the described offsets compared to the state of the art and does not require a-priori knowledge of the fluidic properties, such as surface tension and contact angle. Therefore, the combined measurement of meniscus position and meniscus shape, such as curvature, provides a more accurate pressure sensing than measuring the meniscus position alone.

[0020] The capillary measurement chamber of the pressure measuring apparatus is designed with respect to its dimensions so as to apply capillary action onto fluids therein, that is, the measurement chamber is miniaturized in its dimensions to permit operating conditions of the pressure measuring apparatus, in which the Bond number Bo is significantly smaller than 1 (Bo « 1). The meniscus formed between the fluids in the measurement chamber is then maintained to be stable and greatly independent of gravity. This means that the pressure measuring apparatus is independent of the orientation of the measurement chamber and can also work in micro-gravity and space applications. Thus, the pressure measuring apparatus of the present concept can be operated in micro-gravity conditions and in space, in contrast to pressure sensors based on the classical hydrostatic measurement principles which observe only the position of the meniscus at high Bond numbers.

[0021] Further, the capillary measurement chamber of embodiments of the pressure measuring apparatus is designed such that the Concus-Finn condition [7] is not fulfilled anywhere in the measurement chamber. This ensures that indeed a stable meniscus is formed in the measurement chamber, the position and shape of which can be detected by the sensor.

[0022] The pressure measuring apparatus of embodiments of the present inventive concept may be designed to have a measurement range including ultra-low pressures. Hence, even pressures that are not measurable with state of the art pressure sensors are detectable with embodiments of the pressure measuring apparatus.

[0023] The measurement chamber may be easily integrated into the microfluidic chip using the same fabrication technologies as used for the microfluidic chip, such as low cost injection moulding technology, in addition to functional elements of the microfluidic chip. The microfluidic chip and the capillary measurement chamber comprised therein may be fabricated by the low cost injection moulding technology as disposable parts or devices separately from the sensing system. Therefore, the microfluidic chip representing a fluid contaminable part of the pressure measuring apparatus can be exchanged and disposed at much lower costs than in state of the art pressure sensors comprising MEMS sensors and electronic components fully integrated with the micro channel hosting the fluid.

[0024] Further, the sensing system transducing fluidic signals, such as the position and shape of the meniscus formed in the measurement chamber, to sensor signals, such as electrical signals, does not need to make fluidic and / or mechanical contact to the microfluidic chip. Therefore, the sensing system is safe from contamination and does not need to be exchanged or cleaned before re-use.

[0025] In embodiments, a modular design of the pressure measuring apparatus does not require contact between the sensing system and the microfluidic chip. This allows the sensing system to be easily interfaced with the microfluidic chip comprising the measurement chamber enabling a modular use. For example, for changing the measurement range of the pressure measuring apparatus, only parts, such as the microfluidic chip, may be exchanged. The sensing system may then be the same for a variety of different microfluidic chips, which may even be made from different materials, designed for different pressure ranges and intended for different purposes.

[0026] According to an embodiment, the sensing system is configured to determine that the pressure in the second fluid has a first value if the meniscus has a first position and a first shape, to determine that the pressure in the second fluid has a second value if the meniscus has a first position and a second shape different from the first shape, and to determine that the pressure in the second fluid has a third value if the meniscus has a second position different from the first position.

[0027] Thus, in embodiments, the sensing system is able to detect a change in the shape of the meniscus, such as the second shape being different from the first shape, even when the position of the meniscus is unchanged such as the meniscus being stationary and having the first position. When the position of the contact line of the meniscus remains stationary and the curvature of the meniscus changes, the meniscus may enter an unstable equilibrium state, in which small changes in the pressure across the meniscus may lead to sudden changes in its position until a stable equilibrium is reached again. This behavior is well known in literature as “pinning” or “slip-stick effect” [5, 6], The sensing system is further able to detect the change in the position of the meniscus, such as the meniscus having the second position, and can determine the pressure based on the changed position. For state of the art pressure sensors relying on measuring the position of the meniscus (contact line) alone, measuring the pressure in such situations involves discontinuous jumps in the sensed sensor signal making it difficult to detect small changes in pressure continuously. Thus, the dual measurement of the position and shape of the meniscus makes it possible to compensate for the mentioned “stick-slip effect”, to increase the sensitivity and to be make the measurement result largely independent of variations of the contact angle (in time and space), thereby permitting an improved accuracy of pressure measurements.

[0028] A contact line may be defined by points in space where all the three phases: solid, liquid and gas meet simultaneously i.e. where the free liquid surface makes contact to the solid walls. A meniscus has exactly one closed contact line that makes contact to all the walls of the channel and by this completely separates liquid and gas phase. In contrast to the meniscus, a bubble (or droplet) may have zero, one or more than one closed contact lines, but a maximum of one at each of the channel walls. Since the closed contact lines always remain separated, a bubble is never able to fully separate the liquid from the gas phase in the channel. There always remains a liquid bridge in the edges of the channel, fluidically connecting the liquid columns to both sides of the bubble.

[0029] In embodiments, the sensing system is configured to store allocation data allocating positions and shapes of the meniscus to known pressures of the fluid and to determine the pressure of the fluid using the allocation data.

[0030] In embodiments, the sensing system is configured to determine the allocation data using machine learning and / or artificial intelligence. In embodiments, the sensing system of the pressure measuring apparatus may permit a variety of independent evaluations of the same allocation data by the use of different Al software programs and / or calibration functions and / or analytical system models. This can be exploited for increasing measurement precision, for example by averaging, consistency checking and fault detection. The sensing system can thus be permitted to self-confirm the plausibility of the measurement results in various ways, especially when using a plurality of measurement chambers that measure information, such as pressure, in different ways by different types of measurement chambers.

[0031] In embodiments, the sensing system comprises an optical system configured to generate image data of the position and the shape of the meniscus formed in the measurement chamber and to evaluate the image data to determine the position and the shape of the meniscus. In embodiments, the measurement chamber is in fluidic connection to the ambient environment by a ventilation opening. The ventilation opening is arranged spaced apart from the fluid inlet to permit the stable meniscus to be formed in the measurement chamber between the fluid inlet and the ventilation opening.

[0032] In embodiments, a hydraulic radius of the capillary measurement chamber varies along a longitudinal extension thereof.

[0033] In embodiments, the capillary measurement chamber further comprises a pinning structure configured to permit the position of the meniscus in the measurement chamber to be stationary over a range of pressures and to permit the shape of the meniscus in the measurement chamber to be variable over the range of pressures.

[0034] In embodiments, the pinning structure comprises sharp edges of the cross-sectional area of the measurement chamber, different surface roughness of the inner surface of the measurement chamber and / or chemical or electrical modifications of the inner surface of the measurement chamber.

[0035] Thus, in embodiments, the capillary measurement chamber may be designed in a way that the meniscus is prevented to move further along the measurement chamber over a range of pressures, such as using the aforementioned pinning structure. Thus, in this range of pressures, changes in shape of the meniscus formed in the measurement chamber may indicate predominantly for changes in the pressure to be measured, and outside this range of pressures, changes in the position of the meniscus formed in the measurement chamber may indicate predominantly for changes in the pressure to be measured.

[0036] In embodiments, the capillary measurement chamber is one of a plurality of capillary measurement chambers comprising fluidically coupled fluid inlets, each configured to permit a stable meniscus between a first fluid and a second fluid to be formed in the measurement chamber. The pressure ranges of the plurality of capillary measurement chambers, in which a stable meniscus may be formed, may be different in the plurality of capillary measurement chambers. The plurality of measurement chambers may be readout by a single sensing system of the pressure measuring apparatus. The plurality of measurement chambers may provide complementary information to increase the performance of the pressure measuring apparatus at no costs in addition to the costs for fabricating the plurality of measurement chambers, e.g. by injection moulding, which are greatly independent of the design and the number of the plurality the measurement chambers.

[0037] In embodiments, the capillary measurement chamber is a first capillary measurement chamber. The pressure measuring apparatus further comprises a second capillary measurement chamber configured to permit a stable meniscus between a first fluid and a second fluid to be formed in the measurement chamber. The first pressure measurement chamber is in fluidic connection to the ambient environment by a ventilation opening. The ventilation opening is arranged spaced apart from the fluid inlet to permit the stable meniscus to be formed in the measurement chamber between the fluid inlet and the ventilation opening. The hydraulic diameter of the first capillary measurement chamber decreases with increasing distance from the fluid inlet. The second pressure measurement chamber is a non-vented measurement chamber.

[0038] In embodiments, the pressure measuring apparatus further comprises a pressure fluctuation generating device configured to superimpose time dependent pressure fluctuations to at least one of the fluids so as to cause variations of the position and / or the shape of the meniscus in the measurement chamber. The sensing system is configured to detect the variations of the position and / or the shape of the meniscus and to determine the pressure in the second fluid using the detected variations.

[0039] When subjected to the time dependent pressure fluctuations superimposed by the pressure fluctuation generating device, the meniscus within the measurement chamber will not rest in a stationary position and will change its position and / or shape. By this measure, the pressure fluctuation generating device of the pressure measuring apparatus may generate non-stationary conditions in a controlled way, even when the pressure in the second fluid, or pressures to be measured, are stationary. By continuously reading and averaging the fluctuating pressure values over time, the mean pressure is detected more precisely than by individual pressure measurements at discrete points in time.

[0040] Further, in embodiments, stick-slip effects may be reduced due to the generated non- stationary conditions of the meniscus. The variations of the position and / or the shape of the meniscus introduced by the pressure fluctuation generating device may lead to advancements and recessions of the meniscus oscillating around its equilibrium position, which may then provide a better mobility to the meniscus when the equilibrium position changes due to an applied external pressure. This may permit the pressure measuring apparatus to be more sensitive to smaller changes in the position and the shape of the meniscus. Thus, the pressure fluctuation generating device may be beneficial in preventing stick-slip issues of the meniscus formed in the measurement chamber.

[0041] In embodiments, the sensing system is configured to determine a rheological property of the second fluid using a time series of the detected variations of the position and / or the shape of the meniscus. Thus, embodiments may permit an estimation of rheological properties of the second fluid such as viscosity, surface tension and density.

[0042] According to another aspect of the present inventive concept, a flow sensor comprises a sensor fluid inlet, a sensor fluid outlet and a fluid channel between the sensor fluid inlet and the sensor fluid outlet. The flow sensor further comprises a first pressure measuring apparatus according to an embodiment of the invention described earlier. The fluid inlet of the first pressure measuring apparatus is fluidically coupled to the fluid channel at a first position. The flow sensor further comprises a second pressure measuring apparatus according to an embodiment of the invention described earlier. The fluid inlet of the second pressure measuring apparatus is fluidically coupled to the fluid channel at a second position spaced apart from the first position. The fluid channel forms a measurement channel between the first position and the second position. The flow sensor further comprises a flow rate determiner configured to determine a flow rate through the fluid channel using the pressures determined by the sensing systems of the first and second pressure measuring apparatuses. The first and second pressure measuring apparatuses may be formed by any of the pressure measuring apparatuses disclosed herein and reference is made to the corresponding descriptions thereof.

[0043] In embodiments, the flow sensor comprising an additional connection channel fluidically connecting one of the at least one measurement chamber of the first pressure measuring apparatus to one of the at least one measurement chamber of the second pressure measuring apparatus. By this measure, the flow sensor permits a configuration wherein the measurement chambers of the pressure measuring apparatuses share the same reference pressure. Irrespective of the ambient environment conditions in which the flow sensor is operated, the relative change in the position of the menisci in the measurement chambers permits a determination of the flow rate. This provides the advantage that measuring the relative change in the position of the menisci permits a measurement of a pressure difference without knowledge of the absolute ambient pressure even when the flow sensor is operated in non-standard conditions. Thus, according to embodiments of the invention corrections to the measured pressure difference related to operational (environmental) conditions may be avoided, in contrast to usual flow rate determinations.

[0044] According to another aspect of the present inventive concept, a pressure measuring apparatus comprises a microfluidic chip comprising at least one measurement chamber and a fluid inlet fluidically coupled to the measurement chamber. The measurement chamber and the fluid inlet are configured to permit a stable meniscus between a first fluid and a second fluid to be formed in the measurement chamber when supplying the second fluid (such as under a pressure) via the fluid inlet to the measurement chamber. The pressure measuring apparatus further comprises a pressure fluctuation generating device configured to superimpose time dependent pressure fluctuations to at least one of the fluids so as to cause variations of the position and / or the shape of the meniscus in the measurement chamber. The pressure measuring apparatus further comprises a sensing system configured to detect a position and / or a shape of the meniscus and to determine a pressure in the second fluid based on the position and / or the shape of the meniscus. The sensing system is configured to detect the variations of the position and / or the shape of the meniscus and to determine the pressure in the second fluid using the detected variations.

[0045] In embodiments, the sensing system is further configured to determine a rheological property of the second fluid using a time series of the detected variations of the position and / or shape of the meniscus in the measurement chamber.

[0046] When the pressure is changed dynamically, due to spontaneously, or naturally, occurring fluctuations and / or pressure fluctuations superimposed by the use of the pressure fluctuation generating device, the pressure measuring apparatus of the present concept may allow the determination of rheological properties of the second fluid using the time series of sensing system signals such as variations of the position and / or the shape of the meniscus in the measurement chamber.

[0047] In embodiments, the pressure fluctuation generating device comprises one or more piezoelectric actuators or one or more micro-heaters.

[0048] BRIEF DESCRIPTION OF THE FIGURES Embodiments of the present invention are described herein in brief detail with respect to the appended drawings and figures, in which:

[0049] Fig. 1 shows a schematic diagram of a pressure measuring apparatus according to an embodiment of the present inventive concept;

[0050] Fig. 2 shows a schematic illustration of two implementations of a measurement chamber according to an embodiment of the present inventive concept;

[0051] Fig. 3 shows a schematic illustration of implementations of a measurement chamber according to an embodiment of the present inventive concept;

[0052] Fig. 4 shows a schematic illustration of implementations of a measurement chamber according to an embodiment of the present inventive concept;

[0053] Fig. 5 shows a schematic illustration of implementations of a measurement chamber according to an embodiment of the present inventive concept;

[0054] Fig. 6 shows a schematic illustration of implementations of a measurement chamber comprising a pinning structure according to an embodiment of the present inventive concept;

[0055] Fig. 7 shows a schematic illustration of implementations of a measurement chamber comprising a pinning structure according to an embodiment of the present inventive concept;

[0056] Fig. 8 shows a schematic illustration of an implementation of a pressure measuring apparatus comprising a plurality of measurement chambers according to an embodiment of the present inventive concept;

[0057] Fig. 9 shows a schematic diagram of an implementation of a flow sensor according to an embodiment of the present inventive concept;

[0058] Fig. 10 shows a schematic diagram of an implementation of a flow sensor comprising an additional connection channel according to an embodiment of the present inventive concept; Fig. 11 shows a schematic diagram of a pressure measuring apparatus according to another embodiment of the present inventive concept;

[0059] DETAILED DESCRIPTION OF THE FIGURES

[0060] In the following description, embodiments are discussed in detail, however, it should be appreciated that the embodiments provide many applicable concepts that may be embodied in a wide variety of the field of pressure and flow sensors. The specific embodiments discussed are merely illustrative of specific ways to implement and use the present concept, and do not limit the scope of the embodiments. In the following description of embodiments, the same or similar elements or elements that have the same functionality are provided with the same reference sign or are identified with the same name, and a repeated description of elements provided with the same reference number or being identified with the same name is typically omitted. In the following description, a plurality of details is set forth to provide a more thorough explanation of embodiments of the disclosure.

[0061] However, it will be apparent to one skilled in the art that other embodiments may be practised without these specific details. In other instances, well-known structures and devices are shown in diagram form rather than in detail in order to avoid obscuring examples described herein. In addition, features of the different embodiments described herein may be combined with each other, unless specifically noted otherwise.

[0062] Equal or equivalent elements or elements with equal or equivalent functionality are denoted in the following description by equal or equivalent reference numerals even if occurring in different figures.

[0063] For facilitating the description of the different embodiments, the drawings comprise a Cartesian coordinate system x, y, z, wherein the x-y-plane corresponds, i.e. is parallel, to a cross section of a pressure measuring apparatus, wherein the direction vertically up with respect to the reference plane (x-y-plane) corresponds to the “+z” direction, and wherein the direction vertically down with respect to the reference plane (x-y-plane) corresponds to the “-z” direction. In the following description, the term “lateral” means a direction parallel to the x-direction, the term “longitudinal” means a direction parallel to the y-direction and the term “vertical” means a direction parallel to the z-direction. A pressure measuring apparatus 10, in accordance with an aspect of the present inventive concept, is now described with respect to the schematic diagram of Fig. 1 .

[0064] The pressure measuring apparatus 10 of Fig. 1 comprises a microfluidic chip 20 and a sensing system 90.

[0065] The microfluidic chip 20 comprises at least one capillary measurement chamber and a fluid inlet fluidically coupled to the measurement chamber (not shown in Fig. 1). The measurement chamber and the fluid inlet are configured to permit a stable meniscus between a first fluid and a second fluid to be formed in the measurement chamber when supplying the second fluid via the fluid inlet to the measurement chamber. The sensing system 90 is configured to detect a position and a shape of the meniscus and to determine a pressure in the second fluid based on the position and the shape of the meniscus.

[0066] The transduction principle of the pressure measuring apparatus 10 may comprise using the meniscus formed between the first fluid and the second fluid in the capillary measurement chamber as a pressure transducing mechanism. Determining the pressure in the second fluid from the position and additionally the shape of the fluid meniscus may form a pressure measurement principle of the pressure measuring apparatus 10 in accordance with the present inventive concept. This pressure measurement principle may render the use of any kind of membrane, the bending of which may be a transduction mechanism, obsolete. Instead, the meniscus formed by a free interface between the first fluid and the second fluid may be considered as a pressure sensitive membrane itself, as per the proposed inventive concept.

[0067] It is noted that the pressure measuring apparatus 10 may be supplied with the second fluid under pressure. It may be feasible that the measurement chamber may be filled spontaneously when the second fluid is supplied. That is, it may not be necessary to supply the second fluid under pressure.

[0068] The position and the shape of this “interfacial fluidic membrane” between the first fluid and the second fluid is associated with a certain pressure difference caused by surface tension at the fluidic interface. Any deviation from the undisturbed equilibrium state of the meniscus may be considered as indicator for an additional input pressure that is applied on either side of the free fluidic surface i.e. the meniscus. Whether an additional input pressure is applied or not, surface tension leads to a curved surface of the meniscus with minimum interfacial energy that is exerting a Laplace pressure piapgiven by the Young-Laplace equation: where n denotes the first principal radius (which is the inverse value of the first principal curvature) and denotes the second principal radius (which is the inverse value of the second principal curvature) of the free fluidic surface.

[0069] It is difficult to describe the shape of a meniscus by explicit formulae in general. Depending on the geometry of the measurement chamber, or channel, the shape may mostly be computed numerically. An exception is the shape of a meniscus in a circular capillary which is given by a spherical cap

[0020] ,

[0070] It is understandable that the Laplace pressure piapgenerated by the meniscus is only dependent on the surface tension sigma crand on the curvature k of the meniscus, which in turn depends on the contact angle 0 and the geometrical shape of the measurement chamber hosting the meniscus. Thus, the shape and position of the meniscus in any given channel geometry of the measurement chamber corresponds to a certain pressure difference between both sides of the meniscus given by the Young-Laplace equation. And therefore, based on the Young-Laplace equation, the position and the shape of the meniscus formed by the first fluid and the second fluid in the measurement chamber may provide an exact determination of the pressure in the second fluid.

[0071] In particular, for a circular capillary with an inner diameter of 2r and a contact angle of 0, the Young-Laplace equation given by equation (2) may be simplified to: to obtain an equation exploited in the well-known capillary rise experiment, wherein the capillary pressure pcapis counterbalanced by the hydrostatic pressure of a liquid column rising in a small capillary. In such instances, the capillary pressure cannot be neglected anymore. Taking the capillary pressure of a circular capillary tube according to equation (3) and considering an equilibrium situation with the hydrostatic pressure of the liquid column in the capillary given by equation (1), one arrives at the well-known formula for the rising height h of a liquid level in an upright standing capillary:

[0072] , 2 cos©

[0073] (4) h = <J - pgr

[0074] In this experiment, hydrostatic forces and capillary forces are equally eminent, because the capillary usually has to be quite small, for example, the inner diameter 2r may be 500 pm, to exhibit a visible capillary rise height h. In contrast to the capillary pressure, the hydrostatic pressure is independent of the diameter of the tube (i.e. liquid column), but just depends on the height of the liquid column. Whether or not a significant capillary rise may be observed, or whether a liquid column may settle according to the classical hydrostatic pressure principle, i.e., the hydrostatic pressure balance, is thus a matter of the details of the experimental setup, particularly its dimensions.

[0075] In fluid mechanics, often dimensionless numbers are used to describe significant qualitative similarities respectively differences between certain hydrodynamic situations. The so-called Eotvos number (Eo), also referred to as the Bond number (Bo), is the relevant dimensionless number to qualitatively illustrate the difference between the cases of the classical hydrostatic pressure measurement devices, the capillary rise experiment and other measurement setups that consider the equilibrium position of a meniscus in a cavity under negligible gravity conditions, like done herein. Different values of the Bond number (Bo) indicate for different regimes of dominating forces that lead to the specific equilibrium position and shape of the meniscus. In particular, the Bond number is measuring the importance of gravitational forces compared to surface tension forces for the movement of a fluidic interface. It may be defined as follows:

[0076] (5) Eo = Bo = where Ap refers to a difference in density of the fluids forming the meniscus, g refers to gravitational acceleration, L refers to a characteristic length associated with the measurement chamber and y refers to surface tension associated with the meniscus.

[0077] For classical hydrostatic (pressure) measurement devices, the Bond number is much larger than one (Bo » 1) meaning that hydrodynamic effects caused by surface tension, that is capillary pressure, are negligible as compared to those effects caused by gravity, that is hydrostatic pressure. For the capillary rise experiment, however, capillary effects as well as gravitation effects should be in the same order of magnitude to enable a detectable capillary rise height at equilibrium between capillary pressure and hydrostatic pressure. Therefore, the Bond number will be close to one (Bo ~ 1), which indicates that hydrostatic forces and capillary forces have the same order of magnitude and neither one is dominant nor neglectable. The Bond number is thus a useful indicator whether capillary pressure or hydrostatic pressure will dominate in a certain situation.

[0078] It is to be noted that classical hydrostatic pressure measurement apparatuses cannot be operated at Bo « 1 because a stable equilibrium of the meniscus cannot be attained inside a capillary tube. The general working principle of “measuring liquid column height in a transparent tube” suitable for Bo » 1 and also for Bo ~ 1 , even with proper consideration of the balance of different hydrostatic forces, cannot be transferred straight forward to the microfluidic limit where Bo « 1.

[0079] For the present inventive concept, the position and the shape of the meniscus formed by the first fluid and the second fluid in the capillary measurement chamber may be taken as an indicator for the pressure pm acting on the meniscus from a side of the first fluid or a side of the second fluid, in addition to the Laplace pressure generated by the surface tension. In order to be largely independent from gravitational effects, the Bond number Bo associated with the pressure measuring apparatus 10 thus should be much smaller than one (Bo « 1). By this measure, dimensions of the measurement chamber or a characteristic length L associated with the measurement chamber may be adapted to be small.

[0080] In particular, the dimensions of the measurement chamber or the characteristic length L associated with the measurement chamber may be adapted to be at least of the order of 100 pm. It is possible, in accordance with embodiments of the present inventive concept, that at least one of the dimensions of the measurement chamber may be smaller than at least 600 pm, or at least 500 pm, or at least 400 pm, or at least 300 pm or at least 200 pm. It is even feasible that at least one of the dimensions of the measurement chamber may be smaller than 100 pm. For instance, a typical value of the Bond number Bo when an aqueous liquid, such as water, is used as one of the two fluids and when the characteristic length L of the measurement chamber is 100 pm is 0.004 i.e. Bo » 0.004 indicating that in microfluidic applications, the specification of small Bo numbers may easily be met.

[0081] It is noted that the length L herein refers to the smallest dimension of the capillary measurement chamber extending parallel to its capillary cross section, which is defined by the plane that is perpendicular to the direction of the movement of the meniscus (e.g. the x- z-plane in figure 2).

[0082] The measurement chamber of the microfluidic chip 20 may be configured to permit a Bond number equal to 0.5, with a possible tolerance range, when operated with the first fluid and the second fluid. Preferably, the measurement chamber of the microfluidic chip 20 may be configured to permit a Bond number smaller than 0.05, with a tolerance range of 0.01 or with a tolerance range of 0.02, when operated with the first fluid and the second fluid.

[0083] Due to the strong capillary action at small Bond numbers i.e. Bo « 1 , the pressure measuring apparatus 10 may permit a stable meniscus to form between the first fluid and the second fluid if the so-called Concus-Finn condition [7] is not fulfilled anywhere in the measurement chamber. The stable meniscus may then be formed in accordance with the principle of minimum interfacial surface energy when the two fluids are supplied to the measurement chamber. The Concus-Finn condition means that neighboring surfaces in the measurement chamber do not enclose a too small corner angle of 2a for a contact angle 0 associated with the second fluid, that is:

[0084] (6) 0 + a < 90° .

[0085] In other words, at any point of any of the inner surfaces of the measurement chamber, the angle 2a between any two adjacent inner surfaces of the measurement chamber obey the relation a > 90°- 0, where 0 may be the smallest contact angle of the second fluid in the measurement chamber configured to form the meniscus.

[0086] It is to be noted that a manifold of designs and dimensionalities of the measurement chamber may allow the Concus-Finn condition to be fulfilled. However, the measurement chamber of the pressure measuring apparatus 10 may be configured to not fulfill the Concus-Finn condition in the measurement chamber. In other words, the measurement chamber may be designed in a manner as to not satisfy the Concus-Finn condition anywhere within it.

[0087] Further, the geometry and other properties, for example wetting properties of the inner surfaces, of the measurement chamber may determine, whether and how the position and / or the shape of the meniscus depends on the input pressure. For example, a capillary with constant diameter, an open end and a contact angle smaller 90° may not meet this specification, because the meniscus will not attain a specific equilibrium shape and position inside the capillary, but run to the end of the capillary regardless whether no pressure or a positive input pressure is applied to the second fluid at the inlet of the capillary. Thus, to generate an unambiguous pressure dependence of the meniscus shape and / or the meniscus position on the pressure difference between the first fluid and the second fluid in the measurement chamber, the measurement chamber may be designed so that the Young-Laplace equation, given by equation (2), for any pressure difference between the first fluid and the second fluid has exactly one solution inside the measurement chamber. This may be fulfilled by the design of the measurement chamber in terms of geometry and wetting properties. This may also be fulfilled by additional pressure dependent elements which may be in fluidic connection with the measurement chamber and may generate a pressure dependence of the equilibrium position and / or shape of the meniscus inside the measurement chamber.

[0088] The measurement chamber might comprise additional pressure dependent elements as an elastic element. The elastic element of the measurement chamber may be adapted to be in accordance with the design specifications of the measurement chamber already described in the present invention disclosure. As a non-limiting non-exhaustive example of such a feature, the elastic element may be a gas volume trapped in the measurement chamber. It is feasible that walls, or equivalently inner walls, of the measurement chamber may be configured to be elastic. That is, the inner walls of the measurement chamber may be configured to physically deform (e.g. elastically deform) when supplying the second fluid (under pressure via the fluid inlet 40) or the first fluid. The elastic deformation of the walls then is superimposed on the capillary pressure, in similarity to an equation described further in the disclosure, specifically equation (16), wherein the capacitive pressure (first term) and the capillary pressure (second term) add up to form the total resulting pressure.

[0089] Therefore, the measurement chamber may be designed as described in the present disclosure. The proper design may depend on the contact angle, a minimum required input pressure, a maximum measurable value of the pressure and whether bi-directional operation may be needed. Further, it may be feasible to test any given design of the measurement chamber by investigating the possible stationary solutions of the Young- Laplace-equation for a configuration of the fluids in the measurement chamber, i.e. boundary conditions based on fluid type and pressure range to be measured.

[0090] It is to be noted that the Young-Laplace equation given in eq. (2) and its particular limit described by eq. (3) together show that the pressure difference between both sides of the meniscus depends on the geometrical shape of the measurement chamber in addition to the surface tension crand the contact angle 0. It is evident that this pressure has an explicit dependence on the geometry and dimensions of the measurement chamber, e.g. like the radius of the capillary. Thus, the meniscus shape i.e. meniscus curvature may indicate the pressure. However, the dependence of the pressure on the position of the meniscus may not be obvious.

[0091] According to an embodiment, a hydraulic radius of the capillary measurement chamber may vary along a longitudinal extension thereof. In other words, the hydraulic radius of the measurement chamber may depend on the longitudinal extension i.e., an extension along a y-direction, of the capillary measurement chamber. That is, the hydraulic radius of the capillary measurement chamber may be related to an extension extending along its length. By this measure, the pressure may depend on the position of the meniscus in the measurement chamber.

[0092] The hydraulic radius rhyciof a capillary is defined as two times an area of its cross section A divided by its inner perimeter P. Thus, equation (3) described earlier in the disclosure may even be generalized for capillaries with arbitrary shaped cross-sections. For instance, the hydraulic radius for a capillary with a rectangular cross section A defined by a length d and a width w and thus yields:

[0093] And therefore, using equation (3), the capillary pressure for the capillary with the rectangular cross-section may be expressed as

[0094] For instance, in the case where the width w of the capillary may depend on its longitudinal extension, equation (8) may then relate the capillary pressure to the position of meniscus within the capillary. Thus, a generalization of equation (8) for the measurement chamber whose hydraulic radius varies with its longitudinal extension may be obtained, which may provide an analytical relation between the pressure of the second fluid and the position of the meniscus formed in the measurement chamber as a result of the pressure.

[0095] It is emphasized here that type and nature of the first fluid and the second fluid forming the meniscus between them may not be decisive and may be chosen to be different for different applications. The measurement chamber may even comprise the first fluid as a part of the pressure measuring apparatus 10. For instance, when the second fluid may be a gas and the pressure measuring apparatus 10 may determine the pressure of the gas, the first fluid may be a liquid which may already be present in the measurement chamber as a functional part of the pressure measuring apparatus 10. Alternatively, in embodiments, the first fluid may be a gas and the second fluid may be a liquid. Further, in embodiments, the first fluid may be a first liquid and the second fluid may be a second liquid.

[0096] It is permitted that the pressure measuring apparatus 10 may be configured to not comprise any of the first fluid and the second fluid as a functional part. The meniscus may be formed in the measurement chamber by supplying it with the second fluid. That is, the meniscus may be formed by supplying the measurement chamber with the fluid whose pressure is to be measured.

[0097] Further, the first fluid and the second fluid may comprise immiscible liquids such that the meniscus is formed between them within the measurement chamber.

[0098] Since the pressure measuring apparatus 10 according to the present concept may operate in a microfluidic regime where the Bond number Bo is much smaller than one i.e. Bo « 1 , the position and / or shape of the meniscus formed in the measurement chamber may not be detected simply by the human eye. Therefore, the sensing system 90 of the pressure measuring apparatus 10 is configured to detect the position and the shape of the meniscus at microscopic dimensions.

[0099] The sensing system 90 may be configured to be of any kind and may be configured to use any transduction principle. For example, the transduction principle of the sensing system 90 may comprise any of optical imaging, capacitive sensing, ultrasound based sensing, interferometry based sensing, without limiting or restricting other suitable transduction principles.

[0100] The sensing system 90 may be configured to use the transduction principle provided that there is a well-defined and an invertible relation between sensor signals S generated by the sensing system 90 and the position and / or the shape of the meniscus given by a surface M(x,y,z) in space according to a Cartesian coordinate system. This means that the sensing system 90 may be adapted to generate sensor signals S having an invertible relation with a surface M associated with the meniscus. The surface M associated with the meniscus may be expressed, for instance, as a surface in an Euclidean space i.e. M(x,y,z) where the x,y,z are the spatial coordinates of the meniscus formed in the measurement chamber as per a Cartesian coordinate system. In other words, the sensing system 90 may be adapted to generate sensor signals S based on the position and the shape of the meniscus such that for each spatial configuration of the meniscus there is a corresponding sensor signal based on the spatial configuration. The spatial configurations of the meniscus may be described by a surface M in an Euclidean space, or by the position of the meniscus inside the measurement chamber and its principal curvatures or by any other suitable mathematical representation.

[0101] It was already described in this disclosure that the position and the shape of the meniscus in the measurement chamber may indicate the pressure in the second fluid in accordance with the Young-Laplace equation for a specific geometry, a specific value of surface tension associated with the meniscus and a specific value of contact angle associated with the meniscus. This relation, or dependence, of the pressure P in the second fluid on the position and the shape of the meniscus in the measurement chamber may be denoted by P[M(x,y,z)], where M(x,y,z) refers to the meniscus surface. Thus, the sensing system 90 may determine the pressure in the second fluid using the dependence of the pressure P in the second fluid on the position and the shape of the meniscus in the measurement chamber. In other words, the present inventive concepts exploits a correlation of the position and the shape of the meniscus with a well-defined pressure difference between the first fluid and the second fluid, for boundary conditions relating to specific values of any of surface tension associated with the meniscus, contact angle associated with the meniscus, geometrical shape and dimensions of the measurement chamber.

[0102] The correlation of the position and the shape of the meniscus with the pressure in the second fluid may be specified by an analytical equation. A non-limiting example of such an analytic equation, or a mathematical description, may be the Young-Laplace equation given by eq (2) of the present disclosure. Since gravitational influence may be neglected for operating conditions of the pressure measuring apparatus 10, which is justified by Bo « 1 , the position and the shape of the meniscus may be determined by the Young-Laplace equation alone to a very good approximation. Additionally, or alternatively, other approximations may provide a mathematical relation between the pressure in the second fluid and the position and / or the shape of the meniscus. However, this correlation of the spatial configuration of the meniscus with the pressure to be measured may also be described by other means. It is to be noted that, preferably, the sensing system 90 may be configured to not have mechanical contact with the measurement chamber. Additionally, or alternatively, the sensing system 90 may be configured to not have a fluidic connection with the measurement chamber. In particular, the second fluid may not be in fluidic connection with the sensing system 90. It is also feasible in embodiments that the sensing system 90 altogether may be configured to not have a mechanical connection or to not have a fluidic connection with the microfluidic chip 20. Further, it is even feasible in embodiments that the sensing system 90 may be configured to not have an electrical connection with the microfluidic chip 20. Thus, the pressure measuring apparatus 10 of the present concept allows for an easy exchange of the microfluidic chip 20 indicating its modular and exchangeable design.

[0103] According to an embodiment, the sensing system 90 may be configured to store allocation data allocating positions and shapes of the meniscus to known pressures of the second fluid and to determine the pressure of the second fluid using the allocation data. By this measure, the sensing system 90 may store the allocation data which correlates the positions and the shapes of the meniscus to pre-determined pressures of the second fluid, and thereby may generate sensor signals based on the stored allocation data. The sensing system 90 may be configured to determine the pressure of the second fluid using the sensor signals based on the stored allocation data.

[0104] Thus, the sensing system 90 may be configured to derive a calibration relationship relating sensor signals generated by the sensing system 90 based on the allocation data to pressures of the second fluid. This means that the sensing system 90 may be configured to associate specific positions and specific shapes of the meniscus with already known pressures of the second fluid, and thus determine pressures of the second fluid using the association.

[0105] It is feasible that this relationship between the sensor signals and the pressures of the second fluid may be determined by using analytical descriptions such as the one provided by the Young-Laplace equation given in eq. (2).

[0106] Additionally, or alternatively, the relationship specifying the association between sensor signals generated by the sensing system 90 with the positions and the shapes of the meniscus may be determined by empirical means using the pressure measuring apparatus 10. The empirical means may comprise an experiment involving the pressure measuring apparatus 10 configured to derive the allocation data. Further, the empirical means may even comprise a series of experiments configured to determine the allocation data.

[0107] Therefore, it is emphasized that an explicit analytical description relating the positions and the shapes of the meniscus in the measurement chamber to the pressures of the second fluid may not be needed for the pressure measuring apparatus 10 of the present concept. It is even permitted that the explicit analytic description may not exist, or may not be derivable from the allocation data. In such cases, the allocation data and / or the relationship between sensor signals and the pressures of the second fluid may be determined using empirical means.

[0108] According to an embodiment, the sensing system 90 may be configured to determine the allocation data using machine learning and / or artificial intelligence.

[0109] In other words, the sensing system 90 may be configured to determine the relationship between the sensor signals and the known pressures of the second fluid as the allocation data by means of a software based algorithm using machine learning and / or artificial intelligence. For example, a neural network may be configured to determine the relationship between the known pressure in the second fluid based on the sensor signals generated by the sensing system 90 for the positions and the shapes of the meniscus in the measurement chamber.

[0110] Further, the allocation data may be determined once for a particular configuration of the fluids in the measurement chamber. This may depend on the design, material and surface properties of the measurement chamber. For example, variations in material properties or large fabrication tolerances of the measurement chamber may lead to variations of the allocation data. Therefore, the allocation data obtained from several experiments may be averaged, and the averaged allocation data may be used to determine the pressure value and to predict uncertainty estimates of the measured result.

[0111] It may be a justified assumption for persons skilled in the art that the measurement chamber is fabricated with high consistency and quality, thus it may be separated from the sensing system and may be replaced by a new measurement chamber with similar fabrication characteristics without a need for repeated calibration i.e. without a need for repeated determination of the allocation data when the configuration of fluids used is the same. Repeated determination of the allocation data may even be avoided for an exchange of the measurement chamber when the configuration of fluids may not exactly be identical but may allowed to be similar, that is, surface tension and other rheological properties of the fluids before the chamber exchange and after the chamber exchange may not differ by a large value. Thus, the microfluidic chip 20 comprising the measurement chamber may achieve the specification of a low-cost single use item that may be replaced and separated from the more costly, reusable sensing system 90. Thus, the complete sensor system 90 according to the present invention may achieve more precise pressure sensing with low- cost single use components.

[0112] According to an embodiment, the sensing system 90 may comprise an optical system configured to generate image data of the position and the shape of the meniscus formed in the measurement chamber and to evaluate the image data to determine the position and the shape of the meniscus.

[0113] For example, the sensing system may be configured to: use a first set of image data of configurations of the meniscus related to known pressures in the second fluid (and / or pressures in the first fluid), and determine pressures in the second fluid by comparing a second set of image data of configurations of the meniscus of unknown pressures in the second fluid (and / or pressures in the first fluid) with the first set of image data . The first set of image data may be provided to the sensing system by external empirical means. It is also feasible that the first set of image data may be established using the allocation data. The second set of image data may be generated by the optical system described earlier. Additionally, or alternatively, the first set of image data may be combined with the allocation data so as to determine pressures in the second fluid using the second set of image data.

[0114] The optical system may be configured to generate image data of the position and the shape of the meniscus formed in the measurement chamber with a specific optical magnification characteristic. This specific optical magnification characteristic may be selected to permit a detailed imaging of the shape and the position of the meniscus formed in the measurement chamber. That is, the specific optical magnification characteristic may be specified to optically resolve the position and the shape of the meniscus formed in the measurement chamber with sufficient detail to enable a precise determination of the position and the shape of the meniscus. In particular, the specific optical magnification characteristic may even be configured to optically discern the contact angle associated with the meniscus in the measurement chamber. In other words, the specific optical magnification characteristic may be configured to provide detail of the contact angle made by the meniscus with inner walls of the measurement chamber. For example, the optical system may comprise a charged coupled device (CCD) camera system configured to generate image data of the meniscus based on machine vision.

[0115] The generated image data associated with the meniscus, such as the image data of the position and the shape of the meniscus, may be used to derive image data relating to an average position of the meniscus and an average shape of the meniscus. That is, the average position and the average shape of the meniscus may be obtained using a curved line of a two dimensional projection of the fluidic interface between the first fluid and the second fluid. For example, optical systems that have been used to image fluidic interfaces can be found in [8-11],

[0116] For instance, the generated image data may be processed by image detection algorithms to generate processed binary image data, and features such as meniscus curvature and meniscus position may be extracted from the processed binary image data. In particular, as a specific non-limiting example, the image data generated by the optical system may be adapted to binary image data by a thresholding algorithm such as Otsu algorithm

[0012] , Additionally, or alternatively, the image data generated by the optical system may be adapted by other edge detection algorithms. The meniscus shape may be approximated by interface between black (1) and white (0) pixels in the binary image data. The position of the meniscus and its curvature may then be determined from the binary image data by using approximative formulas, as described in more detail in

[0013] ,

[0117] The derived image data associated with the average position and the average shape of the meniscus may be combined with the allocation data to determine the pressure of the second fluid. A combination of the image data relating to the average position and the average shape of the meniscus with the allocation data to determine the pressure of the second fluid may be performed by using a software program.

[0118] It is preferable that the measurement chamber may be designed to permit the meniscus to be formed with a high degree of symmetry. That is, the measurement chamber may be configured to allow the shape of the meniscus to be symmetric. For example, the capillary measurement chamber comprising a circular cross section may be configured to allow the meniscus to have the shape of a spherical cap. In this case, a two dimensional projection of the meniscus shape may lead to a reasonably precise estimate of the curvature of the meniscus. Additionally, or alternatively, the optical system may use stereoscopic imaging methods which obtain image data relating to a full three dimensional reconstruction of the meniscus using two dimensional image data of the meniscus obtained using different two dimensional projections.

[0119] The sensing system 90 may comprise a capacitive system configured to generate electronic data corresponding to the position and the shape of the meniscus formed in the measurement chamber and to evaluate the electronic data to determine the position and the shape of the meniscus. The generation of the electronic data relating to the position and the shape of the meniscus may be achieved using capacitive sensing principles with at least one electrode or a multitude of spatially distributed electrodes. The capacitive system may be configured to not establish physical contact with the fluids in the measurement chamber.

[0120] In the following an example illustrating a possible embodiment of the inventive concept is provided without limiting other possible embodiments of the present inventive concept, wherein the sensing system 90 may comprise the capacitive system. For example, the capillary measurement chamber of the pressure measuring apparatus 10 may be arranged with an electrode structure, such as a pair of electrodes, forming an electric capacitor structure. By this measure, a capacitance of the formed electric capacitor structure may change based on the position and the shape of the meniscus in the measurement chamber, from which the sensing system 90 may determine the pressure in the second fluid.

[0121] Since the capacitive system may not directly and explicitly determine the position and the shape of the meniscus, in contrast to the optical system described earlier, the allocation data may be obtained by empirical means for a particular configuration of the pressure measuring apparatus 10 comprising the capacitive system. This particular configuration may comprise a particular design of the measurement chamber, a particular arrangement of the electrode structure and a particular configuration of the fluids for the pressure measuring apparatus 10.

[0122] According to an embodiment, the sensing system 90 may be configured to determine that the pressure in the second fluid has a first value if the meniscus has a first position and a first shape, to determine that the pressure in the second fluid has a second value if the meniscus has a first position and a second shape different from the first shape, and to determine that the pressure in the second fluid has a third value if the meniscus has a second position different from the first position.

[0123] By this measure, the pressure measuring apparatus 10 may detect a change in the pressure of the meniscus even if the position of the contact line of the meniscus does not shift. The sensing system may distinguish between states of the meniscus when it remains stuck at the first position having the first shape from when it is deformed at the first position and has the second shape. The sensing system may then also distinguish these states from a state when the meniscus is no longer stuck and is at the second position, such as in a stable equilibrium.

[0124] The accuracy of pressure measurements by the pressure measuring apparatus 10 may be increased since the determination of both the position of the contact line and the shape of the meniscus may permit the apparatus 10 to detect situations when the meniscus sticks at the same position within the measurement chamber though the input pressure is still changing. Of course the measuring apparatus 10 may also detect situations when the meniscus slips within the measurement chamber. The sensing system 90 may be configured to determine stick configurations and slip configurations of the meniscus in the measurement chamber and determine the pressure of the meniscus based on the configurations using machine learning, ML, or artificial intelligence, Al. In particular, software programs based on ML and / or Al may be configured to store data relating to the stick configurations and the slip configurations and determine the corresponding pressures of the meniscus.

[0125] According to an embodiment, the capillary measurement chamber may be one of a plurality of capillary measurement chambers comprising fluidically coupled fluid inlets, each configured to permit a stable meniscus between a first fluid and a second fluid to be formed in the measurement chamber, wherein pressure ranges of the plurality of capillary measurement chambers, in which a stable meniscus can be formed, are different in the plurality of capillary measurement chambers.

[0126] As will also be described later in the present disclosure, the pressure measuring apparatus 10 may comprise more than one capillary measurement chamber. Each of the measurement chambers may be configured to fulfill design aspects of the pressure measuring apparatus 10 having the measurement chamber described earlier. That is, each of the measurement chambers may be: miniaturized so as to allow operating conditions with Bond number much smaller than one, preferably equal to or smaller than 0.5 within a tolerance range; may not fulfill the Concus-Finn condition anywhere within itself; may be designed so as to allow one solution of the Young-Laplace equation within itself.

[0127] The plurality of measurement chambers may be arranged in a series configuration. The Alternatively, the plurality of measurement chambers may be arranged in a parallel configuration.

[0128] The plurality of the measurement chambers may be configured to have the sensing system 90 generate sensor signals based on shapes and positions of menisci in the plurality of the measurement chambers. That is, the shapes and the positions of the menisci formed in the measurement chambers may be readout by one sensing system 90. Thus, the plurality of the measurement chambers may provide complementary information to the sensing system 90 and thereby improve its performance without incurring extra costs.

[0129] Although not shown in the schematic illustration of Fig. 1 , in accordance with an embodiment, the pressure measuring apparatus 10 may further comprise a pressure fluctuation generating device. The pressure fluctuation generating device may be configured to superimpose time dependent pressure fluctuations to at least one of the fluids so as to cause variations of the position and / or the shape of the meniscus in the measurement chamber. The sensing system 90 may be configured to detect the variations of the position and / or the shape of the meniscus and to determine the pressure in the second fluid using the detected variations.

[0130] It is to be noted that, preferably, the pressure fluctuation generating device may be an external device configured to not have a mechanical connection with the measurement chamber. Additionally, or alternatively, the pressure fluctuation generating device may be configured to not have a fluidic connection with the measurement chamber. In particular, at least one of the fluids may not be in direct fluidic connection with the pressure fluctuation generating device. It is also feasible that the pressure fluctuation generating device altogether may be configured to not have a mechanical connection or to not have a fluidic connection with the microfluidic chip 20. Thus, the pressure measuring apparatus 10 of the present concept may still allow an easy exchange of the microfluidic chip 20 even when extended with the pressure fluctuation generating device, indicating the advantageous modular and exchangeable design of the pressure measuring apparatus 10. The time dependent pressure fluctuations may permit conditions of at least one of the fluids, wherein the variations of the position and / or the shape of the meniscus in the measurement chamber are constantly adapting, that is, they vary as a function of time. Therefore, these variations may permit non-stationary flow conditions. Thus, the pressure measuring apparatus 10 may be extended by the pressure fluctuation generating device to generate non-stationary flow conditions in a controllable way. These non-stationary flow conditions may even be generated when the pressure and / or the flow to be measured are stationary.

[0131] Further, the time dependent pressure fluctuations may allow oscillations of the meniscus around their stable position and thus, prevent undesired pinning of the meniscus in the measurement chamber.

[0132] The time dependent pressure fluctuations may be adapted so as to permit changes in the pressure associated with the at least one of fluids within a specific pressure range.

[0133] According to an embodiment, the pressure fluctuations may comprise one or more pressure pulses. For example, the one or more pressure pulses may be provided to the measurement chamber and adapted so as to permit a determination of step responses associated with the meniscus in the measurement chamber.

[0134] According to an embodiment, the pressure fluctuations may comprise periodic pressure fluctuations.

[0135] For example, a piezo actuator apparatus may be configured to be in mechanical connection with the microfluidic chip. The piezo actuator may be provided with time dependent electrical signals, such as but not limited to time dependent voltage signals, so as to mechanically act on the microfluidic chip 20, superimposing time dependent pressure fluctuations on at least one of the fluids. For instance, as a non-limiting example, the voltage signals may comprise sine wave signals or rectangular signals. The superimposed time dependent pressure fluctuations may be induced in at least one of the fluids through the mechanical action of the piezo actuator apparatus. In particular, the piezo actuator apparatus may be configured to be in mechanical connection with outer surfaces of the microfluidic chip 20. Additionally or alternatively, the piezo actuator apparatus or a micro heater apparatus may even be comprised in the microfluidic chip 20, similar to configurations permitted in inkjetprintheads. Size, type and driving mechanism of the signals provided to the pressure fluctuation generating device may be similar to those used in inkjet devices. According to an embodiment, the sensing system 90 may be configured to determine a rheological property of the second fluid using a time series of the detected variations of the position and / or the shape of the meniscus.

[0136] A continuous monitoring of the positions and / or the shapes of the meniscus using the sensing system 90 such as an optical system may be adapted to generate video data. This generated video data may be evaluated to derive the time series of the detected variations of the position and / or the shape of the meniscus. This time series may carry information on the rheological properties of the fluid such as surface tension, viscosity and density. Mean values of the meniscus shape and the meniscus position may be then determined more accurately by time averaging than from a single measurement. An Al based software may be adapted to use the generated video data and determine mean values associated with the pressure and rheological properties of the fluid. Thus, time series of sensor signals generated by the sensing system 90 may be provided to Al based software program to determine pressure and rheological properties and to permit an increase in accuracy of the determined pressure and rheological properties.

[0137] The allocation data may be evaluated based on a classical empirical calibration curve. The allocation data may also be evaluated based on a computational / mathematical model such a numerical model based on Computational Fluid Dynamics (CFD). These approaches which may be configured to evaluate the allocation data may be combined with AI / ML-based software programs, such as but not limited to - deep learning, supervised learning or neural networks, only briefly described in the present disclosure, but well-known by persons skilled in the art of these software programs.

[0138] According to a particular implementation of the sensing system 90, the determined allocation data, or calibration relationship P[S], may be implemented as a software program. That is, a software program may be configured to determine the pressure P provided at the fluid inlet using the sensor signal S (or a time course series of sensor signals {S(ti), S(t2), ... S(tn)}) generated by the sensing system 90. This approach may be particularly useful when the sensor signals may comprise a digital image of the meniscus or a series of such images, for example, a video recording. In this context, a wealth of image recognition software algorithms and artificial intelligence (Al) software programs exist that may be trained to “recognize”, or identify, a certain meniscus shape and / or position and to relate it to a specific pressure value. This may be achieved by means of “training” a suitable neuronal network or any other suitable Al software. Therefore, a sufficiently large training set of images, and / or videos, of the meniscus shape and position in the measurement chamber under varying pressure conditions may be recorded. This set of images, and / or videos, may be annotated by the corresponding pressure value that is determined by a reference sensor of the sensing system 90 for the training set.

[0139] Therefore, it may be understandable to persons skilled in the art that with existing or customized Al or machine learning software the allocation data, or the calibration curve P[S], may be implemented as an Al software program. This means, a neuronal network configured, i.e. sufficiently trained, to relate the sensor signal S (i.e. a digital image or a video recording) to a specific pressure value may be used to return the measurement result P[S] when it is provided with the sensor signal S, i.e. a single or a series of digital images of the meniscus inside the measurement chamber. The Al software based approach may be used instead of a classical calibration curve based on a mathematical model or a classical empirical calibration function. The Al software based approach may even be used in combination with a classical calibration curve based on a mathematical model or a classical empirical calibration function

[0140] It is to be emphasized that a pressure measuring apparatus 10 according to the present inventive concept may measure pressure by detecting the shape and the position of the meniscus regardless of the compressibility properties of the fluids. That is, the first fluid and the second fluid may be compressible or incompressible, without affecting the operation of the apparatus.

[0141] After having described different details of an aspect of the inventive concept with respect to Fig. 1 , the present disclosure proceeds with a description of different implementations of the pressure measuring apparatus 10 given in Figs. 2 to 8. In particular, embodiments of the pressure measuring apparatus 10 with varying realizations of the capillary measurement chamber are henceforth described.

[0142] Fig. 2 exemplarily shows a schematic cross-sectional view (parallel to an x-y plane) of two implementations of the microfluidic chip 20 of the pressure measuring apparatus 10. Both the implementations show the microfluidic chip 20 comprising a capillary measurement chamber 30 and a fluid inlet 40 fluidically coupled to the measurement chamber 30. A second fluid 70 may be supplied via the fluid inlet 40 to the capillary measurement chamber 30. The capillary measurement chamber 30 and the fluid inlet 40 may be configured to permit a stable meniscus 50 between the first fluid 60 and the second fluid 70 to be formed in the measurement chamber 30.

[0143] According to embodiments, as shown in Fig. 2, the measurement chamber 30 may be in fluidic connection to the ambient environment by a ventilation opening 80, wherein the ventilation opening 80 is arranged spaced apart from the fluid inlet 40 to permit the stable meniscus 50 to be formed in the measurement chamber 30 between the fluid inlet 40 and the ventilation opening 80. In examples, the fluid inlet 40 may be formed at one end of the measurement chamber 30 and the ventilation opening 80 may be formed at an opposite end of the measurement chamber. While the fluid inlet 40 is shown as a simple opening in Fig. 2, in embodiments it can be formed differently, such as by an inlet channel or the like.

[0144] In accordance with the two implementations exemplarily shown in Fig. 2, the ventilation opening 80 may establish the measurement chamber 80, and consequently the second fluid 70, to be in fluidic connection to the ambient environment. The ventilation opening 80 may be spaced apart in a longitudinal direction, parallel to a y-direction, from the fluid inlet 40. The ventilation opening 80 may permit the stable meniscus 50 to be formed in the chamber 30 between the fluid inlet 40 and the ventilation opening 80, as seen in Fig. 2.

[0145] The capillary measurement chamber 30 may comprise at least one of a circular cross section, an elliptical cross section, a rectangular cross section and a polygonal crosssection. The ventilation channel 80 may comprise at least one of a circular cross section, an elliptical cross section, a rectangular cross section and a polygonal cross-section.

[0146] It is also seen from Fig. 2 in both implementations that the hydraulic radius, or equivalently the hydraulic diameter, of the measurement chamber 30 varies with the longitudinal extension i.e. the extension of the measurement chamber 30 in a direction along its length, parallel to a y-direction. In accordance with an embodiment, and with respect to implementations illustrated in Fig. 2, the capillary measurement chamber 30 may comprise tapered side walls 36 to vary the hydraulic radius of the capillary measurement chamber 30 along the longitudinal extension thereof.

[0147] Both implementations in Fig. 2 show two differently tapered side walls 36 of the measurement chamber 30, each of which varies the hydraulic radius of the chamber 30 along its longitudinal extension in a manner of variation different from each other. According to an embodiment, and also with respect to the implementation shown on the left of Fig. 2, the measurement chamber 30 may be made of a hydrophobic material. The contact angle associated with the material forming the measurement chamber 30 having hydrophobic properties may permit the shape 56 of the meniscus 50 to comprise a convex configuration. That is, the meniscus 50 formed in the measurement chamber comprising the hydrophobic material has a contact angle at least greater than 90°. By this measure, the second fluid 70 may be supplied with a specific positive value of the pressure, i.e. pin > 0, via the fluid inlet 40 to the measurement chamber 30 and the meniscus 50 may be formed within it. Therefore, the measurement chamber 30 made of the hydrophobic material may be configured to measure positive values of the pressure in the second fluid 70.

[0148] Also seen in the left illustration of Fig. 2, the meniscus shape 56 is convex, i.e. curved away from the fluid inlet 40, and the position 54 of the meniscus 50 may range, along a y-direction, between the fluid inlet 40 and the ventilation opening 80.

[0149] In accordance with an embodiment, and in accordance with the left illustration of Fig. 2, the hydraulic diameter, or equivalently the hydraulic radius, of the capillary measurement chamber 30 may at least partially decrease with increasing distance from the fluid inlet 40. The hydraulic diameter of the hydrophobic measurement chamber 30, that is the measurement chamber 30 made of the hydrophobic material, may taper from the fluid inlet 40 towards the ventilation opening 80. In other words, the hydraulic diameter of the hydrophobic measurement chamber 30 adjacent to the fluid inlet 40 may be larger than the hydraulic diameter of the hydrophobic measurement chamber 30 adjacent to the ventilation opening 80. Equivalently, the side walls 36 of the hydrophobic chamber 30 may be adapted to permit the hydraulic radius to diminish along a direction towards the ventilation opening 80.

[0150] For instance, the hydraulic diameter of the capillary measurement chamber 30 may at least partially decrease linearly with increasing distance from the fluid inlet 40. As per the implementation on the left of Fig. 2, at least one of the side walls 36 may be sloping, or inclined at an angle, to allow a linearly decreasing variation of the hydraulic radius with increasing distance from the fluid inlet 40 of the hydrophobic capillary measurement chamber 30. This means that another side wall of the side walls 36 of the hydrophobic measurement chamber 30 may not be sloping, i.e. may be straight, to still allow a linearly decreasing hydraulic diameter with increasing distance from the fluid inlet 40. According to an embodiment, and also with respect to the implementation shown on the right of Fig. 2, the measurement chamber 30 may be made of a hydrophilic material. The contact angle associated with the material forming the measurement chamber 30 having hydrophilic properties may permit the shape 56 of the meniscus 50 to comprise a concave configuration. That is, the meniscus 50 formed in the measurement chamber comprising the hydrophilic material may have a contact angle smaller than 90°.

[0151] This means that the second fluid 70 may not be supplied with any pressure via the fluid inlet 40 to the measurement chamber 30 to form the meniscus 50 in the chamber 30. That is, due to capillary wicking, the second fluid 70 may enter the hydrophilic measurement chamber spontaneously via the fluid inlet 40 and may form the meniscus 50 inside it. This means that the second fluid 70 may be supplied with either a specific positive value of the pressure, i.e. pin > 0, or a specific negative value of the pressure , i.e. pm < 0, or even a vanishing value of the pressure, i.e. pin = 0, via the fluid inlet 40 to the hydrophilic capillary measurement chamber 30 and the meniscus 50 may be formed within it. Therefore, the measurement chamber 30 made of the hydrophilic material may be configured to measure negative as well as positive values of the pressure in the second fluid, thereby resulting in a bi-directional operation.

[0152] Also seen in the right illustration of Fig. 2, the meniscus shape 56 may be concave, i.e., the shape 56 of the meniscus 50 is curved towards the fluid inlet 40, and the position 54 of the meniscus 50 may range, along a y-direction, between the fluid inlet 40 and the ventilation opening 80.

[0153] In accordance with an embodiment, and in accordance with illustration on the right in Fig. 2, the hydraulic diameter, or equivalently the hydraulic radius, of the capillary measurement chamber 30 may increase at least partially with increasing distance from the fluid inlet 40. In particular, the hydraulic diameter, or equivalently the hydraulic radius, of the capillary measurement chamber 30 may partially increase super-linearly with increasing distance from the fluid inlet 40. That is, a variation of increase in the hydraulic diameter of the measurement chamber 30 with a distance from the fluid inlet 40 may be greater than a linear variation. As exemplarily shown in the Fig. 2, the hydraulic radius of the capillary measurement chamber 30 may increase super-linearly with increasing distance from the fluid inlet 40. The hydraulic diameter of the hydrophilic measurement chamber 30, that is the measurement chamber 30 made of the hydrophilic material, may taper super-linearly from the ventilation opening 80 towards the fluid inlet 40, in contrast to the illustration on the left. In other words, the hydraulic diameter of the hydrophilic measurement chamber 30 adjacent to the ventilation opening 80 may be larger than the hydraulic diameter of the hydrophilic measurement chamber 30 adjacent to the fluid inlet 40. Equivalently, the side walls 36 of the hydrophilic chamber 30 may be adapted to permit the hydraulic radius to diminish along a direction away from the ventilation opening 80.

[0154] According to another embodiment, and also with respect to the illustration on the right of Fig. 2, the capillary measurement chamber 30 comprises a convex inner wall that forms a super-linearly increasing hydraulic diameter.

[0155] For instance, the side walls 36 of the hydrophilic chamber 30 in the right illustration of Fig. 2 both comprise the convex inner wall to form the super-linearly increasing hydraulic diameter. However, it is also feasible that one of the side walls 36 may comprise a convex shape to obtain the super-linearly increasing hydraulic diameter of the measurement chamber 30. That is, another side wall of the side walls 36 may not be convex-shaped and thus, may be linearly tapered to permit the super-linearly increasing hydraulic diameter. It is even feasible then that the another side wall of the side walls 36 may be straight and lack any tapering provided that the one side wall may comprise the convex shape to still achieve the super-linear increase of the hydraulic diameter of the chamber 30. In other words, at least one of the side walls 36 of the hydrophilic chamber 30 may be curved so as to achieve super-linearly increasing hydraulic diameter with increasing distance from the fluid inlet 40.

[0156] Fig. 3 exemplarily shows a schematic cross-sectional view (parallel to an x-y plane) of an implementation of the microfluidic chip 20 of the pressure measuring apparatus 10 illustrating three different configurations of the meniscus 50 formed in the hydrophobic measurement chamber 30. The microfluidic chip 20 comprising the hydrophobic measurement chamber 30 shown in Fig. 3 may be considered to be in accordance with the illustration on the left of Fig. 2. Details described herein in connection to Fig. 3 may be combined with the details previously described in connection to Fig. 2.

[0157] The schematic illustrations describe three different configurations - a first position 54-1 , a second position 54-2 and a third position 54-3, of the meniscus 50 in the same hydrophobic measurement chamber 30. This means that each position of the positions 54-1 , 54-2, 54-3 in the hydrophobic chamber 30 may correspond to a different value of the pressure in the second fluid 70. It can be seen that the position, or height h, 54-1 , 54-2, 54-3 may be defined relative to the fluid inlet 40, where the height h may be zero i.e. h = 0. In the first configuration, the meniscus 50 has the first position 56-1 and the first shape 54- 1. In the second configuration, the meniscus 50 has the second position 54-2 and the second shape 56-2. In the third configuration, the meniscus 50 has the third position 54-3 and the third shape 56-3.

[0158] The width w, as described earlier in the disclosure for capillaries with rectangular cross section, of the hydrophobic measurement chamber 30 of Fig. 3 decreases linearly from the fluid inlet 40 towards the ventilation opening 80. That is, the width w of the hydrophobic measurement chamber 30 refers to its width at the fluid inlet i.e. h = 0, and therefore, the variation of the width w with height h, is expressed as

[0159] (9) w(Ji) = w — c . h where c refers to a constant factor. Thus, using equation (8), the capillary pressure of the meniscus in the capillary measurement chamber 30 is related to the position, or height, of the meniscus in the capillary measurement chamber 30 as follows:

[0160] For any design of the capillary measurement chamber 30, the position of the meniscus is related to a pressure difference between a pressure pi in the first fluid, a known pressure for the first fluid having a phase 1 e.g. a gaseous phase, and the pressure p2 in the second fluid, i.e. an unknown pressure to be determined, in the capillary measurement chamber as follows:

[0161] (11) Pcap = Pl - P2 + Pin

[0162] This equation is applicable, in general, independent of any specific design or properties of the measurement chamber 30.

[0163] It is noted that the first fluid 60 may be at ambient pressure po at all times since the measurement chamber 30 may be in fluidic communication with the ambient environment via the ventilation opening 80. This means that the first fluid 60 may provide a pressure boundary condition towards the meniscus 50 which is independent of the position 54 and the shape 56 of the meniscus 50. The value of pmmay be given relative to this ambient pressure po, which is not denoted explicitly in equation (11) for simplicity.

[0164] For the hydrophobic measurement chamber 30 with linearly tapered walls as exemplarily shown in Fig. 3, using equations (10) and (11) to calculate the pressure pm of the second fluid, or equivalently input pressure, which may be associated with a specific position h of the meniscus in the chamber 30 leads to:

[0165] Thus, the position h, which may be determined by the sensing system 90, can be readily converted by equation (12) into the pressure pm of the second fluid supplied via the fluid inlet 40 into the measurement chamber 30. The parameters in equation (12) are either known by design of the measurement chamber 30 such as the length d and the width w, or can be known due to the properties of the second fluid and the first fluid such as the contact angle 0 and the surface tension o. Additionally or alternatively, these may be determined by empirical means of calibration of the pressure measuring apparatus 10.

[0166] It should be noted that equation (12) is valid for the measurement chamber 30 made of a hydrophobic material i.e. 0 > 90° and for the pressure in the second fluid 70, or equivalently, input pressures, pin> Apcap(h = 0). If the pressure in the second fluid 70 may be smaller than the capillary pressure, the meniscus 50 may not enter into the measurement chamber 30 due to capillary depression and a measurement may not be possible.

[0167] It is evident from Fig. 3 that the third position 54-3 of the meniscus 50 is higher than the second position 54-2, which is then higher than the first position 54-1. Therefore, using equation (12), the pressure pc associated with the third position 54-3 is greater than the pressure PB associated with the second position 54-2, which is then greater than the pressure PA associated with the first position 54-1 , which is greater than zero.

[0168] Fig. 4 exemplarily shows a schematic cross-sectional view (parallel to an x-y plane) of an implementation of the microfluidic chip 20 of the pressure measuring apparatus 10 illustrating three different configurations of the meniscus 50 formed in the hydrophobic measurement chamber 30. The implementation shown in Fig. 4 may be considered to be in accordance with the illustration on the left of Fig. 2 and with the implementation of Fig. 3. Details described herein in connection to Fig. 4 may be combined with the details previously described in connection to Figs. 2 and 3.

[0169] The hydrophobic measurement chamber 30 comprises a first channel 84 and a second channel 85, wherein the first channel 84 comprises non-tapered, straight side walls and the second channel 85 comprises linearly tapered side walls. Therefore, the hydraulic radius of the hydrophobic measurement chamber 30 partially decreases with increasing distance from the fluid inlet 40. As can be exemplarily be seen in Fig. 4, a base of the second channel 85 extends laterally as wide as the first channel 84. That is, a hydraulic radius of the first channel 84 is equal to a hydraulic radius of the base of the second channel 85. Further, the first channel 84 and the second channel 85 may be adapted to form sharp edges, which may allow a pinning action of the meniscus 50 in the measurement chamber. Further implementations of the measurement chamber 30 with sharp edges permitting the pinning action of the meniscus 50 will be described in embodiments of the invention with respect to other figures later in the present disclosure.

[0170] The schematic illustrations describe three different configurations of the meniscus 50 formed in the hydrophobic measurement chamber 30. The first configuration shows that the meniscus 50 has the first position 54-1 and the first shape 56-1 , and may be associated with the pressure in the second fluid 70 having the first value, denoted by PA. The second configuration shows that the meniscus 50 has the first position 54-1 and the second shape 56-2, wherein the second shape 56-2 is different from the first shape 56-1 , and may be associated with the pressure in the second fluid 70 having the second value, denoted by PB. The third configuration shows that the meniscus 50 has the second position 54-2 and the third shape 56-3, wherein the second position 54-2 is different from the first position 54- 1 , and may be associated with the pressure in the second fluid 70 having the third value, denoted by PB + E. That is, the third value is different from the second value by a small value, denoted by E. The meniscus 50 at position 56-1 having the second shape 56-2 at can be considered to be sticking at this position until a small perturbation E discontinuously makes the meniscus 50 slip to the position 56-2 and acquiring shape 56-3. This sequence of three different configurations of the meniscus 50 illustrates how the three different pressure levels PA, PB and pc can be distinguished from each other, even when meniscus position 56-1 (i.e. the position of the contact line) is the same for pressure levels PA and PB.

[0171] Since the second position 54-2 is higher than the first position 54-1 , the third value of the pressure PB + E is greater than the second value of the pressure PB and the first value of the pressure PA i.e. E > 0 and PB + E > PB > PA. Since a radius of curvature associated with the second shape 54-2 is smaller than a radius of curvature associated with the first shape 54- 1 , the second value of the pressure PB is greater than the first value of the pressure PA, i.e. PB > PA. Since the first position 54-1 is higher than a position associated with a vanishing height, h = 0, of the meniscus 50 within the measurement chamber 30, i.e. the meniscus 50 has its position at a level of the fluid inlet, the first value of the pressure may be positive, i.e. PA > 0.

[0172] It may then be seen that when the pressure value PA is increased to the pressure value PB, the contact line of the meniscus 50 remains stationary, or stuck, at the first position 54-1 , or height hstick, associated with the pressure value PA. Only the shape of the meniscus 50 changes from the first shape 56-1 to the second shape 56-2 due to the increased pressure PB. The second configuration may not be a stable equilibrium state of the meniscus 50. When the pressure value PB is further slightly increased by a small value E to the pressure value PB + E, the position of the meniscus 50 then suddenly jumps from the first position 54- 1 to the second position 54-2, or height hSiiP, and thus, achieves a stable equilibrium wherein the curvature associated with it corresponds to the stationary contact angle.

[0173] If only the position of the contact line is be used as a measurement variable, then the sensor signals generated by the sensing system 90 may exhibit discontinuous jumps. That is, the signals generated based on the stick configuration, wherein the first position 54-1 is stably maintained even though pressure values increase, and the slip configuration, wherein the second position 54-2 may be suddenly achieved even though pressure value is increased by a small amount E, may comprise irregularities or discontinuities.

[0174] Further, deformation associated with the shape of the meniscus, that is, when the meniscus gets stuck, i.e. has no change in position 54-1 and has the change in its shape, from the first shape 56-1 to the second shape 56-2, may also be detected by an electrical sensor. However, such an electrical sensor may not be able to distinguish between the shape deformations of the meniscus 50 in stick configuration. These deformations may trigger the same electrical value, or for example, capacitance value, at the sensor but these deformations correspond to different pressure values. Therefore, the accuracy of the pressure measurement may be improved if both the positions 54 and the shape 56 of the meniscus 50 may be determined together. The pressure value then may be determined based on the positional and the curvature based data generated by the sensing system 90. This determination may be performed using at least one of an analytical model or an Al based software.

[0175] The pressure measurement of the present concept may also allow to detect if the stick configurations exist in the measurement chamber 30, in contrast to prior art devices wherein this may be achieved only retrospectively after the generated sensor signal exhibits a sudden discontinuous change. Further, the pressure measuring apparatus 10 may be configured to detect and determine the stick configurations of the meniscus 50 before the slip configurations.

[0176] Therefore, as per the present inventive concept, the sensing system 90 may be configured to measure different pressure values corresponding to the three configurations described exemplarily shown in Fig. 4, thereby reducing errors in pressure measurements due to the stick-slip effect.

[0177] It is also a feasible variation of the embodiment shown in Fig. 4 that parts of the first channel 84, or possibly the entirety of the first channel 84, are not a part of the measurement chamber, but form the fluid inlet 40, such as in the case where pressures in the second fluid 70 to be detected span such a pressure range that the lowest pressure in the pressure range already permits the second fluid 70 to enter the second channel 85.

[0178] Fig. 5 exemplarily shows a schematic cross-sectional view (parallel to an x-y plane) of an implementation of the microfluidic chip 20 of the pressure measuring apparatus 10 illustrating three different configurations of the meniscus 50 formed in the hydrophilic measurement chamber 30. The microfluidic chip 20 comprising the hydrophilic measurement chamber 30 shown in Fig. 5 may be considered to be in accordance with the illustration on the right of Fig. 2. Details described herein with respect to Fig. 5 may be combined with the details previously described with respect to Fig. 2.

[0179] The schematic illustrations describe three different configurations of the meniscus 50 in the same hydrophilic measurement chamber 30. This means that each configuration in the hydrophilic chamber 30 may correspond to a different value of the pressure in the second fluid 70. It is noted that the position, or height h, 54-# may be defined relative to the fluid inlet 40, where the height h may be zero i.e. h = 0. As exemplarily shown in Fig. 5, the capillary chamber 30 is formed with a rectangular cross section with tapered side walls 36, wherein the side walls 36 taper in a direction from the ventilation opening 80 towards the fluid inlet 40. In other words, the hydraulic radius at top of the chamber 30, adjacent to the ventilation opening 80, is larger than the hydraulic radius at bottom of the chamber 30, adjacent to the fluid inlet 40.

[0180] The first configuration of the meniscus 50 in the hydrophilic chamber 30, depicted by the illustration on the left of Fig. 5, shows that the meniscus 50 has a first position 54-1 and a first shape 56-1 , wherein the first configuration corresponds to a first value, denoted by p , of the pressure in the second fluid 70. The second configuration of the meniscus 50 in the hydrophilic chamber 30, depicted by the illustration in the center of Fig. 5, shows that the meniscus 50 has a second position 54-2 and a second shape 56-2, wherein the second configuration corresponds to a second value, denoted by pB, of the pressure in the second fluid 70. The third configuration of the meniscus 50 in the hydrophilic chamber 30, depicted by the illustration on the right of Fig. 5, shows that the meniscus 50 has a third position 54- 3 and a third shape 56-3, wherein the third configuration corresponds to a third value, denoted by pc, of the pressure in the second fluid 70.

[0181] It can be seen in Fig. 5 that the second shape 56-2 comprises a flat surface depicted as straight line. This second configuration may correspond to a case when the pressure in the second fluid 70 is zero, i.e. pm = 0, and consequently the meniscus 50 has the second position 54-2 as an equilibrium position lacking any input pressure, denoted by heq, in the chamber 30. As per the Young-Laplace equation given in eq. (2), this equilibrium state corresponds to zero curvature, i.e. k = 0 in accordance with the straight shape 56-2 of the meniscus 50. The pressure in the second fluid 70 is then given by pB= peq. Any additional pressure pinthat is applied at the fluid inlet 40 to the measurement chamber 30 displaces the meniscus 50 from its equilibrium position 56-2, heq, to either retract from the chamber 30, i.e. pm < 0, or to intrude further into the measurement chamber 30, i.e. pm > 0.

[0182] The illustration on the left of Fig. 5 shows that the meniscus 50 having the first position 54- 1 , which is lower than the second position 54-2, and the first shape 56-1 retracts from the measurement chamber 30 when the additional pressure in the second fluid 70 at the fluid inlet 40 is negative, i.e. pin< 0, and therefore, the first shape 56-1 comprises a shape curved towards the fluid inlet 40. The pressure value associated with this configuration is then expressed as pA= peq- |pf„| . The illustration on the right of Fig. 5 shows that the meniscus 50 advances further into the measurement chamber 30 having the third position 54-3, which is higher than the second position 54-2, and the third shape 56-3 when the additional pressure in the second fluid 70 at the fluid inlet 40 is positive, i.e. pm > 0, and therefore, the third shape 56-3 comprises a shape curved away from the fluid inlet 40. The pressure value associated with this configuration is then expressed as pc= peq+ |pf„| .

[0183] Thus, the different positions 54-1 , 54-2, 54-3 and shapes 56-1 , 56-2, 56-3 of the meniscus 50 in the hydrophilic chamber 30 may be correlated to the applied pressure in the second fluid 70. For the hydrophilic chamber 30 with tapered side walls 36 as shown in Fig. 5, a complete calibration relationship, which may relate the position and / or the shape of the meniscus 50 in the chamber 30 to the applied pressure in the second fluid 70 may not be easily expressed in an analytical equation. This may be due to the fact that the hydraulic radius increases super-linearly to form the convex inner wall on at least one side wall of the capillary chamber 30. The specific convex shape may be preferred so that the meniscus 50 finds an equilibrium position with zero curvature, such as the second position 54-2 shown in Fig. 5, somewhere inside the measurement chamber 30.

[0184] When the side walls 36 of the hydrophilic capillary measurement chamber 30 may be linearly tapered, instead of the super-linear tapering shown in the chambers of Fig. 5, the capillary pressure may not be zero and the meniscus 50 may fill the measurement chamber 30 up to the ventilation opening 80, i.e. up to the top of the chamber 30, even if no input pressure may be applied.

[0185] The convex shape of the side walls 36 permits the tangents to the contact line of the meniscus 50, i.e. the line where the different fluidic phases meet, to be parallel. At this point, the curvature of the free surface 50 is zero, k = 0, and therefore, the capillary pressure is zero, pcap = 0 and an equilibrium of the meniscus 50 is reached.

[0186] That is, the side walls of the measurement chamber 30 may be configured so as to permit the meniscus 50 to establish equilibrium within the measurement chamber 30. In particular, the side walls 36 and the longitudinal extension of the chamber 30 may be adapted to allow the meniscus to establish equilibrium at a specific position, heq, within the chamber. This equilibrium situation is not established for a concave tapering of the side walls 36, where the curvature of the free surface 50 is not zero. For linearly tapered walls 36, the curvature of the meniscus 50 decreases continuously with increasing height h of the chamber 30 but does not reach a zero value. For example, the curvature of the meniscus 50 in a circular, linearly tapered capillary does not decrease sufficiently enough to transform from a spherical cap with a constant curvature surface into a completely flat surface with zero curvature, k = 0.

[0187] Therefore, in theory ignoring possible pinning effects of the side walls 36 of the chamber 30, for linearly tapered walls 36, the capillary pressure may remain positive and the meniscus 50 may fill the chamber 30 fully even when no input pressure in the second fluid 70 is provided, i.e. pin= 0. Thus, theoretically, no fluidic interface 50 is established in the hydrophilic chamber 30 with linearly tapered side walls 36, unless a specific minimum negative pressure, pin< 0, is provided at the inlet 40. This specific minimum negative pressure prevents the meniscus 50 from completely filling the measurement chamber 30, in accordance with the configuration shown in the left illustration of Fig. 5.

[0188] However, in practice, linear tapering of the side walls 36 may permit the curvature of the meniscus 50 to have a zero value within the chamber 30, due to pinning effects which stop the contact line of the meniscus 50 at a specific position.

[0189] In the case of pinning, the capillary pressure difference will not lead to a further movement, but to a deformation of the meniscus 50. The shape 56 of the meniscus 50 may not be convex with a constant curvature k all over the surface. However, the curvature associated with the shape 56 may be locally different. That is, the curvature of the meniscus 50 may comprise positive curvature regions comprising positive curvature values and negative curvature regions comprising negative curvature values, wherein the positive curvature regions and the negative curvature regions may permit the total curvature of the meniscus 50 to be a zero value. In other words, the curvature surface of the meniscus 50, i.e. 3D- surface associated with the curvature of the meniscus 50, may comprise a first group of regions having a positive local curvature and a second group of regions having a negative local curvature, wherein the curvature surface may have a zero global curvature integrated over the entirety of its surface. Therefore, for the equilibrium configuration, the shape 56 of the meniscus 50 may not be a flat surface with k=0 everywhere on it, in practice.

[0190] Fig. 6 exemplarily shows a schematic cross-sectional view (parallel to an x-y plane) of an implementation of the capillary measurement chamber 30 comprising a pinning structure 38, illustrating three different configurations of the meniscus 50 formed in the same measurement chamber 30. The configurations relate to possible deformations of the meniscus 50 in the chamber 30 comprising the pinning structure 38.

[0191] It is a well-known fact that an advancing fluidic meniscus 50 can be held back by irregularities in the surface energy which may be caused by sharp edges, surface roughness or, chemical and / or electrical modifications of the surface. In such situations, the contact line formed between the measurement chamber 30 and the fluids, such as a solidliquid contact line, does not move, even when a pressure is applied to the meniscus 50. This so-called pinning effect is exploited in many microfluidic applications and may be used to design the measurement chamber 30, in accordance with the present concept. An example of the shape evolution of a meniscus 50 overcoming a pinning edge is described and sketched in the following publication

[0021] ,

[0192] According to an embodiment, the capillary measurement chamber 40 may comprise the pinning structure 38 configured to permit the position 54 of the meniscus 50 in the measurement chamber 30 to be stationary over a range of pressures and to permit the shape 56 of the meniscus 50 in the measurement chamber 30 to be variable over the range of pressures.

[0193] According to another embodiment, the pinning structure 38 may comprise sharp edges 39 of the cross-sectional area of the measurement chamber 30, different surface roughness of the inner surface of the measurement chamber 30 and / or chemical or electrical modifications of the inner surface of the measurement chamber 30.

[0194] The measurement chamber 30 comprising the pinning structure 38 shown in Fig. 6 may be made of a hydrophilic material, however it is equally feasible that the measurement chamber 30 comprising the pinning structure 38 may be made of a hydrophobic material, as will be described further according to another figure below in the present disclosure.

[0195] As exemplarily shown in Fig. 6, the measurement chamber 30 comprises the pinning structure 38, a first channel 84 and a second channel 85. The pinning structure 38, the first channel 84 and the second channel 85 are in fluidic connection with each other. The first channel 84 is fluidically connected to the fluid inlet 40 on one end of the chamber 30. The second channel 85 is fluidically connected to the ventilation opening 80 on another end of the chamber 30. For instance, as shown in Fig. 6, both the channels 84, 85 of the measurement chamber 30 comprise non-tapered, straight side walls 36. However, any of the channels 84, 85 may comprise tapered side walls 36 to allow variations of the hydraulic radius of the chamber 30, in accordance with already described embodiments of the present invention. The second channel 85 is adapted to have a larger hydraulic radius than that of the first channel 84. That is, the second channel 85 comprises a lateral extension, extension along a x-direction, wider than that of the first channel 84.

[0196] The pinning structure 38 comprises sharp edges 39 of the cross-section area of the chamber 30. In particular, the pinning structure 38, as shown in Fig. 6, comprises four sharp edges 39 of the cross-sectional area of the chamber and is arranged at another end of the first channel 84, wherein another end is opposite to the one end. These sharp edges 39 lead to a pinning of the meniscus 50 in the measurement chamber 30. That is, the sharp edges 39 are configured to not permit the meniscus 50 to advance further along the longitudinal extension of the measurement chamber 30. In other words, the sharp edges 39 are adapted to not allow the position 54 of the meniscus 50 to vary and to allow the shape 56 of the meniscus 50 to vary. By this measure, changes in the shape 56 of the meniscus 50, while having its position in the chamber 30 remain stationary, are correlated with the pressure applied in the second fluid 70 via the inlet 40. The different configurations of the meniscus 50 as it deforms as per the pinning structure 38 are illustrated in Fig. 6.

[0197] The illustration in the center of Fig. 6 shows the meniscus 50 in a second configuration wherein the additional input pressure in the second fluid 70 is zero, i.e. pm = 0, and consequently the meniscus 50 has the second position 54-2 and the second shape 56-2, as an equilibrium state stably formed between the sharp edges 39 of the pinning structure 38. The second shape 56-2 of the meniscus is flat in accordance with its equilibrium state. The pressure value associated with this configuration is then be expressed as PB = peq.

[0198] The illustration on the left of Fig. 6 shows the meniscus 50 in a first configuration where it enters the measurement chamber 30 and forms a first position 54-1 and a first shape 56-1 within the circular capillary channel 84 when the additional pressure in the second fluid 70 at the fluid inlet 40 is negative, i.e. pin< 0, and therefore, the first shape 56-1 is curved towards the fluid inlet 40. The pressure value associated with this configuration is then be expressed as pA= peq- |pf„|.

[0199] The illustration on the right of Fig. 6 shows the meniscus 50 in a third configuration where it changes its shape 56 after being pinned at the sharp edges 39 of the pinning structure 48 and thus, still has the second position 54-2 and a third shape 56-1 , different from the second shape 56-2, when the additional pressure in the second fluid 70 at the fluid inlet 40 is positive, i.e. pm > 0. Therefore, the third shape 56-3 is curved away from the fluid inlet 40. The pressure value associated with this configuration is then be expressed as pA= peq+ \Pin I ■

[0200] For instance, the first channel 84 and the second channel 85 may comprise circular crosssections. In embodiments, the first channel 84 may comprise at least one of a circular cross section, an elliptical cross section, a rectangular cross section and a polygonal crosssection. In embodiments, the second channel 85 may comprise at least one of a circular cross section, an elliptical cross section, a rectangular cross section and a polygonal crosssection.

[0201] For the third configuration, the meniscus 50 can be well approximated by a spherical cap with curvature k = 2 / r’, where r’ = r / cosQ may be a radius of the spherical cap, r is a radius of the first channel 84 and 0 is the contact angle associated with the meniscus 50 and the first channel 84. Thus, by measuring the curvature k, i.e. the shape 56 of the meniscus 50, the pressure difference between the first fluid 60 and the second fluid 70 is determined using the Young-Laplace equation (2) and thus, the input pressure pinis also determined explicitly from the curvature.

[0202] Fig. 7 exemplarily shows a schematic cross-sectional view (parallel to an x-y plane) of another implementation of the capillary measurement chamber 30 comprising the pinning structure 38, illustrating two different configurations of the meniscus 50 formed in the same measurement chamber 30. The configurations relate to possible deformations of the meniscus 50 in the chamber 30 comprising the pinning structure 38.

[0203] In particular, the implementation of the chamber 30 comprising the pinning structure 38 exemplarily shown in Fig. 7 is a variation of the implementation of the chamber 30 depicted in Fig. 6, in accordance with embodiments of the present invention. The measurement chamber 30 comprising the pinning structure 38 shown in Fig. 7 may be made of a hydrophobic material.

[0204] As exemplarily shown in Fig. 7, the measurement chamber 30 comprises the pinning structure 38, the first channel 84 and the second channel 85. A first portion 84-1 of the first channel 84 comprises straight, non-tapering side walls 36, and a second portion 84-2 of the first channel 84 comprises tapering side walls 36, wherein the side walls 36 of the chamber 30 associated with second portion 84-2 taper in a direction away from the fluid inlet 40, i.e. towards the ventilation opening 80. As shown in Fig. 7, the hydraulic diameter of the first portion 84-1 of the first channel 84 equals the hydraulic diameter of one end of the second portion 84-2 of the first channel 84. That is, the first portion 84-1 of the first channel 84 extends laterally as wide as the one end of the second portion 84-2 of the first channel 84. In other words, the first portion 84-1 has a same width as the second portion 84-2 at its base.

[0205] In the case wherein the first portion 84-1 extends laterally narrower the base of the second portion 84-2, the fluid, for instance the second fluid 70, when entering the second portion 84-2 of the first channel 84 would fill up all of the second portion 84-2, i.e. the tapered portion, of the first channel 84 to the top, i.e. to an end of the second portion 84-2 of the first channel 84 which is opposite to the one end. This is due to the second portion 84-2 having a larger hydraulic radius everywhere than the first portion 84-1. By this measure, the pressure in the fluid, for instance the second fluid 70, has to be so large as to move the meniscus 50 into the second portion 84-2 that it is no longer possible to attain an equilibrium position somewhere in the second portion 84-2, or the tapered portion. The fluid, for instance the second fluid 70, would flood all of the second portion 84-2 of the first channel 84 and maybe even top out at the pinning structure 38 above. To prevent this, the first portion 84-1 of the first channel 84-1 cannot have a larger hydraulic radius than the second portion 84-2 at its base.

[0206] In accordance with embodiments, the hydraulic diameter of the first channel 84, and thus the capillary measurement chamber 30, at least partially decreases with increasing distance from the fluid inlet 40. In particular, the hydraulic diameter of the first channel 84, and thus the capillary measurement chamber 30, at least partially decrease linearly with increasing distance from the fluid inlet 40. In contrast to the second portion 84-2 of the first channel 84, the side walls of the second channel 85 in the chamber 30 are straight or non-tapered. That is, the hydraulic diameter of the second channel 84 does not vary along its longitudinal extension.

[0207] As shown in Fig. 7, the first channel 84 and the second channel 85 are configured to form the pinning structure 38 as sharp edges 39 of the cross-sectional area of the chamber 30, which permits pinning of the meniscus 50 formed in the chamber 30. That is, orifices of the first channel 84 and the second channel 85 are configured to form the pinning structure 38 as sharp edges, or pointed edges, 39 of the cross-sectional area of the chamber 30. The illustration on the left of Fig. 7 shows the meniscus 50 in the configuration where it enters the measurement chamber 30 and forms a first position 54-1 and a first shape 56-1 within the second portion 84-2 of the first channel 84 when the additional pressure in the second fluid 70 at the fluid inlet 40 is negative, i.e. pm < 0. The first shape 56-1 is also curved away from the fluid inlet 40, that is, it is curved towards the ventilation opening 80. The pressure value associated with this configuration is then expressed as pA= peq-

[0208] The illustration on the right of Fig. 7 shows the meniscus 50 in the configuration wherein the additional input pressure in the second fluid 70 is zero, i.e. pin= 0, the meniscus 50 has the second position 54-2 and the second shape 56-2, as an equilibrium state stably formed between the sharp edges 39 of the pinning structure 38. The second shape 56-2 is curved away from the fluid inlet 40, and towards the ventilation opening 80, in accordance with its equilibrium state and the hydrophobicity of the material of the chamber 30. The pressure value associated with this configuration is then expressed as PB = peq. In this configuration, the meniscus 50 is pinned between the sharp edges 39, i.e, when the contact line of the meniscus 50 reaches a narrower end of the tapered portion 84-2 of the first channel 84.

[0209] An application of further input pressure in the second fluid 70 changes the shape of the meniscus 50, which further modifies the curvature of the meniscus 50 pinned, or held stationary positionally, between the sharp edges 39 of the pinning structure 38. In particular, due to the further input pressure in the second fluid 70, the curvature of the meniscus 50 increases, and thus the radius of the curvature decreases, while still being pinned between the sharp edges 39. When the input pressure is increased even further, the second fluid 70 may suddenly enter the second channel 85 of the chamber 30. That is, for a specific value of the input pressure substantially larger than the pressure value associated with the equilibrium configuration, PB > pin, the meniscus may not be pinned and may move into the wider channel 85 of the chamber 30.

[0210] Thus, during the pinning of the meniscus 30 by the pinning structure 38, pressure changes are associated, and are determined, using corresponding changes in the shape 56, or curvature, of the meniscus 50, thereby permitting an improved pressure sensing in pinning situations by the pressure measuring apparatus 10 of the present concept.

[0211] It is to be noted that, as exemplarily shown in the illustrations of Fig. 7, the first portion 84- 1 of the first channel 84 and the second portion 84-2 of the first channel 84 together also represent sharp edges of the cross-sectional area of the measurement chamber. Additionally, or alternatively to the pinning structure described so far with respect to Fig. 7, these sharp edges within the first channel 84 may also be regarded as embodiment of the pinning structure 38. In other words, the contact line of the meniscus 50 may also be stuck at the sharp edges within the first channel 84. Thus, the sharp edges within the first channel 84 may permit a further improvement in the pressure measurement range of the chamber 30.

[0212] It is also feasible the measurement chamber 30 itself may comprise a plurality of channels, each of which may permit the meniscus 50 to be formed in the chamber 30 between the first fluid 60 and the second fluid 70. Therefore, using the plurality of channels the measurement chamber 30 may be designed to further extend the measurement range of the pressure measuring apparatus 10.

[0213] Fig. 8 exemplarily shows a schematic cross-sectional view (parallel to an x-y plane) of another implementation of the microfluidic chip 20 comprising three capillary measurement chambers 30-1 , 30-2, 30-3 in accordance with an embodiment of the present invention.

[0214] The first measurement chamber 30-1 , the second measurement chamber 30-2 and the third measurement chamber 30-3 are fluidically coupled to each other and fluidically coupled to one fluid inlet 40. In other words, the three measurement chambers 30-1 , 30-2, 30-3 have the common fluid inlet 40, that is, the fluid inlet 40 being common for the three measurement chambers 30-1 , 30-2, 30-3. The three measurement chambers 30-1 , 30-2, 30-3 are configured to permit the menisci 50-1 , 50-2, 50-3 between the first fluid 60 and the second fluid 70 to be formed within them. Pressure ranges of the three capillary measurement chambers 30-1 , 30-2, 30-3 may be different from each other. That is, each of the three measurement chambers 30-1 , 30-2, 30-3 may be configured to permit the meniscus 50-# to be formed within it for a range values associated with the pressure in the second fluid 70. In other words, the first measurement chamber 30-1 may have the first pressure range, the second measurement chamber 30-2 may have the second pressure range and the third measurement chamber 30-3 may have the third pressure range. The first pressure range may be different from the second pressure range, and the third pressure range may be different from both the first pressure range and the second pressure range.

[0215] It is noted that alternatively, the measurement chambers 30-1 , 30-2, 30-3 may be configured so as to permit the pressure ranges of at least two of the measurement chambers 30-1 , 30- 2, 30-3 to coincide with each other. In particular, according to another feasible embodiment, the three measurement chambers 30-1 , 30-2, 30-3 may be configured to have their pressure ranges coinciding with each other. By this measure, pressure measurement may be improved by means of averaging, or cross-checking , with each other.

[0216] The first measurement chamber 30-1 is configured to permit the first meniscus 50-1 to be formed in the chamber having the first position 54-1 and the first shape 56-1. The first measurement chamber 30-1 is non-vented and therefore, lacks a fluidic connection to the ambient environment. The first measurement chamber 30-1 further comprises the pinning structure 38 formed by sharp edges 39 of the cross-sectional area of the chamber 30-1 , in accordance with the implementations of the measurement chamber 30 as illustrated in Fig. 6 previously described in the present disclosure. It may thus be understood as a variation of the measurement chamber of Fig. 6.

[0217] The second measurement chamber 30-2 may be in accordance with the implementations of the hydrophobic measurement chamber 30 as illustrated in left illustration of Figs. 2, 3 & 4 as previously described in the present disclosure. The second measurement chamber 30- 2 is configured to permit the second meniscus 50-2 to be formed in the chamber having the second position 54-2 and the second shape 56-2.

[0218] The third measurement chamber 30-3 comprises straight, non-tapered side walls i.e. a hydraulic radius of the chamber 30-3 is constant and does not vary along its longitudinal extension. The chamber 30-3 is non-vented, lacking a fluidic connection to the ambient environment. In particular, the third capillary measurement chamber 30-3 comprises the first fluid 60 configured to form the meniscus 50 between the first fluid 60 and the second fluid 70 by compressing the first fluid 60. By this measure, the position 54 of the meniscus 50 formed depends on a volume of the first fluid 60 enclosed in the chamber 30-3. Thus, the third measurement chamber 30-3 is configured to determine the pressure in the second fluid 70 based on a volumetric compression of the first fluid 60 within the chamber 30-3. The third measurement chamber 30-3 is configured to permit the second meniscus 50-3 to be formed in the chamber having the third position 54-3 and the third shape 56-3. Further details of this type of pressure measurement by the chamber 30-3 are provided in the following.

[0219] When the second fluid 70, such as a liquid, enters into the chamber 30-3 and the meniscus 50-3 is formed, a constant amount i.e. volume of the first fluid 60, such as a gas, is trapped in the measurement chamber 30-3, which is characterized by a certain number of molecules A / gas. The pressure inside the enclosed first fluidic volume can then be estimated by the ideal gas law: where k indicates Boltzmann’s constant, V indicates the volume of the enclosed first fluid 60 (e.g. gas) and T indicates the temperature associated with the first fluid, or gas. The index “0” describes pressure and volume at ambient conditions before the second fluid 70, or liquid for instance, enters the measurement chamber 30-3.

[0220] Assuming that the measurement chamber 30-3 is formed by a circular capillary with radius r and length I closed at one end, the pressure in the gas phase can be expressed as a function of the rising height h 54-3 of the meniscus 50-3 as follows:

[0221] The first fluidic, or gas for instance, pressure is in balance with the capillary pressure plus any additional input pressure applied via the common fluid inlet 40. Thus, an equation for the input pressure applied in the second fluid 70 can be derived like follows:

[0222] Using equations (3), (13) and (14) one can calculate the applied input pressure in the second fluid 70 as a function of the position 54-3 of the meniscus 50-3 in the measurement chamber 30-3, Pin(h), explicitly:

[0223] For example, in this chamber 30-3, the trapped first fluidic, or gas, volume forms a fluidic capacity similar to the fluidic capacity used in air suspension systems. It is understandable to the persons skilled in the art that the volumetric or capacitive effect caused by the compressibility of the first fluidic, or gas, phase may be replaced or combined with other elastic elements. For example, the inner walls of the measurement chamber 30-3 may be configured to be elastic. That is, the inner walls of the measurement chamber 30-3 may be configured to physically deform when supplying the second fluid via the fluid inlet 40. The physical deformation of the inner walls of the measurement chamber 30-3 is then correlated to the applied pressure in the second fluid, and thus a pressure measuring apparatus comprising the measurement chamber described here determines the pressure.

[0224] It is also understandable to the persons skilled in the art that the configurations discussed with respect to Fig. 8 may be combined to make the position 54 of the meniscus 50 depend on possible tapering of the side walls 36 of the measurement chamber 30 as well as on the compressibility of the enclosed first fluidic volume. Therefore, in accordance with other embodiments of the present inventive concept, the measurement chamber may be configured to not be fluidically connected to the ambient environment i.e. it may be configured to lack the ventilation opening. The measurement chamber may further comprise tapered side walls, similar to the chambers in Fig. 2, 3 and 4, and may comprise the first fluid configured to form the meniscus between the first fluid and the second fluid by compressing the first fluid. By this measure, the position and the shape, or curvature, of the meniscus formed may depend on a volume of the first fluid enclosed in the chamber, thus, yielding an embodiment of the combined concept where capillary pressure as well as volume of the trapped first fluid, or gas, change as a function of meniscus position. It is also a feasible embodiment that this measurement chamber may, additionally or alternatively, comprise the pinning structure as described before with respect to Figs. 6 and 7.

[0225] Combining different concepts may be of high practical relevance because the accessible measurement range and / or the sensitivity of the measurement chamber may be enlarged and the shape and slope of the calibration relationship P[S] may be influenced by such combinations.

[0226] Thus, the microfluidic chip 20 comprising the three measurement chambers 30-1 , 30-2, 30- 3, as exemplarily shown in Fig. 8, each of which may be operated and evaluated in parallel, increases dynamic range, precision and robustness of the pressure measuring apparatus 10 in accordance with the present inventive concept.

[0227] A flow sensor 100 in accordance with another aspect of the present inventive concept is now described with respect to the schematic diagram of Fig. 9. Fig. 9 exemplarily shows a schematic cross-sectional view, parallel to an x-y plane, of an implementation of the flow sensor 100. The flow sensor 100 comprises a sensor fluid inlet 110, a sensor fluid outlet 120 and a fluid channel 150 between the sensor fluid inlet 110 and the sensor fluid outlet 120. The flow sensor 100 further comprises a first pressure measuring apparatus 200 according to the aspect of the inventive concept already described in the present disclosure. The fluid inlet 210 of the first pressure measuring apparatus 200 is fluidically coupled to the fluid channel 150 at a first position. The flow sensor 100 further comprises a second pressure measuring apparatus 400 according to the aspect of the inventive concept already described in the present disclosure. The fluid inlet 410 of the second pressure measuring apparatus 400 is fluidically coupled to the fluid channel 150 at a second position spaced apart from the first position. The fluid channel 150 forms a measurement channel 160 between the first position and the second position.

[0228] Although not shown in Fig. 9, the flow sensor 100 further comprises a flow rate determiner configured to determine a flow rate through the fluid channel 150 using the pressures determined by the sensing system of the first pressure measuring apparatus 200 and the sensing system of the second pressure measuring apparatus 400.

[0229] Additionally in accordance with Fig. 9, the first pressure measuring apparatus 200 comprises a first capillary measurement chamber 220 and a second capillary measurement chamber 240. The first and the second measurement chambers 220, 240 are arranged upstream of the measurement channel 160, such as on opposite sides at a first position 104 as shown in Fig. 9.

[0230] The first measurement chamber 220 is in fluidic connection to the ambient environment by a ventilation opening 225. The ventilation opening 225 is spaced apart from the fluid inlet 210.

[0231] The second pressure measuring apparatus 400 comprises a third capillary measurement chamber 420 and a fourth capillary measurement chamber 440. The third and the fourth measurement chambers 420, 440 are arranged at the second position 108 downstream of the measurement channel 160, such as on opposite sides at a second position 108 as shown in Fig. 9. The third measurement chamber 420 is in fluidic connection to the ambient environment by a ventilation opening 425. The ventilation opening 425 is spaced apart from the fluid inlet 410.

[0232] The first measurement chamber 220 of the first pressure measuring apparatus 200 and the third measurement chamber 420 of the second pressure measuring apparatus 400 comprise tapered side walls, in accordance with embodiments of the measurement chamber described earlier with respect to Figs. 2, 3 and 4.

[0233] The second measurement chamber 240 of the first pressure measuring apparatus 200 and the fourth measurement chamber 440 of the second pressure measuring apparatus 400 comprise straight, non-tapered side walls, in accordance with a part of the embodiment with multiple measurement chambers described earlier with respect to Fig. 8.

[0234] As exemplarily shown in Fig. 9, the two pressure measuring apparatuses 200, 440, and thus the measurement chambers 220, 240, 420, 440, along with the sensor fluid inlet 110, the sensor fluid outlet 120 and the fluid channel 150 are comprised in a single microfluidic chip 500. Therefore, this implementation of multiple measurement chambers on the same microfluidic chip 500 is advantageous since it reduces overall costs associated with the flow sensor 100.

[0235] The flow sensor 100 is provided with the first fluid 610 via the ambient environment. The second fluid 620 is supplied into the flow sensor 100 via the sensor fluid inlet 110 and is be supplied out of the flow sensor 100 via the sensor fluid outlet 120.

[0236] It can be seen that Fig. 9 depicts a configuration of the flow sensor 100, wherein menisci 630-1 , 630-2, 630-3, 630-4 are formed between the first fluid 610 and the second fluid 620 in the measurement chambers 220, 240, 420, 440. In particular, the configuration exemplarily shows that a meniscus 630-# is formed in each of the four measurement chambers 220, 240, 420, 440.

[0237] It is understandable to the persons skilled in the art that, according to the differential pressure principle, the pressure difference between the first position 104 i.e. the upstream position (pup) and the second position 108 i.e. the downstream position (pdown) of the flow measurement channel 160, having the length L and the flow resistance RL, is measured. From the pressure difference Ap between these two pressure values and the known value of RL, the flow rate can be calculated according to the following formula:

[0238] For laminar flows, RL can be estimated by the Hagen-Poiseuille formula for known measurement channel 160 geometries and viscosity of the second fluid 620 (given as approximate formula for a circular channel with radius rand length I in equation (17)). More details about the differential pressure principle for sensing fluid flows and more sophisticated formulas to more accurately estimate the flow in specific channel geometries can be found, for instance in [1], Independent of a specific design of the measurement channel 160 or formula applied for flow calculation, the measured pressure difference Ap between the upstream end 104 and downstream end 108 of the measurement channel 160 is the essential quantity to be determined by the measurement. The flow rate determiner of the flow sensor 100 is configured to determine the flow rate through the fluid channel 150 using the pressure difference of the pressures determined by the sensing systems of the first and the second pressure measuring apparatuses 200, 400. According to the preferred embodiment shown in figure 9, the measurement channel 160 having a constant cross section may be used and laminar flow conditions as well as constant viscosity and density may be assumed, such that formula (16) holds in good approximation.

[0239] The pressure drop Ap over the measurement channel 160 is measured by the pressure measuring apparatuses, or pressure sensors, 200, 400 in accordance with the pressure measuring apparatus 10 and embodiments thereof described in the present disclosure of the present inventive concept. Therefore, the two measurement chambers 220, 240 are connected upstream, parallel to the measurement channel 160. The two measurement chambers 420, 440 are connected downstream, in parallel to the measurement channel 160.

[0240] It is to emphasized that, in accordance with the embodiment of the invention, at least one pair of measurement chambers is specified to determine the pressure difference Ap that is used for flow calculation according to equation (14). That is, either a pair comprising the first measurement chamber 220 and the third measurement chamber 420 or a pair comprising the second measurement chamber 240 and the fourth measurement chamber 440 is sufficient for measuring flow rate of the second fluid. Thus, the presented preferred embodiment of a flow sensor also works with either one of the two sensing systems associated with the two pressure measuring apparatuses 200, 400.

[0241] However, using more than one pair of sensing systems has several benefits and comes at no additional cost. For example, an optical system comprising an optical camera may be used as the single sensing system. The optical camera may be configured to simultaneously generate image data of the menisci formed in the measurement chambers 220, 240, 420, 440. The measurement chambers of the flow sensor may be adapted so as to be optically readable simultaneously by the sensing system. In particular, the measurement chambers of the flow sensor may be arranged to be in a field of view of the sensing system. This may generate better image data which may be provided to an ML- and / or Al-based software program based on a Al- and / or ML-based algorithm, which may enhance prediction accuracy of the pressure difference Ap .

[0242] In addition to increasing accuracy by using a plurality of measurement chambers, pairs of different types of measurement chambers may be configured to comprise different pressure ranges, which extend the dynamic flow measurement range of the flow sensor. In accordance with the preferred embodiment exemplarily shown in Fig. 9, the measurement chamber pair 220, 240 are designed to work at higher pressure values, while the pair 420,440 is already very sensitive at lower pressure values. In the case when measurement ranges of several measurement chamber pairs overlap, the flow rate determiner may use the pressure values determined using different pairs of the measurement chambers for averaging and / or for comparing to each other for consistency, which further enhances the reliability and the precision of the measurements of the flow sensor. The flow rate determiner may be interfaced with a computer program for determining the flow rate through the flow channel based on the pressures determined by the pressure measuring apparatuses.

[0243] Further, pairs of measurement chambers may also be connected in different ways to the ambient environment, in addition to as exemplarily shown in Fig. 9. As per Fig. 9, the first fluid 610, or gas phase, of the pair comprising measurement chambers 220, 420 is connected to the ambient pressure p0through a fluidic connection via the ventilation openings 225, 425, while the pair comprising measurement chambers 240, 440 is not connected to the ambient environment. As a consequence, the first and third measurement chambers 220, 420 measure relative to the ambient pressure p0, while the second and the fourth measurement chambers 240, 440 measure relative to a same floating pressure value.

[0244] This same floating pressure value depends on:

[0245] • the capillary pressure exerted by the menisci in the different measurement chambers 240, 440,

[0246] • the flow rate in the measurement channel 160,

[0247] • a temperature associated with the first fluid or the working conditions, and

[0248] • the ambient pressure p0, pressure value related to the ambient environment

[0249] After filling the flow sensor with the second fluid for the first time, a defined first fluid, or gas, volume is enclosed between the menisci in the second measurement chamber 240 and the fourth measurement chamber 440. At this point, reference pressures for both pairs will be the same, i.e. p0+ pcap, where pcapindicates the pressure associated with the capillary pressure of the menisci. However, when the ambient pressure p0changes, the volume of the trapped first fluid, or gas, changes as well and thus, equilibrium positions of the menisci change correspondingly in the second and the fourth measurement chamber 240, 440, while equilibrium positions of the menisci in the first and the third measurement chambers 220, 420 are independent of the ambient pressure p0. A variation between the pressures determined between the pair of the first and the second measurement chambers 220, 240 and the pair of the second and the fourth measurement chambers 420, 440 may thus be used to estimate an effective value of the ambient pressure.

[0250] The sensing systems and the flow rate determiner may be configured to store allocate data allocating positions and shapes of menisci in the measurement chambers 220, 240, 420, 440 to known flow rates of the second fluid and to determine the flow rate through the fluid channel.

[0251] By calibrations of the measurement chambers 220, 240, 420, 440 at different flow rates and at different ambient pressure values, a change of the ambient pressure p0over time may also be measured by the preferred embodiment as exemplarily illustrated in Fig. 9.

[0252] It may be understood by persons skilled in the art that the use of a plurality of measurement chambers may have various use cases and benefits, and therefore, a number of measurement chambers comprised in the flow sensor may not increase the total costs of the flow sensor, since the plurality of the measurement chambers may be implemented on the same microfluidic chip and may be read out by the same sensing system, for example, an optical camera with a suitable field of view and optical magnification characteristics.

[0253] In non-stationary flows, the associated flow rate changes as a function of time, which leads to constantly adapting positions and shapes of the menisci in the measurement chambers. A dynamic transition from one stable flow rate 1 to another stable flow rate <p 2 is however very much dependent on the rheological properties of the liquid. The state of the menisci is continuously monitored during the dynamic transition, and thus a series of sensor signals, for instance a series based on image data, carry information on the rheological properties of the liquid such as surface tension, viscosity and density. Therefore, software using algorithms based on Al may determine the rheological properties of the liquid from the series of sensor signals. This is similar to estimations of rheological properties made from video recordings of droplets in flight

[0010] and movement of menisci in micro channels

[0011] , using Al software.

[0254] Thus, the use of machine learning and Al software programs provides additional information on fluid properties beyond pressure and flow. This information may be also related to improper filling of the flow sensor or debris / bubbles which may be transported by the flow of the fluids that might be detrimental for certain applications of the flow sensor. Such qualitative parameters can be detected from the continuously recorded image data, which may provide additional benefits in certain applications of the flow sensor.

[0255] For quantitative measurement of rheological properties or fluid dynamic parameters, usually non-stationary flow conditions are important. In some cases these conditions appear spontaneously as part of the application, for instance, varying flow levels. In the case, the non-stationary flow conditions are not naturally provided, small perturbations may be added to the flow by active components such as a pressure fluctuation generating device.

[0256] The details of the pressure fluctuation generating device described earlier in the present disclosure in relation to the pressure measuring apparatus 10 depicted in Fig. 1 may be combined here with respect to the flow sensor of the present inventive concept. Therefore, features and technical effects relating to the embodiment of the pressure measuring apparatus comprising the pressure fluctuation generating device, as described earlier, may also be present in the embodiment of the flow sensor according to Fig. 9. Thus, dynamic fluctuations to stationary fluid flow, whether appearing spontaneously or induced by active means such as the pressure fluctuation generating device, enable the detection of rheological properties of fluids through Al based software.

[0257] The software algorithms based on Al may be also be used to correct for the viscosity dependence of the resistance R of the measurement channel of the flow sensor. For example, the measured viscosity can be used to calculate R by the formula of Hagen- Poiseuille. Equation (16) can then be used to determine the flow rate from the measured pressure difference, even when the viscosity of the liquid may not be known previously. Thus, errors in the flow measurement caused by changes of viscosity, e.g. due to temperature variations of variations of the liquid type, are automatically compensated, if the viscosity is measured from time to time by observation of the generated non-stationary flow conditions.

[0258] Flow measurement results obtained by Al software programs in different ways can be compared or averaged to increase measurement reliability and accuracy. For example, the flow rate determiner of the flow sensor may be adapted to use an first Al software, wherein the Al software may be trained to provide a flow rate based on a specific image data sequence. The flow rate determiner of the flow sensor may be adapted to use a second Al software, wherein the second Al software may be trained to provide a pressure difference over the measurement channel. The flow rate determiner of the flow sensor may be adapted to use a third Al software, wherein the third Al software may estimate a value of fluid viscosity at a specific temporal value based on a known value of fluid viscosity at a known temporal value. The results obtained by the different Al software programs satisfy equation (17) simultaneously when the same set of data generated by the sensing systems of the flow sensor is evaluated. Thus, operations such as averaging, triangulation and / or consistency checking can be performed on the data. In the case of significant inconsistencies between the different evaluation methods based on the Al software are detected, a message for re-calibration and / or for checking the system may be signalized to the user. This additional performance comes at no extra cost of the described apparatuses.

[0259] Fig 10 exemplarily shows a schematic cross-sectional view, parallel to a x-y plane, of a different implementation / embodiment of the flow sensor 100 with respect to the implementation / embodiment depicted in Fig. 9. Details described here in connection to Fig. 10 may be combined with the details previously described in connection to Fig. 9. Although not shown in this embodiment of the flow sensor 100 depicted in Fig. 10, the flow sensor 100 also comprises the flow rate determiner as described in reference to Fig. 9. The flow sensor 100 comprises the first pressure measuring apparatus 200 and the second pressure measuring apparatus 400, each of the pressure measuring apparatuses 200, 400 are in accordance with the described aspect of the inventive concept of the present disclosure. The pressure measuring apparatuses 200, 400 comprise pressure measurement chamber 220, 240, 420, 440. The measurement chambers 220, 240, 420, 440 may be made of a hydrophobic material. The measurement chambers 220, 240, 420, 440 comprise tapered side walls, wherein hydraulic radii of the measurement chambers 220, 240, 420, 440 vary along their longitudinal extensions i.e. extensions along the length of the chambers 220, 240, 420, 440. The hydraulic radii, or equivalently hydraulic diameters, of the measurement chambers 220, 240, 420, 440 at least partially decrease with increasing distance from their fluid inlets. In particular, Fig. 10 exemplarily shows that each of the measurement chambers 220, 240, 420, 440 comprises a first channel and a second channel, wherein the first channel comprises non-tapered, straight side walls and the second channel comprises tapered side walls tapering in a longitudinal direction away from the measurement channel.

[0260] It can be seen that Fig. 10 depicts a configuration of the flow sensor 100, wherein menisci 630-1 , 630-2, 630-3, 630-4 are formed between the first fluid 610 and the second fluid 620 in the hydrophobic capillary measurement chambers 220, 240, 420, 440. In particular, the configuration exemplarily shows that a meniscus 630-# is formed in each of the four measurement chambers 220, 240, 420, 440.

[0261] Also as per Fig. 10, the first fluid 610, or a fluid in a gas phase, of the pair comprising measurement chambers 220, 420 are connected to the ambient pressure p0through a fluidic connection via the ventilation openings 225, 425, while the pair comprising measurement chambers 240, 440 are not be connected to the ambient environment.

[0262] In accordance with an embodiment, and with respect to Fig. 9, the flow sensor 100 comprises an additional connection channel 700 fluidically connecting one of the at least one measurement chamber 240 of the first pressure measuring apparatus 200 to one of the at least one measurement chamber 440 of the second pressure measuring apparatus 400. The connectional channel 700 is connecting the distant end of the measurement chamber 240 -to the distant end of the measurement chamber 440. Thus, both measurement chambers 240 and 440 share the same reference pressure inside the first fluid. Also the total volume of the first fluid is the same for both chambers, which it is bound on the one end by the meniscus residing in chamber 240 and on the opposite end by the meniscus residing in chamber 440.

[0263] The measurement chambers 240, 440 are configured to determine the pressure in the second fluid 620 based on volumetric compression of the first fluid 610 already present in the measurement chambers and the connection channel 700. Thus, the positions of the menisci in the chambers 240, 440 depend on the pressure difference between the upstream position 104 and the downstream position 108. They are directly related to each other, due to the equilibration of the first fluid 610 in the connection channel 700, and they directly show the relative pressure difference between second fluid in chamber 240 and 440 caused by the flow in the measurement channel according to the equation (17).

[0264] In embodiments, the connection channel 700 may not have a constant hydraulic diameter. In other words, the hydraulic diameter of the connection channel 700 may vary along its channel length. It is noted that the connection channel may be configured to comprise any shape so as to fluidically connect the connection channel 700 with the measurement chambers 240, 440 and permit the same pressure across the measurement chambers 240, 440. It is further noted that the connection channel may be configured to comprise any dimension so as to fluidically connect the connection channel 700 with the measurement chambers 240, 440 and permit the same pressure across the measurement chambers 240, 440.

[0265] Thus, regardless of any changes in ambient pressure conditions, the relative change of the meniscus position in chamber 240 in relation to the position in chamber 440 indicates the pressure difference Ap that is needed in equation (17) to calculate the flow. By measuring the pressure difference directly one does not need to know the absolute ambient pressure which otherwise would be required to correct the values obtained by the measurement chambers at non-standard conditions.

[0266] In Figure 11 , a schematic illustration of an embodiment of a pressure measuring apparatus in accordance with an independent aspect of the present inventive concept is exemplarily shown. Any of the details of the pressure measuring apparatus 10 with respect to Figs. 1 to 8 may be combined with the details of the embodiment of the pressure measuring apparatus described in the following. The pressure measuring apparatus 1000 according to Fig. 11 comprises a microfluidic chip 1200, a pressure fluctuation generating device 1400 and a sensing system 1600.

[0267] The microfluidic chip 1200 comprises at least one measurement chamber and a fluid inlet fluidically coupled to the measurement chamber. The measurement chamber and the fluid inlet are configured to permit a stable meniscus between a first fluid and a second fluid to be formed in the measurement chamber when supplying the second fluid (such as under pressure) via the fluid inlet to the measurement chamber.

[0268] The pressure fluctuation generating device 1400 is configured to superimpose time dependent pressure fluctuations to either one of the fluids so as to cause variations of the position and / or the shape of the meniscus in the measurement chamber.

[0269] The sensing system 1600 is configured to detect a position and / or a shape of the meniscus and to determine a pressure in the second fluid based on the position and the shape of the meniscus. The sensing system 1600 is further configured to detect the variations of the position and / or the shape of the meniscus and to determine the pressure in the second fluid using the detected variations.

[0270] The transduction principle of the pressure measuring apparatus 1000 comprises using the meniscus formed between the first fluid and the second fluid in the capillary measurement chamber as a pressure transducing mechanism. Determining the pressure in the second fluid from the position and / or the shape of the fluid meniscus, and the variations of the position and / or the shape of the fluid meniscus may form a pressure measurement principle of the pressure measuring apparatus 1000 in accordance with the present inventive concept.

[0271] It is to be noted and emphasized that, in accordance with embodiments of the measuring apparatus 1000 that the pressure in the second fluid may be determined only from the position of the meniscus and variations thereof, due to the pressure fluctuations provided by the pressure fluctuation generating device. It is also to be noted and emphasized that in accordance with embodiments of the measuring apparatus 1000 that the pressure in the second fluid may be determined only from the-shape of the meniscus and variations thereof. It is thus also feasible that according to embodiments of the measuring apparatus 1000 that the pressure in the second fluid may be determined both from the position and the shape of the meniscus and variations thereof. This pressure measurement principle may render the use of any kind of membrane, the bending of which may be a transduction mechanism, obsolete. Instead, the meniscus formed by a free interface between the first fluid and the second fluid may be considered as a pressure sensitive membrane itself, as per the proposed inventive concept.

[0272] Thus, using the pressure fluctuations superimposed on the measurement chamber by the pressure fluctuation generating device, an improved pressure measurement may be achieved by the pressure measuring apparatus. Further, stick-slip effects may be diminished by advancing and receding positions of the meniscus created by oscillations around its equilibrium position, thereby providing better mobility to the meniscus and permitting the associated sensing system to be more sensitive towards smaller changes.

[0273] According to an embodiment, the sensing system 1600 may be further configured to determine a rheological property of the second fluid using a time series of the detected variations of the position and / or shape of the meniscus in the measurement chamber.

[0274] The time series of the detected variations of the position and the shape of the meniscus may be evaluated by Al software algorithms. The Al software algorithms may be configured to determine mean pressure and / or mean flow associated with the variations, along with rheological properties of the second fluid. In other words, the time series of the sensor signals generated by the sensing system 1600 may be provided to the Al software algorithms to increase accuracy of pressure and / or flow measurements, and to determine rheological properties in non-stationary flow conditions.

[0275] According to an embodiment, the pressure fluctuation generating device 1400 may comprise one or more piezo-electric actuators or one or more micro-heaters.

[0276] According to an embodiment, the fluctuations may comprise one or more pressure pulses.

[0277] According to an embodiment, the fluctuations may comprise periodic pressure fluctuations.

[0278] Other embodiments of the invention are directed to corresponding methods for measuring pressure. Such methods may be implemented by the operation of the apparatuses already described in the disclosure. Thus, embodiments of the invention provide a method for measuring pressure, the method comprising: providing a microfluidic chip comprising a measurement chamber and a fluid inlet fluidically coupled to the measurement chamber; supplying a second fluid to the fluid inlet so as to form a stable meniscus between a first fluid and the second fluid in the measurement chamber; detecting a position and a shape of the meniscus using a sensing system; and determining a pressure in the second fluid based on the position and shape of the meniscus detected using the sensing system.

[0279] According to an embodiment, the method for measuring pressure further comprising imaging the position and the shape of the meniscus formed in the measurement chamber using the sensing system to generate image data and evaluating the image data to determine the position and the shape of the meniscus.

[0280] According to an embodiment, the method for measuring pressure further comprising determining that the pressure in the second fluid has a first value if the meniscus has a first position and a first shape; determining that the pressure in the second fluid has a second value if the meniscus has a first position and a second shape different from the first shape; and determining that the pressure in the second fluid has a third value if the meniscus has a second position different from the first position.

[0281] According to an embodiment, the method for measuring pressure further comprising determining the pressure of the second fluid using allocation data allocating positions and shapes of the meniscus to known pressures of the second fluid.

[0282] According to an embodiment, the method for measuring pressure further comprising determining the allocation data using machine learning and / or artificial intelligence.

[0283] According to an embodiment, the method for measuring pressure further comprising superimposing time dependent pressure fluctuations to either one of the fluids so as to cause variations of the position and / or the shape of the meniscus in the measurement chamber; and detecting the variations of the position and / or the shape of the meniscus and determining the pressure in the second fluid, on which the pressure variations are superimposed, using the detected variations.

[0284] According to an embodiment, the method for measuring pressure, wherein the fluctuations comprise one or more pressure pulses. According to an embodiment, the method for measuring pressure, wherein the fluctuations comprise periodic pressure fluctuations.

[0285] According to an embodiment, the method for measuring pressure further comprising determining a rheological property of the second fluid using a time series of the detected variations of the position and / or the shape of the meniscus.

[0286] Thus, embodiment of the invention also provide another method, the method comprising: providing a microfluidic chip comprising a measurement chamber and a fluid inlet fluidically coupled to the measurement chamber; supplying a second fluid to the fluid inlet so as to form a stable meniscus between a first fluid and the second fluid in the measurement chamber; detecting a position and / or a shape of the meniscus using a sensing system; determining a pressure in the second fluid based on the position and / or shape of the meniscus using the sensing system; superimposing time dependent pressure fluctuations to the second fluid so as to cause variations of the position and / or the shape of the meniscus in the measurement chamber; and detecting the variations of the position and / or the shape of the meniscus and determining the pressure in the second fluid, on which the pressure fluctuations are superimposed, using the detected variations.

[0287] According to an embodiment, the method further comprising: determining a rheological property of the second fluid based using a time series of the detected variations of the position and / or the shape of the meniscus in the measurement chamber.

[0288] According to an embodiment, the method, wherein the fluctuations comprise one or more pressure pulses.

[0289] According to an embodiment, the method, wherein the fluctuations comprise periodic pressure fluctuations.

[0290] Thus, embodiments of the invention provide a method for measuring viscosity and hydraulic resistance, the method may comprise a step of supplying a second fluid having a flow rate into a flow sensor, in accordance to the aspect of the present inventive concept described in the present disclosure, such that the measurement channel of the flow sensor may be filled. The method further comprising a step of storing video data relating to the filling of the measurement channel of the flow sensor. The method further comprising a step of supplying the second fluid out of the flow sensor such that the measurement channel of the flow sensor may be emptied. The method further comprising a step of storing video data relating to the emptying of the measurement channel of the flow sensor. The method may even comprise a step of providing the flow sensor with an ambient environment comprising a first fluid.

[0291] The method for measuring the viscosity and the hydraulic resistance RLof the measurement channel may involve a determination of calibration constants, which may be required to use eq. (17) This determination may be provided by an observation of the measurement channel while it is filled for the first time with liquid. From a video sequence of the filling process, a time ti may be derived when the second fluid enters the measurement channel as well as a time t2when the second fluid has completely filled the measurement channel. Since the length L and cross section area A of the measurement channel may be known, the filling flow rates may be calculated like follows:

[0292] (18)

[0293] Shortly after filling the measurement channel completely, the flow rate may also be calculated based on the measured pressure difference Ap using equation (17). Assuming that in the short time between the two measurements the flow is not changing significantly, equation (17) and (18) have to yield the same result. Thus, combining the two equations and solving for RLyields the value for the fluidic resistance of the measurement channel:

[0294] Assuming laminar flow conditions and that the viscosity of the second fluid may not vary during the method, the viscosity may be calculated using the estimated values for Ap, <pfmand RLfrom the first filling observation and the Hagen-Poiseuille equation which is to be solved for viscloisty p. Thus, during the filling of the measurement channel of the flow sensor, the viscosity of the second fluid may be automatically detected, and the proper calibration curve for the second fluid may be chosen. Thus, using the described method rheological properties such as the viscosity of the fluid and the hydraulic resistance of the measurement channel of the flow sensor described by the present invention, may be measured.

[0295] Additionally, or alternatively, other mathematical descriptions may be used in the method for measuring the viscosity and the hydraulic resistance RL of the measurement channel It is understandable to the persons skilled in the art that numerical, or equivalently computational, methods may be used in the method. It is feasible that a combination of the above described equations and numerical / computational methods may be used.

[0296] An embodiment of the invention provides an apparatus for measuring pressure and flow in fluids consisting of a microfluidic chip operated at a Bond number smaller than Bo=0.5 and preferably even smaller than Bo=0.05 and a sensor that can detect the shape and position of a liquid meniscus inside the microfluidic chip, whereas the microfluidic chip features at least one measurement chamber with at least one inlet for the supply of fluid, wherein the Concus-Finn-Condition is not fulfilled anywhere in the measurement chamber for the fluid to be used inside the apparatus, and the Young-Laplace equation has exactly one solution inside the measurement chamber for the used fluid for any value of the pressure difference between the two sides of the liquid meniscus in the anticipated measurement range. Embodiments provide a method for measuring pressure using such an apparatus.

[0297] In embodiments, a specific geometry of the at least one measurement chamber is used.(e.g. using the hydraulic radius as quantity that is different anywhere in the measurement chamber).

[0298] In embodiments, readout by digital optical camera is permitted.

[0299] In embodiments, the evaluation of the sensor signal by Al software program is permitted Additionally, or alternatively, empirical calibration function or mathematical modelling based on Young-Laplace equation are used.

[0300] An embodiment of the invention provides a sensor system consisting of: sensor device to detect meniscus shape and / or position, and a microfluidic chip hosting at least one measurement chamber which is separable I modularly exchangeable and preferably does not make fluidic / mechanical contact to the sensor device. In embodiments, sensor device is sensitive to position and / or shape variation of the liquid meniscus inside the measurement chamber.

[0301] In embodiments , position and / or shape of meniscus inside the measurement chamber can be unambiguously correlated to a pressure difference between the two sides of the meniscus i.e., equivalently the Young-Laplace equation has exactly one solution for a stationary meniscus in equilibrium for each pressure value in the measurement chamber.

[0302] In embodiments, a meniscus needs to form at all in the measurement chamber under normal operation conditions i.e., Concus-Finn-Condition is not be attained anywhere in the measurement chamber.

[0303] In embodiments, Bond number Bo has to be small in order that hydrostatic effects due to gravity can be neglected.

[0304] In embodiments, measurement chambers with changing hydraulic resistance along the direction of filling when input pressure is increase are permitted.

[0305] In embodiments, measurement chambers having tapered walls are permitted.

[0306] In embodiments, measurement chambers with no outlet are permitted.

[0307] In embodiments, hydrophilic measurement chambers are permitted.

[0308] In embodiments, hydrophobic measurement chambers are permitted.

[0309] In embodiments, measurement chambers with theta ~ 90° are permitted.

[0310] In embodiments, combination of measurement chambers with different designs and working principles either connected in series or connected in parallel.

[0311] In embodiments, several measurement chambers integrated into a microfluidic chip ,in addition to the channels that are present in embodiments of the invention, to enable integrated pressure / flow measurement without any external interfaces are permitted. In embodiments, sensor system featuring an actuator to impose pressure perturbations onto the meniscus and / or the fluid flow to generate non-stationary flow conditions is permitted.

[0312] In embodiments, use of either empirical calibration relationship, mathematical model based on Young-Laplace-equation, numerical model based on Computation fluid dynamics (CFD) to determine pressure from sensor signal, or any of these methods in combination are permitted.

[0313] In embodiments, use of machine learning respectively Al software to determine pressure from a time series of sensor signals or from one single sensor signal is permitted.

[0314] In embodiments, combination of Al software with empiric calibration relationship and / or mathematical model based on Young-Laplace-equation and / or numerical model based on Computation fluid dynamics (CFD) is permitted.

[0315] In embodiments, using Deep Learning, supervised learning, neuronal networks as methods alone or in combination to establish the Al software program is permitted.

[0316] In embodiments, calibration of the sensor during filling by measuring the time the meniscus needs to move from the inlet from the first measurement chamber to the inlet of the second measurement chamber to estimate a filling flow rate and from this filling flow rate and the pressure difference the value of the resistance R of the measurement channel and / or the viscosity of the second fluid is permitted.

[0317] In embodiments, determining viscosity and other rheological parameters of the liquid by using Al software program to evaluate sensor readings under non-stationary flow conditions is permitted.

[0318] Using embodiments of the apparatus presented before, a pressure measurement is carried out by:

[0319] • filling the measurement chamber with a liquid. A meniscus is spontaneously established inside the measurement chamber due to the small Bo number if the measurement chamber is designed according to the aspects, or features, described earlier; • establishing a calibration relationship P[S] for the specific liquid that relates pressure at the inlet port to the sensor signal by either empirical measurements, a mathematical model (e.g. based on the Young-Laplace Equation) or by software algorithms. This calibration is not renewed each time the sensor is used or the microfluidic chips is replaced, but is just established once for a given liquid class (i.e. liquids with similar surface tension and rheological properties). The calibration can then be reused for measurements of this type of liquids in a given type of measurement chamber;

[0320] • fluidically connecting the measurement chamber inlet port to the pressure source to be measured; and

[0321] • reading the sensor signal S (or a time course series of sensor signals {S(ti), S(t2), ... S(tn)} ) and relating it (them) to the pressure value P through the previously established calibration relationship P[S] or a suitable software algorithm.

[0322] Although some aspects have been described in the context of an apparatus, it is obvious that these aspects also represent a description of the corresponding method, such that a block or device of an apparatus also corresponds to a respective method step or a feature of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or detail or feature of a corresponding apparatus.

[0323] Some or all of the methods steps may be performed by a hardware apparatus (or using a hardware apparatus), such as a microprocessor, a programmable computer or an electronic circuit. In some embodiments, some or several of the most important method steps may be performed by such an apparatus.

[0324] In the foregoing detailed description, it can be seen that various features are grouped together in examples for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed examples require more features than are expressly recited in each claim. Rather, as the following claims reflect, subject matter may lie in less than all features of a single disclosed example. Thus, the following claims are hereby incorporated into the detailed description, where each claim may stand on its own as a separate example. While each claim may stand on its own as a separate example, it is to be noted that, although a dependent claim may refer in the claims to a specific combination with one or more other claims, other examples may also include a combination of the dependent claim with the subject matter of each other dependent claim or a combination of each feature with other dependent or independent claims. Such combinations are proposed herein unless it is stated that a specific combination is not intended. Furthermore, it is intended to include also features of a claim to any other independent claim even if this claim is not directly made dependent to the independent claim.

[0325] While this invention has been described in terms of several embodiments, there are alterations, permutations, and equivalents which fall within the scope of this invention. It should also be noted that there are many alternative ways of implementing the methods and compositions of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations and equivalents as fall within the scope of the present invention as defined by the appended claims.

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Claims

CLAIMS1. A pressure measuring apparatus (10) comprising: a microfluidic chip (20) comprising at least one capillary measurement chamber (30) and a fluid inlet (40) fluidically coupled to the measurement chamber (30), wherein the measurement chamber (30) and the fluid inlet (40) are configured to permit a stable meniscus (50) between a first fluid (60) and a second fluid (70) to be formed in the measurement chamber (30) when supplying the second fluid (70) via the fluid inlet (40) to the measurement chamber (30); and a sensing system (90) configured to detect a position (54) and a shape (56) of the meniscus (50) and to determine a pressure in the second fluid (70) based on the position (54) and the shape (56) of the meniscus.

2. The pressure measuring apparatus (10) of claim 1 , wherein the sensing system (90) is configured to determine that the pressure in the second fluid (70) has a first value if the meniscus (50) has a first position (54-1) and a first shape (56-1), to determine that the pressure in the second fluid (70) has a second value if the meniscus (50) has a first position (54-1) and a second shape (56-2) different from the first shape (56-1), and to determine that the pressure in the second fluid (70) has a third value if the meniscus (50) has a second position (54-2) different from the first position (54- 1).

3. The pressure measuring apparatus (10) of claim 1 or 2, wherein the sensing system (90) is configured to store allocation data allocating positions (54) and shapes (56) of the meniscus (50) to known pressures of the second fluid (70) and to determine the pressure of the second fluid (70) using the allocation data.

4. The pressure measuring apparatus (10) of claim 3, wherein the sensing system (90) is configured to determine the allocation data using machine learning and / or artificial intelligence.

5. The pressure measuring apparatus (10) of any of the previous claims 1 to 4, wherein the sensing system (90) comprises an optical system configured to generate image data of the position (54) and the shape (56) of the meniscus (30) formed in themeasurement chamber (30) and to evaluate the image data to determine the position (54) and the shape (56) of the meniscus (50).

6. The pressure measuring apparatus (10) of any of the previous claims 1 to 5, wherein the measurement chamber (30) is in fluidic connection to the ambient environment by a ventilation opening (80), wherein the ventilation opening (80) is arranged spaced apart from the fluid inlet (40) to permit the stable meniscus (50) to be formed in the measurement chamber (30) between the fluid inlet (40) and the ventilation opening (80).

7. The pressure measuring apparatus (10) of any of claims 1 to 6, wherein a hydraulic radius of the capillary measurement chamber (30) varies along a longitudinal extension thereof.

8. The pressure measuring apparatus (10) of claim 7, wherein the capillary measurement chamber (30) comprises tapered side walls (36) to vary the hydraulic radius of the capillary measurement chamber (30) along the longitudinal extension thereof.

9. The pressure measuring apparatus (10) of any of claim 7 or 8, wherein the hydraulic diameter of the capillary measurement chamber (30) at least partially decreases with increasing distance from the fluid inlet (40).

10. The pressure measuring apparatus (10) of claim 9, wherein the measurement chamber (30) is made of a hydrophobic material.

11. The pressure measuring apparatus (10) of claim 7 or 8, wherein the hydraulic diameter of the capillary measurement chamber (30) increases at least partially with increasing distance from the fluid inlet (40).

12. The pressure measuring apparatus (10) of any of claim 11 , wherein the capillary measurement chamber (36) comprises a convex inner wall that forms a super- linearly increasing hydraulic diameter.

13. The pressure measuring apparatus (10) of claim 11 or 12, wherein the measurement chamber (30) is made of a hydrophilic material.

14. The pressure measuring apparatus (10) of one of claims 1 to 13, wherein the capillary measurement chamber (30) further comprises a pinning structure (38) configured to permit the position (54) of the meniscus (50) in the measurement chamber (50) to be stationary over a range of pressures and to permit the shape (56) of the meniscus (50) in the measurement chamber (30) to be variable over the range of pressures.

15. The pressure measuring apparatus (10) according to claim 14, wherein the pinning structure (38) comprises sharp edges (39) of the cross-sectional area of the measurement chamber (30), different surface roughness of the inner surface of the measurement chamber (30) and / or chemical or electrical modifications of the inner surface of the measurement chamber (30).

16. The pressure measuring apparatus (10) of one of claims 1 to 15, wherein the capillary measurement chamber (30) is one of a plurality of capillary measurement chambers (30-1 , 30-2, ...) comprising fluidically coupled fluid inlets (40), each configured to permit a stable meniscus (50) between a first fluid (60) and a second fluid (70) to be formed in the measurement chamber (30-#), wherein pressure ranges of the plurality of capillary measurement chambers (30-1 , 30-2, ... ), in which a stable meniscus (50) can be formed, are different in the plurality of capillary measurement chambers (30-1 , 30-2, ...).

17. The pressure measuring apparatus (10) of one of claims 1 to 16, wherein the capillary measurement chamber (30) is a first capillary measurement chamber (30-1), the pressure measuring apparatus (10) further comprising a second capillary measurement chamber (30-2) configured to permit a stable meniscus (50) between a first fluid (60) and a second fluid (70) to be formed in the measurement chamber (30-2), the first pressure measurement chamber (30-1) is in fluidic connection to the ambient environment by a ventilation opening (80), wherein the ventilation opening (80) is arranged spaced apart from the fluid inlet (40) to permit the stable meniscus (50) to be formed in the measurement chamber (30-1) between the fluid inlet (40) and the ventilation opening (80), and wherein the hydraulic diameter of the firstcapillary measurement chamber (30-1) decreases with increasing distance from the fluid inlet (40), and wherein the second pressure measurement chamber (30-2) is a non-vented measurement chamber.

18. The pressure measuring apparatus (10) according to any of the claims 1 to 17, further comprising a pressure fluctuation generating device configured to superimpose time dependent pressure fluctuations to at least one of the fluids (60, 70) so as to cause variations of the position (54) and / or the shape (56) of the meniscus (50) in the measurement chamber (30); and wherein the sensing system (90) is configured to detect the variations of the position (54) and / or the shape (56) of the meniscus (50) and to determine the pressure in the second fluid (70), using the detected variations.

19. The pressure measuring apparatus (10) of claim 18, wherein the fluctuations comprise one or more pressure pulses.

20. The pressure measuring apparatus (10) of claim 18 or 19, wherein the fluctuations comprise periodic pressure fluctuations.

21. The pressure measuring apparatus (10) of one of claims 18 to 20, wherein the sensing system (90) is configured to determine a rheological property of the second fluid (70) using a time series of the detected variations of the position (54) and / or the shape (56) of the meniscus (50).

22. A flow sensor (100) comprising: a sensor fluid inlet (110), a sensor fluid outlet (120) and a fluid channel (150) between the sensor fluid inlet (110) and the sensor fluid outlet (120); a first pressure measuring apparatus (200) according to one of claims 1 to 21 , wherein the fluid inlet (210) of the first pressure measuring apparatus (200) is fluidically coupled to the fluid channel (150) at a first position (104);a second pressure measuring apparatus (400) according to one of clams 1 to 21 , wherein the fluid inlet (410) of the second pressure measuring apparatus (400) is fluidically coupled to the fluid channel (150) at a second position (108) spaced apart from the first position (104), wherein the fluid channel (150) forms a measurement channel (160) between the first position (104) and the second position (108); and a flow rate determiner configured to determine a flow rate through the fluid channel (150) using the pressures determined by the sensing systems of the first and second pressure measuring apparatuses (200, 400).

23. The flow sensor (100) of claim 22, comprising an additional connection channel (700) fluidically connecting one of the at least one measurement chamber of the first pressure measuring apparatus (200) to one of the at least one measurement chamber of the second pressure measuring apparatus (400).

24. A method for measuring pressure, the method comprising: providing a microfluidic chip (20) comprising a measurement chamber (30) and a fluid inlet (40) fluidically coupled to the measurement chamber (30); supplying a second fluid (70) to the fluid inlet (40) so as to form a stable meniscus (50) between a first fluid (60) and the second fluid (70) in the measurement chamber (30); detecting a position (54) and a shape (56) of the meniscus (50) using a sensing system (90); and determining a pressure in the second fluid (70) based on the position (54) and shape (56) of the meniscus (50) detected using the sensing system (90).

25. The method of claim 24, further comprising: imaging the position (54) and the shape (56) of the meniscus (50) formed in the measurement chamber (30) using the sensing system (90) to generate image data and evaluating the image data to determine the position (54) and the shape (56) of the meniscus (50).

26. The method of claim 24 or 25, comprising: determining that the pressure in the second fluid (70) has a first value if the meniscus (50) has a first position (54-1) and a first shape (56-1); determining that the pressure in the second fluid (70) has a second value if the meniscus (50) has a first position (54-1) and a second shape (56-2) different from the first shape (56-1); and determining that the pressure in the second fluid (70) has a third value if the meniscus (50) has a second position (54-2) different from the first position (54-1).

27. The method of one of claims 24 to 26, comprising determining the pressure of the second fluid (70) using allocation data allocating positions (54) and shapes (56) of the meniscus (50) to known pressures of the second fluid (70).

28. The method of claim 27, comprising determining the allocation data using machine learning and / or artificial intelligence29. The method of one of claims 24 to 28, comprising: superimposing time dependent pressure fluctuations to at least one of the fluids (60, 70) so as to cause variations of the position (54) and / or the shape (56) of the meniscus (50) in the measurement chamber (30); and detecting the variations of the position (54) and / or the shape (56) of the meniscus (50) and determining the pressure in the second fluid (70), on which the pressure variations are superimposed, using the detected variations.

30. The method of claim 29, wherein the fluctuations comprise one or more pressure pulses.

31. The method of claim 29 or 30, wherein the fluctuations comprise periodic pressure fluctuations.

32. The method of one of claims 29 to 31 , comprising: determining a rheological property of the second fluid (70) using a time series of the detected variations of the position (54) and / or the shape (56) of the meniscus (50).

33. A pressure measuring apparatus (1000) comprising: a microfluidic chip (1200) comprising at least one measurement chamber and a fluid inlet fluidically coupled to the measurement chamber, wherein the measurement chamber and the fluid inlet are configured to permit a stable meniscus between a first fluid and a second fluid to be formed in the measurement chamber when supplying the second fluid via the fluid inlet to the measurement chamber; a pressure fluctuation generating device (1400) configured to superimpose time dependent pressure fluctuations to at least one of the fluids so as to cause variations of the position and / or the shape of the meniscus in the measurement chamber; and a sensing system (1600) configured to detect a position and / or a shape of the meniscus and to determine a pressure in the second fluid based on the position and the shape of the meniscus, wherein the sensing system (1600) is configured to detect the variations of the position and / or the shape of the meniscus and to determine the pressure in the second fluid, using the detected variations.

34. The pressure measuring apparatus (1000) of claim 33, wherein the sensing system (1600) is configured to determine a rheological property of the second fluid using a time series of the detected variations of the position and / or shape of the meniscus in the measurement chamber.

35. The pressure measuring apparatus (1000) of claim 33 or 34, wherein the pressure fluctuation generating device (1400) comprises one or more piezo-electric actuators or one or more micro- heaters.

36. The pressure measuring apparatus (1000) of one of claims 33 to 35, wherein the fluctuations comprise one or more pressure pulses.

37. The pressure measuring apparatus (1000) of one of claims 33 to 36, wherein the fluctuations comprise periodic pressure fluctuations.

38. A method comprising: providing a microfluidic chip (1200) comprising a measurement chamber and a fluid inlet fluidically coupled to the measurement chamber; supplying a second fluid to the fluid inlet so as to form a stable meniscus between a first fluid and the second fluid in the measurement chamber; detecting a position and / or a shape of the meniscus using a sensing system (1600); determining a pressure in the second fluid based on the position and / or shape of the meniscus using the sensing system (1600); superimposing time dependent pressure fluctuations to the second fluid so as to cause variations of the position and / or the shape of the meniscus in the measurement chamber; and detecting the variations of the position and / or the shape of the meniscus and determining the pressure in the second fluid, on which the pressure fluctuations are superimposed, using the detected variations.

39. The method of claim 38, comprising determining a rheological property of the second fluid based using a time series of the detected variations of the position and / or the shape of the meniscus in the measurement chamber.

40. The method of claim 38 or 39, wherein the fluctuations comprise one or more pressure pulses.

41. The method of one of claims 38 to 40, wherein the fluctuations comprise periodic pressure fluctuations.

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