Method and device for determining a pressure of a liquid flowing in a channel

Abstract

The invention relates to a measurement system (1) suitable for determining a pressure Pheq of a liquid of interest having a compressibility km flowing in a channel with a radius rint, which are chosen such that the product of km x rint is less than or equal to 12.5x10-11 mm / Pa, and comprising: a flow actuator (20) for causing the liquid of interest to flow in the channel (10) at a Mach number less than or equal to 0.3; a thermal measuring device (30) for measuring a temperature Theq of the liquid of interest flowing in the channel (10); and a processing unit (40) suitable for determining the pressure Pheq from the measured temperature Theq and a predetermined calibration function f.

Description

METHOD AND SYSTEM FOR DETERMINING THE PRESSURE OF A FLOWING LIQUID IN A CHANNEL TECHNICAL FIELD

[0001] The field of the invention is that of determining the pressure of a liquid flowing in a channel, and in particular in a millifluidic or even microfluidic channel. PREVIOUS STATE OF THE ART

[0002] Microfluidics concerns the flow of liquids in channels with submillimeter transverse dimensions, and its applications usually cover the physical, chemical, life sciences, biology, medical, environmental, process engineering and engineering fields.

[0003] Depending on the application, it can be important to know the pressure of the liquid flowing in a microfluidic channel. This is typically achieved using a pressure sensor, which may consist of a deformable membrane or diaphragm separating two spaces: one where the liquid flows, and the other at a reference pressure. The pressure difference between the two spaces causes the membrane to deform, and measuring the intensity of this deformation (or the vibration frequency) allows the pressure of the flowing liquid to be deduced. However, due to the membrane's dimensions, the pressure sensor is usually positioned upstream or downstream of the channel, in an area of ​​the fluid circuit where the cross-sectional dimensions are sufficiently large. Therefore, the pressure is not measured within the microfluidic channel itself, which can lead to inaccurate readings.In addition, the pressure sensor may be subject to measurement drift, particularly if it undergoes progressive degradation or fouling of the membrane, especially during long periods of use. DESCRIPTION OF THE INVENTION

[0004] The invention aims to remedy, at least in part, the drawbacks of the prior art, and more particularly to provide a measurement system and method for determining the pressure of a liquid flowing in a channel. Such a measurement system offers improved reliability because the pressure is determined from a thermal measurement and a predetermined calibration function, rather than indirectly from values ​​from a remote pressure sensor whose performance is also likely to degrade.

[0005] To this end, an object of the invention is a measuring system adapted to determine at least one pressure Pheq of a liquid of interest with compressibility k m in flow in a channel of internal radius r^t, the liquid of interest and the channel being chosen such that the product k m xr in t is less than or equal to 12.5xl0 -11 mm / Pa. It comprises: the channel; a flow actuator, adapted to flow the liquid of interest into the channel, so that the liquid of interest has a ratio V m / c less than or equal to 0.3, where V mis a maximum velocity of the fluid of interest in the channel, and where c is the speed of sound in the fluid of interest; a thermal measuring device adapted to measure at least one temperature Theq of the fluid of interest flowing in the channel; and a processing unit adapted to determine the pressure Pheq from the measured temperature Theq and a predetermined calibration function f, expressing the evolution of a pressure difference AP between the pressure Pheq and a reference pressure P eq predefined temperature of the liquid of interest at rest in the channel, as a function of a temperature difference AT between the measured temperature Theq and a reference temperature T eq predefined of the fluid of interest at rest in the channel.

[0006] The temperature difference AT between the measured value Theq and the value T eq The predefined value can be determined by the processing unit. The T value eqA predefined value can be stored in the processing unit's memory. Alternatively, this temperature difference AT can be determined by the thermal measuring device itself, which would then incorporate the T value. eq predefined in a memory and would provide the AT value directly to the processing unit.

[0007] The calibration function f expresses a variation, that is, a change, in the pressure difference AP as a function of the temperature difference AT: AP = f(AT). It is therefore clear that the terms 'variation' and 'change' have the same meaning. This variation or change can be positive or negative. Furthermore, the calibration function f can be a linear function defined by the relation: AP = pxAT, where P is a predetermined constant, positive or negative (and for example, positive), with AP = Ph eq -Peq and AT=Theq-T eq .

[0008] The canal may have a length less than or equal to 5cm.

[0009] It can be straight along its entire length and have a constant inner radius r,nt.

[0010] The flow actuator may include conduits connecting the channel to a pump and a reservoir of the liquid of interest, the conduits having an inside radius greater than n n t.

[0011] The thermal measurement device can be adapted to detect infrared radiation emitted by the liquid of interest and transmitted through a peripheral wall of the channel and to deduce the temperature Theq, the peripheral wall being made of a material transparent to infrared radiation.

[0012] The thermal measurement device may include at least one contact thermal sensor, positioned in contact with a peripheral wall of the channel.

[0013] The thermal contact sensor can be placed in contact with an outer face of the peripheral wall, the latter being made of a thermally conductive material so that the temperature of the outer face is equal to the temperature Theq of the liquid.

[0014] The channel may have an internal diameter of between 1 Opm and 1 mm.

[0015] The thermal measurement device can be adapted to acquire a thermal image of the liquid of interest, and the processing unit can be adapted to determine a pressure image from the acquired thermal image and the calibration function f.

[0016] Another object of the invention is a method for determining the pressure Pheq of a fluid of interest moving in the channel of the measuring system according to any one of the preceding characteristics, the method comprising a measurement phase including the following steps: o selection of a fluid of interest with compressibility k m and the inner radius channel n n t, so that a product k m xr in t is less than or equal to 12.5xio -11 mm / Pa; o flow of the liquid of interest into the channel at a flow rate predefined by the flow actuator, so that it has a ratio V m / c less than or equal to 0.3, where V mis a maximum velocity of the liquid in the channel and where c is the speed of sound in the liquid of interest; o measurement of a temperature Theq of the liquid of interest flowing in the channel by the thermal measuring device, and determination of a non-zero temperature difference AT between the measured temperature Theq and a reference temperature T eq predefined pressure of the fluid of interest at rest; determination of the pressure Pheq of the fluid of interest by the processing unit, from the determined temperature difference AT, and a predetermined calibration function f, expressing an evolution of a pressure difference AP between the pressure Pheq of the fluid of interest flowing in the channel and a reference pressure P eq predefined of the liquid of interest at rest, as a function of the temperature difference AT.

[0017] The process may include a calibration phase, carried out before the measurement phase, comprising the following steps: o selection of a liquid with compressibility k c and an internal radius channel r,nt of a calibration system, so that a product k c xri n t is less than or equal to 12.5xl0 -11 mm / Pa; o The liquid is flowed into the channel by a flow actuator of the calibration system at a predefined flow rate, so that it has a ratio V m / c less than or equal to 0.3, where V m is a maximum velocity of the liquid in the channel and where c is the speed of sound in the liquid; o measurement of a temperature Theq of the liquid flowing in the channel by a thermal measurement device of the calibration system, and determination of a non-zero temperature difference AT between the measured temperature Theq and a reference temperature T eqpredefined pressure of the liquid at rest; measurement of a pressure Pheq of the liquid flowing in the channel by a pressure sensor of the calibration system, and determination of a non-zero pressure difference AP between the measured pressure Pheq and a reference pressure P eq predefined of the liquid at rest; o reiteration of the steps of measuring the temperature Theq and the pressure Pheq for different flow rates of the liquid in the channel; o determination of the calibration function f, by a processing unit of the calibration system from the different values ​​of the temperature deviation AT and the corresponding values ​​of the pressure deviation AP.

[0018] The liquid of interest can be chosen from water, an alcohol, and glycerol.

[0019] The liquid of interest can be the same as the liquid used during the calibration phase.

[0020] The flow of the liquid of interest can be achieved by suction, so that the measured temperature Theq is then lower than the reference temperature T eq and corresponds to a cooling of the liquid of interest; or it can be carried out by pumping, so that the measured temperature Theq is then higher than the reference temperature T eq and corresponds to a warming of the liquid of interest.

[0021] The channel can be made of a thermally conductive material, and in thermal contact with an external device, so that the cooling or heating of the liquid of interest results respectively in a cooling or heating of the external device. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Other aspects, objectives, advantages, and features of the invention will become clearer upon reading the following detailed description of preferred embodiments thereof, given by way of non-limiting example, and made with reference to the accompanying drawings in which: Figure IA is a schematic and partial view of a measurement system according to one embodiment, adapted to determine the pressure of a liquid flowing in a channel; Figure IB is a schematic and partial longitudinal section view of the channel of the measurement system; Figure IC is a schematic and partial cross-sectional view of the channel and the thermal measurement device of the measurement system; Figure 2A illustrates an example of a calibration function f expressing an evolution of a pressure deviation AP as a function of a temperature deviation AT; Figure 2B is a schematic and partial view of a calibration system according to one embodiment, adapted to determine the calibration function f; Figure 3 is a flowchart of a method for determining the pressure of the liquid flowing in the channel, including here a preliminary phase of determining the calibration function f. DETAILED DESCRIPTION OF SPECIFIC METHODS OF IMPLEMENTATION

[0023] In the figures and throughout the description, the same reference numerals represent identical or similar elements. Furthermore, the various elements are not drawn to scale to ensure clarity. Moreover, the different embodiments and variants are not mutually exclusive and may be combined. Unless otherwise stated, the terms "approximately," "around," and "in the order of" mean within 10%, and preferably within 5%. Furthermore, the terms "between ... and ..." and equivalents mean inclusive of the bounds, unless otherwise specified.

[0024] The invention relates to determining the pressure Pheq of a liquid flowing in a channel, not from a dedicated pressure sensor, but from a measurement of the liquid's temperature (more precisely, a temperature difference AT) and by means of a predetermined calibration function f. The liquid whose pressure is to be determined is hereafter referred to as the 'liquid of interest', to distinguish it from the liquid used to establish the calibration function beforehand. The liquid of interest, like the calibration liquid, is a liquid with density ρ, dynamic viscosity ρ, and compressibility k.

[0025] In the usual theoretical framework of fluid mechanics, a liquid is considered incompressible when its volume, and consequently the density of each liquid particle, remains constant during its motion. Therefore, the density ρ is constant throughout the flow and at every instant. This is particularly true when the corresponding Mach number is low, usually less than 0.3, or even less than 0.1. The Mach number is defined by the relation: Ma = V m / c where V m is the maximum velocity of the flowing liquid and c is the speed of sound in the liquid in question.

[0026] Thus, in an incompressible liquid, since the velocity field is by definition zero-divergence, the effects of expansion and compression of the liquid are assumed to be nonexistent. Therefore, the equations of the classical model of fluid mechanics for an incompressible liquid (continuity, dynamics, and energy equations) lead to decoupling the dynamic problem (velocity, pressure) from the thermal problem. Thus, in incompressible flow, it is usually considered that the liquid pressure has no thermodynamic influence, and that the dynamic and thermal problems can be solved independently of each other.

[0027] However, the inventors observed that this classical theoretical framework is not always valid for moving liquids when a condition on the product of the liquid's compressibility k and a characteristic transverse dimension r,nt of the channel is met (this condition is explained later). This is particularly true for channels with millimeter, micrometer, or even nanometer dimensions. They thus demonstrated that liquids usually considered incompressible in flow exhibit a certain compressibility, that is, a property related to elasticity (called shear elasticity), the physical effect of which is greater the smaller the characteristic dimension r,nt of the channel.

[0028] Also, to move such a liquid in a channel while respecting the condition on the kxr product intThis amounts to exploiting the shear elasticity of the liquid, and thus pushing it out of thermodynamic equilibrium through a thermoelastic effect (an effect that could also be called "elasto-caloric"). Indeed, a thermoelastic coupling is then present, such that the flow of the liquid results in heating (compressive mechanical stress) or cooling (tensile mechanical stress). A presentation of thermoelasticity related to mesoscopic shear elasticity can be found in the article by Kume et al. entitled "Strain-induced violation of temperature uniformity in mesoscale liquids," Sci Rep, 10, 13340 (2020).

[0029] The inventors developed a measurement system and a method for determining liquid pressure, taking advantage of this thermoelastic effect applied to flow in channels whose characteristic dimension r,nt satisfies the condition on the product kxrint . Such a measurement system makes it possible to eliminate the disadvantages of the prior art pressure sensors mentioned previously, insofar as the pressure of the flowing liquid is determined in situ in a measurement zone of the channel, from a thermal measurement (therefore by a measurement which does not disturb the flow of the liquid), and a predetermined calibration function.

[0030] It should also be noted that this variation in the temperature of the liquid of interest due to a thermoelastic effect differs from heating linked to a viscous friction effect (such an effect is not capable of causing the liquid to cool). Indeed, heating by viscous dissipation is conventionally expected when the liquid flows at a speed close to that of sound (Ma = 1), which does not correspond to the operational framework of the invention.

[0031] Figure IA is a schematic and partial view of a measuring system 1 according to an embodiment, adapted to determine a pressure of a liquid of interest flowing in a channel 10. Figures IB and IC are schematic and partial views, in longitudinal and transverse sections, of the channel 10 of the measuring system 1 of Fig. IA.

[0032] In general, the measuring system 1 includes the channel 10, a device for setting in motion 20 the liquid of interest in the channel 10 (called a flow actuator), a thermal measuring device 30 adapted to measure a temperature of the liquid in the channel 10, and a processing unit 40 adapted to determine the pressure of the liquid in the channel 10 from the measured temperature (and more precisely from a temperature deviation AT) and the predetermined calibration function f.

[0033] The channel 10 is a flow conduit formed by a peripheral wall 11 having an inner face 12, which delimits the fluid passage section, and an opposing outer face 13. The channel 10 extends longitudinally between a first end 10.1 and a second end 10.2, over a length L. The cross-sectional fluid flow of the channel 10 can be circular (tube) or oval, or polygonal, for example, square, octagonal, etc. The channel 10 preferably has an aspect ratio of 1, the aspect ratio being defined by two orthogonal transverse internal dimensions of the channel 10. A transverse internal dimension dint of the channel 10, called the internal diameter or equivalent internal diameter, is defined as the diameter of a disk having the same area as the fluid flow section of the channel 10. The internal radius r,nt is equal to half the internal diameter - In the following description, for illustration purposes, channel 10 is a cylindrical tube with a circular cross-section.

[0034] The inner radius r,nt is chosen according to the value of the compressibility k m of the liquid such that the following condition is satisfied: k m xr in t < 12.5xl0 -11 mm / Pa. When this condition is met, the inventors observed that the liquid flowing in channel 10 exhibits a thermoelastic effect which leads to a variation in the temperature Theq of the liquid relative to the temperature T eq of the liquid at rest. Also, when the compressibility k m the liquid is on the order of 10 -9 at 10 11 Pa 1(Here in the case of a liquid), the inner radius r,nt of channel 10 can be on the order of a few microns, or even tens or hundreds of microns, or even on the order of a millimeter or tens of millimeters. Thus, in the context of a microfluidic or millifluidic flow, the inner diameter dint can be between 1pm and 10 mm, or even between 10pm and 1 mm.

[0035] Channel 10 can extend in a straight line along its entire length, or even in a curved direction. It can also be straight or curved within the thermal measurement zone. Its diameter d, n t can be constant over its entire length, or it can vary. The length L can be less than or equal to 5cm if it is desired to limit or avoid the presence of thermal instabilities along the longitudinal axis of the channel 10.

[0036] The peripheral wall 11 of the channel 10 can be made of a material transparent to infrared light, for example, in the LWIR (Long Wavelength Infrared) range, if the thermal measuring device 30 relies on infrared detection. Alternatively, if the thermal measuring device 30 includes one or more thermistors in contact with the outer face 13 of the peripheral wall 11, the latter is made of a material with sufficient thermal conductivity so that the outer face 13 reaches a temperature equal to that of the liquid. Thus, the material of the peripheral wall 11 (and therefore its optical and thermal properties) depends on the type of thermal measuring device 30 used, as described in detail below.

[0037] The fluid of interest is a material that can flow through the channel. It can be, for example, a viscous liquid, Newtonian or non-Newtonian, such as water, glycerol, an alcohol, a molten polymer, physiological or organic fluids (blood, lymph, serous fluid, etc.), colloidal solutions, among others. It exhibits a dynamic viscosity p m , with a density p m and of a compressibility k m The compressibility k m may be equal to a few units or a few hundred of 10 11 Pa 1 For example, k m is equal to 3.7xio -11 Pa 1 for mercury, at 45.8xl0 -11 Pa 1 for water, and to HOxlO 11 Pa 1 for ethanol.

[0038] As previously stated, the liquid of interest has compressibility k m and the channel 10 of inner radius r,nt are chosen such that the following condition is satisfied: k m xrin t < 12.5xl0 -11 mm / Pa. When this condition is met, the liquid flowing in channel 10 exhibits a homogeneous thermoelastic effect which leads to a variation in the temperature Theq of the liquid relative to the temperature T eq of the liquid at rest.

[0039] The measuring system 1 includes a flow initiation device 20, also called a flow actuator, adapted to ensure the flow of the liquid of interest in the channel 10 at a predefined flow rate D, which may be constant or variable. The flow can thus be continuous in a direction or time-dependent, and can exhibit a flow rate that may vary or remain constant.

[0040] The flow actuator 20 thus comprises at least one pump 21 (i.e. a device adapted to set the liquid in motion by discharge or suction), at least one reservoir 22 of the liquid of interest, and connecting conduits 23 which ensure the fluidic connection of the channel 10 to the pump 21 and to the reservoir 22. The pump(s) 21 are connected directly to the conduits 23, and are not located in the channel 10 so as to avoid disturbing the flow of the liquid in the channel 10 and thus to avoid degrading the quality of the measurement of the temperature of the liquid.

[0041] In this example, the measuring system 1 comprises a single pump 21, positioned between the reservoir 22 and the first end 10.1 of the channel 10. This could be a micropump, such as a peristaltic micropump, or any equivalent device (e.g., a syringe pump). The pump 21 is adapted to ensure the flow of liquid into the channel 10 at a predefined flow rate D, which may or may not be constant.

[0042] A flow meter 24 is preferably connected to channel 10 and is located here between the pump 21 and the first end 10.1 of channel 10. From the value measured by the flow meter 24, the flow rate D of the liquid in channel 10 can be deduced. Preferably, the pump 21 is configured so that the flow rate of the liquid in channel 10 is less than or equal to a maximum value D m predefined if one wishes to avoid the presence of thermal instabilities along the longitudinal axis of channel 10. The maximum flow rate D mdepends in particular on the nature of the liquid, and is 416mm 3 approximately / s in the case of water, and 2.5mm 3 / s for an alcohol.

[0043] The liquid reservoir 22 is connected here to the two ends of the channel 10. The liquid there has a predefined pressure, which in this case can be atmospheric pressure P atm This pressure also corresponds to the reference pressure P eq of the liquid when it is at rest in the canal 10.

[0044] The connecting conduits 23 therefore ensure the fluid connection between the reservoir 22, the pump 21 and the channel 10. They have an internal diameter which can be greater than the internal diameter of the channel 10, for example by a ratio of 2, 5, 10 or even more.

[0045] Other configurations are of course possible. For example, a second pump can be located between reservoir 22 and the second end 10.2. Furthermore, several reservoirs can be used. The reservoir(s) can also contain the liquid of interest under positive pressure, in which case the pump(s) may not be necessary, and a valve is provided to allow or block the flow of the liquid.

[0046] Note that the arrangement of the pump 21 with respect to the channel 10 and the direction of the imposed flow define the type of mechanical stress, in compression or in tension, undergone by the liquid in the channel 10, and therefore the sign of the variation in temperature AT (heating or cooling).

[0047] Thus, in this example where the pump 21 is located between the reservoir 22 and the first end 10.1 of the channel 10, a flow direction from the first end 10.1 to the second end 10.2 results in the liquid in the channel 10 undergoing compressive mechanical stress, leading to heating through thermoelasticity. The liquid then exhibits a temperature difference AT = Theq - T eq of positive sign and a pressure difference AP = Pheq - Peq, also of positive sign. Here we denote T eq and P eq the temperature and pressure of the liquid at rest in channel 10 (“eq” corresponds to “in thermodynamic equilibrium”), and Theq and Pheq the temperature and pressure of the liquid flowing in channel 10 (“heq” corresponds to “out of thermodynamic equilibrium”).

[0048] Conversely, if the flow direction imposed by pump 21 is from the second end 10.2 to the first end 10.1, the liquid flowing in channel 10 is subjected to tensile mechanical stress, resulting in cooling by thermoelastic effect. The liquid then exhibits a negative temperature difference AT and a negative pressure difference AP.

[0049] Finally, it should be noted that the thermoelastic effect leads to the temperature Theq and pressure Pheq of the liquid flowing in channel 10 being essentially constant along the longitudinal axis of channel 10 (in the case where there is no flow instability), while the temperature in the conduits 23 can be essentially equal to the reference temperature (ambient temperature), and that the pressure difference between a high pressure imposed by the pump 21 and the ambient pressure of the reservoir 22 induces the flow of the liquid. The fact that the pressure of the liquid flowing in channel 10 is essentially constant is due to the fact that, When the pump 21 is activated, the liquid in the channel 10 initially resists flow due to interactions with the peripheral wall 11 up to a certain threshold, and is then set in motion. Thermoelastic coupling is then present, such that the liquid exhibits a spatially approximately constant temperature Theq and pressure Pheq along the longitudinal axis of the channel 10, which corresponds to the non-thermodynamic equilibrium state of the liquid.

[0050] The measuring system 1 also includes a thermal measuring device 30, adapted to determine a value of the temperature of the liquid in the channel 10. It can be of the non-contact type, for example by optical detection of infrared radiation, or of the contact type.

[0051] Preferably, the thermal measurement device 30 is non-contact and includes a photodetector 31 for light emitted from or originating from the liquid in the channel 10, for example, infrared radiation. The photodetector 31 can be a matrix (imager) or non-matrix (photodiode) photodetector. It can be a bolometer or microbolometer, a CCD or CMOS sensor (or equivalent, for example, BS-CMOS), or an optical pyrometer. The light radiation to be detected can be in the infrared, i.e., with a wavelength between approximately 0.7 pm and 16 pm. It can be in the near-infrared (NIR) range from approximately 0.78 to 1 pm, or in the short-wavelength infrared (SWIR) range from 1 to 2 pm.At approximately 7pm, be in the mid-infrared (MWIR) range from approximately 3 to 5pm, or even be in the far-infrared (LWIR) range from approximately 7pm to 2pm.

[0052] In this example, a matrix photodetector 31 (imager) is used, comprising an array of microbolometers forming 382 x 288 detection pixels. Each detection pixel has dimensions of 20 µm on each side in the focal plane. The thermal sensitivity is on the order of ±0.02°C within a nominal range of approximately 15–25°C. The thermal measurement device 30 also includes one or more optical elements 32 for shaping the incident light radiation, for example, one or more lenses. The depth of field depends, in particular, on the liquid and can be on the order of a hundred microns or even more. Furthermore, the detected thermal image corresponds to a measurement area of ​​the channel 10, which can have a height H zm at least equal to the internal diameter of channel 10, and a length L zm which can be equal to one or more times dint, for example equal to approximately 5mm.

[0053] From the detected thermal image, the thermal measurement device 30 determines a temperature value for the liquid in the channel 10. This value can be an average, possibly weighted, calculated from the values ​​in the thermal image or a map detailed thermal analysis. This allows us to give more weight, or not, to values ​​further from the peripheral wall 11. The determined value thus corresponds to the temperature T of the liquid in the channel 10, that is to say, the temperature T eq The temperature is recorded when the liquid is at rest, and the temperature Theq is recorded when the liquid is flowing. This temperature value is transmitted to the processing unit 40. Alternatively, the thermal image (thermal map) is transmitted to the processing unit 40, which will deduce a pressure image (pressure map) from it.

[0054] In the case where the thermal measuring device 30 is of the optical type, the peripheral wall 11 is made of a material that is either transparent to the light radiation to be detected, i.e., that the transmission coefficient is at least equal to 50%, or even 75%, or even 90% of the light radiation to be detected, or opaque to the light radiation to be detected but having a high thermal conductivity coefficient such that the light radiation is that emitted by the outer face 13 of the peripheral wall 11. A transparent material may be calcium fluoride (CaF2), germanium (Ge), potassium bromide (KBr), or certain plastics, among others. In the case where the material is opaque, the thickness of the peripheral wall 11 is preferably less than or equal to the inner diameter dint.

[0055] Alternatively, or in addition, the thermal measuring device 30 may include one or more contact thermal sensors, each formed of a thermistor material in contact with the peripheral wall. If the thermistor material is in contact with the inner face 12 of the peripheral wall 11, it is in contact with the liquid and is connected to the processing unit 40 by means of an electrical cable passing through the peripheral wall 11 in a sealed manner. Preferably, however, the thermistor material is in contact with the outer face 13 of the peripheral wall 11, in which case the peripheral wall 11 is made of a thermally conductive material such that the temperature of the outer face 13 of the peripheral wall 11 is substantially equal to that of the liquid, or such that the temperature of the liquid can be deduced from the temperature of the peripheral wall 11 by means of a predefined physical model of thermal conductivity.

[0056] The processing unit 40 is adapted to determine the liquid pressure in the channel 10, based on part of the temperature T eq measured by the thermal measuring device 30 (and more precisely from a temperature difference AT) and, on the other hand, by the calibration function f. It therefore includes a computer comprising at least one microprocessor and at least one memory where the calibration function f is stored. As indicated previously, the processing unit 40 can receive at least one temperature value, for example one or more thermal values, and for example a thermal image (thermal map), in order to deduce at least one corresponding pressure value, or even a pressure image (pressure mapping).

[0057] The calibration function f expresses an evolution (i.e., a variation) of the pressure difference AP = Pheq - Peq as a function of the temperature difference AT = Theq - T eqThe temperature difference in the liquid in channel 10 is given by: AP = f(AT). This is a continuous function, preferably a linear function, but it can also be a polynomial, logarithmic, or even exponential function. It is parameterized during the preliminary calibration phase, as detailed later. Thus, when the temperature difference AT is zero, the pressure difference AP is also zero. As mentioned previously, the temperature difference AT can have positive values ​​(heating) so that the pressure difference AP is also positive (liquid under compression), but it can also have negative values ​​(cooling) so that the pressure difference AP is also negative (liquid under tension).

[0058] Figure 2A illustrates an example of such a calibration function f, determined for water flowing in a tubular channel 10 with a diameter of 0.3 mm, where the temperature T eqThe temperature of the liquid at rest is approximately 20°C. The temperature was measured using a contact thermal sensor. The peripheral wall of channel 10 is made of a material opaque to infrared radiation, in this case silicate glass, which has high thermal conductivity. The peripheral wall 11 has an outer diameter of 0.8 mm. A variation |AT| of 0.34°C ± 0.02°C leads to a variation |AP| of 0.68 bar. The calibration function f is an affine function AP = pxAT, where P is a constant equal to approximately 2 bar / °C. Preferably, the pressure difference AP is between -1 bar and +1 bar, and preferably between -0.5 bar and +0.5 bar.

[0059] Figure 2B is a schematic and partial view of an example of a calibration system 100, adapted to determine the calibration function f which is then recorded in the processing unit 40 of the measuring system 1.

[0060] The calibration system 100 is similar to the measurement system 1, in that it includes a channel 110, a flow actuator 120, a thermal measuring device 130, and a processing unit 140. However, unlike the measurement system 1, it includes at least one pressure sensor 150 adapted to measure the liquid pressure in the channel 10. The pressure sensor 150 can be a strain gauge, capacitive, piezoelectric, etc. type. Several pressure sensors 150 can be arranged along the channel 10 to obtain a more accurate liquid pressure reading. Furthermore, the channel 110 has the same dimensions as that of the measurement system 1.

[0061] The calibration system 100 and the measurement system 1 are advantageously two separate systems, such that the calibration system 100 is used to determine the calibration function f only once, and the measurement system 1 is then used to determine the pressure of the liquid flowing in the channel 10 based on the calibration function f thus determined. It could be the same system, where the measurement system 1 corresponds to the calibration system 100 in which the pressure sensor(s) 150 have been removed. Note that the liquid whose pressure is to be determined by the measurement system 1 may be different from that used to determine the calibration function f, except that they both obviously satisfy the condition on the product kxr intPreferably, these two liquids have the same compressibility value k (within 10%, or even within 5%, or even less), and preferably they are the same liquids.

[0062] Figure 3 illustrates different stages of a process for determining the pressure of the liquid flowing in the channel 10 of a measuring system 1, as well as a preliminary phase of determining the calibration function f.

[0063] The calibration phase 10 is first carried out by the calibration system 100.

[0064] In step 11, a liquid with density p is chosen c , of viscosity p c and compressibility k c A channel 110 with an inner radius of Tint- is also chosen. The liquid and the channel 110 are therefore chosen so that the product k c xri n t is less than or equal to 12.5xl0 -11mm / Pa. Furthermore, channel 110 has a length L less than or equal to 5cm, and the internal diameter dint is less than or equal to 1mm, and preferably between 1Opm and 1mm.

[0065] During step 12, the liquid is present at rest in channel 110. The temperature T is defined eq and the pressure P eq of the liquid at rest and are recorded in the processing unit 140 of the calibration system 100. These values ​​can be simply defined by the user (without measurements), or can have been previously measured, for example by means of the thermal measuring device 130 or another temperature sensor (not shown), by means of the pressure sensor 150 or another pressure sensor (not shown).

[0066] In step 13, the flow actuator 120 sets the liquid in motion within channel 110 (constant flow rate in this example). More specifically, the pump 121 ensures the flow of liquid from the reservoir 122, through the conduits 123 and into channel 110, before returning to the reservoir. The flow rate D of the liquid in channel 110 is measured to ensure that it does not exceed a maximum value D m predefined, a value that depends on the nature of the liquid. Thus, in the case of water, the flow occurs without the flow rate exceeding 416 mm 3 / s approximately in channel 110.

[0067] In step 14, while the liquid is flowing in channel 110 at a flow rate D(i), the temperature Theq(i) of the liquid in channel 110 is measured using the thermal measuring device 130, and its pressure Pheq(i) is measured using the pressure sensor 140. The increment i thus varies from 1 to N, where N is the total number of measurements taken. The temperature difference AT(i) = Theq(i) - T is then determined. eq and the pressure difference AP;,) = Pheq(i)-Peq- We thus obtain a pair ( AT(,j ; AP;,) ), and we repeat the measurements for different flow rate values ​​D(ij by incrementing the value of i. The number N is at least equal to 1, given that the pair ( AT=0 ; AP=0 ) is present by definition, but it can be at least 6, with at least 3 measurements for AT>0, and at least 3 measurements with AT<0.

[0068] In step 15, the processing unit 140 determines the calibration function f, that is, it determines the parameters of the function (for example, the constant P in the case of a linear function) from the measured values ​​of the temperature and pressure deviations, for example, by linear regression. The calibration system 100 has thus determined the calibration function f, which is then transferred, if necessary, to the processing unit 40 of the measuring system 1.

[0069] The measurement phase 20 of the pressure of the liquid of interest can then be carried out by the measurement system 1.

[0070] In step 21, the liquid of interest is chosen. Like the liquid used for calibration, it is a liquid with a density ρ. m , a viscosity p m and a compressibility k m equal to k cto within 10%, that is, to within 10% or even less. Preferably, the liquid of interest is identical to the liquid used for calibration. Thus, since channel 10 is identical to that of the calibration system, the product k m xr in t satisfies the condition k m xr in t < 12.5xl0 -11 mm / Pa, and this product is equal to the product k c xri n t (to within 10% or even less).

[0071] During step 22, the liquid is present at rest in channel 10, and the temperature T eq and the pressure P eq are defined and stored in the processing unit 40. These values ​​can be directly retrieved from those stored in the calibration system 100. Alternatively, they can be defined and stored by the user in the processing unit 40 without having been directly measured. Alternatively, the temperature T can be measured. equsing the thermal measuring device 30 (or another temperature sensor not shown). The pressure P eq can be measured by a pressure sensor (not shown) placed for example at the level of the tank 22 or of a conduit 23.

[0072] In step 23, the flow actuator 20 sets the liquid in motion in the channel 10 (constant flow rate in this example). The flow rate D is less than or equal to the maximum value D m predefined. The liquid of interest therefore exhibits heating (AT>0) or cooling (AT<0) by thermoelastic effect, depending on the direction of flow imposed by the flow actuator 20.

[0073] In step 24, while the liquid is flowing in channel 10 at a flow rate D, the temperature Theq of the liquid in channel 10 is measured using the thermal measuring device 30. The processing unit 40 then determines the temperature difference AT = Theq-T eq .

[0074] During a step 25, the processing unit 40 determines the pressure deviation AP from the calibration function f and the obtained value of the temperature deviation AT.

[0075] Finally, in step 26, the processing unit 40 determines the value of the pressure P eq of the liquid flowing in channel 10, based on the pressure difference AP and the value of the liquid pressure at rest P eq : Pheq = AP - P eq .

[0076] Thus, measurement system 1 makes it possible to determine the non-equilibrium pressure Pheq of the liquid flowing in channel 10, without having to measure the pressure of the flowing liquid in the channel, by taking advantage of a thermoelastic effect demonstrated by the inventors. Therefore, not only is the flow of the liquid in the channel not disturbed by the pressure sensor, but the reliability of measurement system 1 is improved because the pressure is not determined by a remote, local, and potentially degradable dedicated pressure sensor, but by a thermal measurement and a calibration function.

[0077] Note that it is possible to generate flow instabilities during the measurement phase, and thus obtain an image of pressure variations of the flowing liquid via the measurement of a thermal image.

[0078] It should also be noted that it is possible to take advantage of the heating or cooling of the flowing liquid to heat or cool the channel, and by the same token, an external device that would be in thermal contact (heat exchanges) with the channel.

[0079] Specific embodiments have just been described. Different variations and modifications will be apparent to those skilled in the art.

Claims

DEMANDS 1. Measuring system (1), adapted to determine at least one pressure Pheq of a liquid of interest with compressibility k m in flow in a channel (10) of inner radius r.nt, the liquid of interest and the channel (10) being chosen such that the product k m xr in t is less than or equal to 12.5xl0 -11 mm / Pa, the measuring system (1) comprising: o the channel (10); o a flow actuator (20), adapted to flow the liquid of interest into the channel (10), so that the liquid of interest has a ratio V m / c less than or equal to 0.3, where V mis a maximum velocity of the liquid of interest in the channel (10) and where c is the speed of sound in the liquid of interest; o a thermal measuring device (30), adapted to measure at least one temperature Theq of the liquid of interest flowing in the channel (10); o a processing unit (40), adapted to determine the pressure Pheq from the measured temperature Theq and a predetermined calibration function f such that AP = f(AT), expressing a change in the pressure difference AP between the pressure Pheq and a reference pressure P eq predefined temperature of the liquid of interest at rest in the channel (10), as a function of a temperature difference AT between the measured temperature Theq and a reference temperature T eq predefined of the fluid of interest at rest in the channel (10).

2. Measuring system (1) according to claim 1, wherein the channel (10) has a length less than or equal to 5cm.

3. Measuring system (1) according to claim 1 or 2, wherein the channel (10) is straight along its entire length and has a constant internal radius r,nt.

4. A measuring system (1) according to any one of claims 1 to 3, wherein the flow actuator (20) comprises conduits (23) connecting the channel (10) to a pump (21) and to a reservoir (22) of the liquid of interest, the conduits (23) having an inside radius greater than n n t.

5. Measurement system (1) according to any one of claims 1 to 4, wherein the thermal measurement device (30) is adapted to detect infrared radiation emitted by the liquid of interest and transmitted through a peripheral wall (11) of the channel (10) and to deduce the temperature Theq, the peripheral wall (11) being made of a material transparent to infrared radiation.

6. Measurement system (1) according to any one of claims 1 to 4, wherein the thermal measurement device (30) comprises at least one contact thermal sensor, disposed in contact with a peripheral wall (11) of the channel (10).

7. Measurement system (1) according to claim 6, wherein the thermal contact sensor is disposed in contact with an outer face (13) of the peripheral wall (11), the latter being made of a thermally conductive material such that the temperature of the outer face (13) is equal to the temperature Theq of the liquid.

8. Measurement system (1) according to any one of claims 1 to 7, wherein the channel has an internal diameter dint between 10m and 1mm.

9. Measurement system (1) according to any one of claims 1 to 8, wherein the thermal measurement device (30) is adapted to acquire a thermal image of the liquid of interest, and the processing unit (40) is adapted to determine a pressure image from the acquired thermal image and the calibration function f.

10. A method for determining the pressure Pheq of a fluid of interest moving in the channel (10) of a measuring system (1) according to any one of the preceding claims, the method comprising a measurement phase including the following steps: o selection of a fluid of interest with compressibility k m and of the channel (10) of inner radius n n t, so that a product k m xr in t is less than or equal to 12.5xio -11 mm / Pa; o flow of the liquid of interest into the channel (10) at a flow rate predefined by the flow actuator (20), so that it has a ratio Vm / c less than or equal to 0.3, where V m is a maximum velocity of the liquid in the channel (10) and where c is the speed of sound in the liquid of interest; o measurement of a temperature Theq of the liquid of interest flowing in the channel (10) by the thermal measuring device (30), and determination of a non-zero temperature difference AT between the measured temperature Theq and a reference temperature T eq predefined pressure of the liquid of interest at rest in the channel (10); determination of the pressure Pheq of the liquid of interest by the processing unit (40), from the determined temperature difference AT, and a predetermined calibration function f, expressing an evolution of a pressure difference AP between the pressure Pheq of the liquid of interest flowing in the channel (10) and a reference pressure P eq predefined of the liquid of interest at rest in the channel (10), as a function of the temperature difference AT.

11. A method according to claim 10, comprising a calibration phase, carried out before the measurement phase, comprising the following steps: o selection of a liquid with compressibility k c and a channel (110) of inner radius r, of a calibration system (100), such that a product k c xri n t is less than or equal to 12.5xl0 -11 mm / Pa; o flow of the liquid into the channel (110) by a flow actuator (120) of the calibration system (100) at a predefined flow rate, so that it has a ratio V m / c less than or equal to 0.3, where V mis a maximum velocity of the liquid in the channel (110) and where c is the speed of sound in the liquid; o measurement of a temperature Theq of the liquid flowing in the channel (110) by a thermal measuring device (130) of the calibration system (100), and determination of a non-zero temperature difference AT between the measured temperature Theq and a reference temperature T eq predefined pressure of the liquid at rest; measurement of a pressure Pheq of the liquid flowing in the channel (110) by a pressure sensor (150) of the calibration system (100), and determination of a non-zero pressure difference AP between the measured pressure Pheq and a reference pressure P eqpredefined of the liquid at rest; o reiteration of the steps of measuring the temperature Theq and the pressure Pheq for different flow rates of the liquid in the channel (110); o determination of the calibration function f, by a processing unit (140) of the calibration system (100) from the different values ​​of the temperature deviation AT and the corresponding values ​​of the pressure deviation AP.

12. A method according to claim 10 or 11, wherein the liquid of interest is selected from water, an alcohol and glycerol.

13. A method according to any one of claims 10 to 12, wherein the liquid of interest used during the measurement phase is identical to the liquid used during the calibration phase.

14. A method according to any one of claims 10 to 13, wherein the flow of the liquid of interest is effected by suction, such that the measured temperature Theq is then lower than the reference temperature T eq and corresponds to a cooling of the liquid of interest; or is carried out by pumping, so that the measured temperature Theq is then higher than the reference temperature T eq and corresponds to a warming of the liquid of interest.

15. A method according to claim 14, wherein the channel (10) is made of a thermally conductive material and is in thermal contact with an external device, such that the Cooling or heating the liquid of interest results respectively in cooling or heating the external device.

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