Multi-oscillator viscoelastic sensing

Abstract

Aspects include using a vibration transducer having a plurality of oscillators including a first oscillator (220) and a second oscillator (210), where the first oscillator and the second oscillator are coupled such that in a viscoelastic fluid (240), excitation (vibration) of the first oscillator excites the second oscillator (causing the second oscillator to vibrate). The frequency response of the double-oscillator combination is influenced by the fluid characteristics; thus measuring one or more of: i) resonant frequency, ii) vibration amplitude, iii) loss factor (or Q factor) of a vibration combination of the first oscillator and the second oscillator in the viscoelastic fluid may be used to determine one or more of: i) density, ii) viscosity (such as dynamic viscosity), iii) elasticity (such as storage modulus) of the viscoelastic fluid.

Description

Technical Field

[0001] This disclosure relates to damping of vibrations within fluids, including using damping to obtain measurements of the physical and rheological properties of materials, such as viscosity. Background Technology

[0002] The physical and rheological properties of a fluid can be measured by applying an oscillatory stimulus to the fluid and observing the hydrodynamic response. Measurements of fluid properties such as viscosity, density, storage modulus, loss modulus, and loss tangent can be obtained from the observed hydrodynamic response (e.g., damping degree and / or stiffness, and / or resonant frequency).

[0003] For example, the degree of damping can be determined based on the amplitude or amplitude variation of the vibration, the resonant frequency or resonant frequency variation, the vibration attenuation rate, the quality (Q) factor or loss factor (which is the reciprocal of the quality factor).

[0004] Resonant viscometers measure viscosity by determining the damping effect of a viscous fluid on a mechanical oscillator immersed in it. The presence of viscosity increases the shear stress at the oscillator surface. This shear stress generates a damping force, which dissipates energy from the oscillator. For a mechanical oscillator operating at resonance, this reduces the Q-factor at resonance. Therefore, the Q-factor is an inverse indicator of viscosity. The loss factor is the reciprocal of the Q-factor, so an increase in viscosity leads to an increase in the loss factor. Historically, resonant viscometers have proven effective for purely viscous fluids and weakly viscoelastic fluids (non-Newtonian fluids where tan Δ (i.e., the loss tangent)) (i.e., the loss factor of the resonant viscometer effectively varies with the fluid viscosity).

[0005] The loss tangent is given by the following expression: ,in, It is the angular frequency of the oscillation. It is the dynamic viscosity of the fluid. It is the storage modulus of the fluid.

[0006] Newtonian fluids are purely viscous, meaning they exhibit no elastic behavior. They have no storage modulus. The loss tangent is... The value is infinity. Examples of such fluids include water, aqueous solutions, syrups, alcohols, most pure oils, most hydrocarbons, and gases.

[0007] Non-Newtonian fluids can be viscoelastic, and therefore possess... Examples of viscoelastic fluids include blood, suspensions, emulsions, and most synthetic materials. Strongly viscoelastic fluids can have... Examples of highly viscoelastic fluids include liquid polymers, polymer melts, rubber solutions, synthetic oils, detergents, and food products. Summary of the Invention

[0008] According to various aspects of this disclosure, a vibration transducer having a plurality of oscillators, including a first oscillator and a second oscillator, wherein the first oscillator and the second oscillator are coupled such that an excitation (vibration) of the first oscillator excites the second oscillator in a viscoelastic fluid (causing the second oscillator to vibrate).

[0009] Since the frequency response of the dual oscillator combination is affected by the fluid properties, one or more (e.g., all three) of the following are measured in the viscoelastic fluid in which the vibration combination of the first and second oscillators is performed: i) Resonant frequency, ii) Vibration amplitude, iii) Loss factor (or Q factor) It can be used to determine one or more (e.g., all three) of the following properties of a viscoelastic fluid: i) Density, ii) Viscosity (such as dynamic viscosity) ), iii) Elasticity (such as energy storage modulus) ).

[0010] The first oscillator and the second oscillator can be configured to vibrate laterally, longitudinally, torsionally, or a combination of these vibration types. For example, the first oscillator can be configured to vibrate torsionally, while the second oscillator can be configured to vibrate laterally.

[0011] In some examples, both the first and second oscillators are configured to contact and vibrate with the fluid. Alternatively, in some other examples, only one oscillator is in contact with the fluid.

[0012] One or both of the first and second oscillators may have dimensions related to fluid properties, thereby achieving geometric damping. For example, the second oscillator may include an elongated member characterized by a width, a half-width equal to half the width, and a length greater than the width, wherein the half-width is less than the propagation depth of the shear wave in the fluid at the vibration frequency. The propagation depth is the distance by which the amplitude of the shear wave propagating in the fluid at the vibration frequency is reduced by a factor of 1 / e, where e is the base of the natural logarithm.

[0013] For example, the propagation depth of a shear wave propagating at a vibration frequency in a fluid can be given by the following expression: in, It is the viscosity of the fluid. It is the density of the fluid. It is the angular frequency of the vibration, and From 0 The variation between π and the loss angle tangent Define, and in which, It is equal to the following expression, where It is the storage modulus of the fluid:

[0014] During vibration, the fluid flow around this elongated member can be laminar during the vibration of the elongated member. Optionally, the elongated member may have a first end and a second end, wherein one or both of the first and second ends are spaced apart from the longitudinal axis of the vibration axis driving the vibration of the elongated member (which may include or form part of a first oscillator) by an offset distance greater than half the width of the elongated member. Optionally or additionally, during the vibration of one or more vibration transducers in the fluid at a vibrational frequency, the Reynolds number (Re) of the fluid flow around the elongated member is less than 1000, preferably less than 100, more preferably less than 10, and even more preferably less than 1, wherein the Reynolds number is given by: in, 'It is the viscosity of the fluid,' It is the density of the fluid. It is half the width of the slender member, and It is the maximum velocity of a slender member relative to the fluid during the vibration of one or more vibrating transducers.

[0015] The excitation frequency of the first oscillator can be close to (e.g., within 30%, 20%, 10%, 5%, 2%, or 1%) the natural frequency of the second oscillator. The natural frequency of the master oscillator can be configured to be close to (e.g., within 50%, 40%, 30%, 20%, 10%, 5%, 2%, or 1%) the natural frequency of the second oscillator. Preferably, one or both of the excitation frequency and the natural frequency of the first oscillator are within 20% of the natural frequency of the second oscillator, more preferably within 10%, even more preferably within 5%, even more preferably within 2%, and even more preferably within 1%.

[0016] According to various aspects of this disclosure, a first oscillator is driven or excited at two different frequencies using the vibration transducer described above, wherein the first frequency is relatively closer to the natural frequency of the second oscillator than the second frequency. The first frequency may be within a threshold value of the natural frequency of the second oscillator (e.g., within 50%, 40%, 30%, 20%, 10%, 5%, 2%, or 1%), while the second frequency is outside that threshold value (e.g., less than the threshold value). Vibration at the second frequency can excite the first oscillator but not the second oscillator. Therefore, measurements can be performed using two different excitation regimes.

[0017] In these techniques, amplitude, loss factor (or Q factor), or frequency (such as resonant frequency) are measured at a first frequency and a second frequency, such that the difference between corresponding measurements, the ratio of corresponding measurements, or some other comparison between corresponding measurements is used to improve fluid viscosity or elasticity measurements. This can be achieved, for example, by suppressing common-mode noise.

[0018] According to various aspects of this disclosure, a first oscillator is driven or excited at a number of different frequencies using the vibration transducer described above, wherein the first frequency is relatively close to the natural frequency of the second oscillator (e.g., within 50%, 40%, 30%, 20%, 10%, 5%, 2%, or 1%), while one or more other frequencies are further away from the natural frequency of the second oscillator.

[0019] Measure amplitude, Q factor (or loss factor), and frequency to reveal the characteristics of fluid measurement and identification from these multi-frequency measurements.

[0020] For example, measurements of an unknown fluid can be obtained and compared with predetermined data that includes characteristics of multiple fluids, thereby determining an estimate of the unknown fluid. For instance, the feature in the predetermined data that is most similar to the measurements of the unknown fluid can be identified to estimate the unknown fluid.

[0021] Various aspects of this disclosure include the use of two coupled oscillators, where the harmonic response of one oscillator under fluid load influences the other oscillator. Various aspects of this disclosure also include an apparatus comprising such coupled oscillators.

[0022] Various aspects of this disclosure include the use of a vibration transducer (device) in which the measured amplitude, Q-factor (loss factor), and frequency vary monotonically with μ' and G'. Various aspects of this disclosure also include such a vibration transducer or an apparatus or system including such a vibration transducer.

[0023] Various aspects of this disclosure include the use of a vibration transducer (device) comprising coupled oscillators, wherein one oscillator is excited at a frequency close to the resonant frequency of a second oscillator, and is also excited at a frequency very different from the resonant frequency of the second oscillator. The ratio and difference of amplitude, loss factor, and frequency provide improvements to the measurements of fluid μ' and G'. Various aspects of this disclosure also include such a vibration transducer or an apparatus or system comprising such a vibration transducer.

[0024] Various aspects of this disclosure include the use of a vibration transducer (device) comprising coupled oscillators, wherein one oscillator is excited at a frequency close to the resonant frequency of a second oscillator, and is also excited at a plurality of frequencies very different from the resonant frequency of the second oscillator. Amplitude, Q-factor, and frequency reveal characteristics of fluid measurements and identification. Various aspects of this disclosure also include such a vibration transducer or an apparatus or system comprising such a vibration transducer.

[0025] The aspects of this disclosure may be particularly applicable to measuring the properties of flowing viscoelastic fluids, including for monitoring viscoelastic fluids in larger processes such as manufacturing processes.

[0026] Various aspects of this disclosure also include apparatus and systems comprising one or more vibration transducers having a plurality of oscillators configured to perform any of the methods described herein. For example, various aspects of this disclosure include devices comprising means for performing any of the methods described herein.

[0027] The present disclosure also includes a computer-readable medium, such as a non-transitory computer-readable medium, having instructions stored thereon, which, when executed by a processor, cause the processor to configure means including one or more vibratory transducers having a plurality of oscillators to perform any of the methods described herein. Attached Figure Description

[0028] The invention will be described in more detail by way of example only, with reference to the accompanying drawings, wherein:

[0029] Figures 1 to 5 A vibration transducer for use in the present disclosure is shown;

[0030] Figure 6 A more detailed diagram of the vibration transducer used in the art disclosed herein;

[0031] Figure 7 It shows Figure 6 The simplified spring-mass-damper model of the vibration transducer shown in the figure;

[0032] Figure 8 Are they different? A graph showing the relationship between the loss factor and viscoelasticity of the material.

[0033] Figure 9 Are they different? A graph showing the relationship between the loss factor and viscoelasticity of the material.

[0034] Figure 10 It is a multi-frequency characteristic analysis curve of the measurement results of loss factor, amplitude and frequency of various fluids with different viscoelasticity.

[0035] Figure 11 It is a graph showing the loss factor versus fluid stiffness and damping under basic excitation;

[0036] Figure 12 It is a graph showing the loss factor versus fluid stiffness and damping under over-excitation.

[0037] Figure 13 The curve of loss factor versus fluid damping under this excitation;

[0038] Figure 17 and Figure 18 The graphs show the loss factor versus fluid stiffness and damping under overexcitation of two different fluids, illustrating two different loss factor curves.

[0039] Figure 19 This illustrates a shear wave propagating radially from a curved surface in a viscoelastic fluid;

[0040] Figure 20 The diagram illustrates a shear wave propagating radially from the curved surface of a cylinder, one of which is deviated from the axis of rotation.

[0041] Figure 21 A graph showing the measured damping factor illustrates the application of the technology disclosed herein;

[0042] Figure 22 A cylindrical element that generates a dipole wave field under transverse vibration is shown;

[0043] Figure 23 Laminar flow around a cylindrical element under lateral vibration is shown;

[0044] Figure 24 A flowchart corresponding to the method according to the technology of this disclosure is shown. Detailed Implementation

[0045] According to various aspects of this disclosure, there are two (or more) coupled mechanical oscillators for a vibratory transducer immersed in a viscoelastic fluid. At least one of the mechanical oscillators is in contact with the viscoelastic fluid.

[0046] The first oscillator can be described as having a natural frequency. The main oscillator. The second oscillator has a natural frequency. The secondary oscillator. When the frequencies of the oscillators are selected to be similar, the primary oscillator will excite the secondary oscillator through a 'basic excitation' process.

[0047] Viscoelastic fluids endow one (or two) oscillators with additional mass (from density), damping (from viscosity), and stiffness (from elasticity). Therefore, the frequency response of a combination of two oscillators is modulated by the fluid properties.

[0048] By measuring the resonant frequency, amplitude, and / or loss factor of the combination, the three key fluid parameters of density, viscosity, and elasticity can be determined.

[0049] Both viscous and elastic forces strongly influence the measured parameters in a uniform, monotonic manner, thus providing information about complex viscosity. The reliability of the determination. Equation 1 in, It is dynamic viscosity, and It is the energy storage modulus.

[0050] The stronger the elastic effect of the viscoelastic fluid, the greater the applicability of the technology disclosed herein. For example, the technology disclosed herein can be applied to fluids with viscoelasticity levels corresponding to... , , , or The fluid, in which the degree of elastic behavior varies with From the corresponding pure viscous behavior Decrease and increase. The technology disclosed herein can be applied to fluids with low elasticity, such as those suitable for a range of applications. or elasticity gradually increases Scope, such as: ,or 45 ,or ,or ,or ,or Any combination of these ranges, regardless of whether the combination produces a continuous range (such as 30) ) or multiple discontinuous subranges (such as by or (The range of combinations indicated).

[0051] Figure 1 A vibration transducer 100 is shown, which includes a primary oscillator 120 and a secondary oscillator 110, both configured to vibrate in a transverse vibration mode, as shown. Figure 1 As indicated by the thick double-headed arrow in the diagram. Lateral vibrations driven by the ground at 130 cause the master oscillator 120 to vibrate, and the secondary oscillator 110 is coupled to the master oscillator 120. The vibrations within the fluid surrounding the master oscillator 120 and the secondary oscillator 110 have a modulation effect on the resonant frequency, amplitude, and loss factor (or Q factor, which is the reciprocal of the loss factor), from which the density, viscosity, and elasticity of the fluid can be determined.

[0052] Figure 2 It shows the relationship with Figure 1 A similar vibration transducer 100 is used, except that for both the main oscillator 120 and the secondary oscillator 110, the vibration modes are longitudinal, indicated by thick double-headed arrows. The longitudinal vibration mode is excited by a longitudinal vibration drive 130.

[0053] Figure 3 It shows the relationship with Figure 1 A similar vibration transducer 100 is used, except that both the primary oscillator 120 and the secondary oscillator 110 exhibit torsional vibration modes, indicated by thick double-headed arrows. Torsional vibration is driven by ground 130 to excite the torsional vibration mode.

[0054] Figure 4 A hybrid vibration transducer 100 is shown, wherein a master oscillator 120 is configured to vibrate in a torsional vibration mode. The master oscillator 120 includes a shaft coupled to ground 130 and a bob at the distal end of the shaft. A secondary oscillator 110 includes a pair of pins extending axially from the bob of the master oscillator 120, wherein these pins vibrate laterally when the master oscillator vibrates torsionally. This is because the pins of the secondary oscillator 110 are offset from the torsional vibration axis of the master oscillator 120.

[0055] Figure 5 Another hybrid vibration transducer 100 is shown, wherein the master oscillator 120 is configured to vibrate in a torsional vibration mode. (See diagram below.) Figure 4 As shown in transducer 100, the master oscillator 120 includes a shaft coupled to ground 130 and a hammer at the distal end of the shaft. The secondary oscillator 110 includes a pair of pins extending radially from the hammer of the master oscillator 120, wherein these pins vibrate laterally when the master oscillator torsional vibration.

[0056] Figure 4 and Figure 5Vibration transducer 100 is shown, which is described as a hybrid vibration transducer because the primary oscillator and secondary oscillator use different vibration modes. In this case, the primary oscillator 120 is in a torsional vibration mode, while the secondary oscillator 110 is in a transverse vibration mode. Other examples may use different combinations of vibration modes, such as a torsional mode plus a longitudinal mode, or a transverse mode plus a longitudinal mode, or even a combination of torsional, transverse, and longitudinal modes.

[0057] exist Figure 4 In the secondary oscillator 110, a pin extends in the same direction as the torsional vibration axis of the primary oscillator. Figure 5 In one example, the secondary oscillator 110 includes a pin extending radially outward from the torsional vibration axis of the primary oscillator. In other examples (not shown), the secondary oscillator 110 includes a pin extending in a direction inclined in both the radial and axial directions relative to the torsional vibration axis of the primary oscillator 120, or in a direction having at least a tangential component.

[0058] Figure 6 A more detailed arrangement of the hybrid vibration transducer in use is shown, wherein the primary oscillator 220 performs torsional vibration, while the secondary oscillator 210, in the form of an axially extending pin, performs lateral vibration, and all vibrations are within a range having characteristic... , and The process is carried out within a viscoelastic fluid of 240°C, wherein... The density is indicated. The torsional vibration of the master oscillator is caused by the vibration of the torsion bar 230 located at the end of the master oscillator 220 opposite to the secondary oscillator 210. In this example, only the secondary oscillator 210 is in contact with the fluid and is configured to vibrate in the fluid. In other examples, both the master oscillator 220 and the secondary oscillator 210 are configured to vibrate in the fluid.

[0059] Figure 7 It shows Figure 6 The system shown is a simplified spring-mass-damper model, where the shaft mass and shaft stiffness of the master oscillator 220 (i.e., the master system) are determined by the mass... and stiffness is The spring indicates that the pin mass and pin stiffness of the secondary oscillator 210 (i.e., the secondary system) are determined by the mass... and stiffness is The spring indicates that the fluid mass load is caused by an additional mass coupled to the pin mass. This indicates that fluid damping and elasticity are represented by an additional damper and spring coupled to the pin mass, with the damping coefficient of the additional damper being... The stiffness of the additional spring is Fluid properties in Figure 7 It is shown as reference numeral 240 in the figure.

[0060] The resonant frequency of the secondary oscillator ( The stiffness of the vibrating part of the oscillator and the stiffness determined by fluid elasticity ( ) and density ( Mass load modulation caused by ).

[0061] The amplitude of the secondary oscillator ( )along with It decreases with the increase of viscous damping.

[0062] The stiffness and mass of the main system allow it to oscillate at frequencies close to or far below the resonant frequency of the secondary system.

[0063] When the frequency of the main system ( ) close to the resonant frequency of the subsystem ( When the primary system excites the secondary system through the fundamental excitation, the result is related to the amplitude of the primary system. In comparison, the subsystem has a higher amplitude Oscillation. In other words, When the oscillation frequency of the main system is low, When the oscillation frequency of the main system is high, .

[0064] There may be an inverse viscoelastic response. At low... and The next oscillator has an amplitude of Free vibration. High amplitude of vibration. This leads to increased shear, which in turn increases energy dissipation due to damping. This increases the loss factor of the main system (i.e., decreases the Q factor) and reduces its amplitude. reduce.

[0065] Beyond the critical viscoelasticity, higher viscous or elastic loads will impede the movement of the secondary oscillator, thereby reducing its efficiency. And fluid shear. The system damping decreases, resulting in an increase in the amplitude of the main oscillator and a decrease in the loss factor (increased Q factor). Viscoelasticity reduces the influence of the secondary oscillator on the main oscillator.

[0066] Figure 8 The diagram illustrates the inverse response to viscous and elastic loads by varying tanΔ. From the graph, it can be seen that for a given complex viscoelasticity, an increase in the elastic load (which leads to...)... The decrease is manifested as a reduction in the loss factor.

[0067] Under the basic excitation, the loss factor (and 1 / amplitude) follows an antiviscoelastic response.

[0068] Beyond the fundamental excitation, when the frequency of the primary system is much lower than the resonant frequency of the secondary system, there exists a known relationship in which the added viscoelastic load provides a loss factor and a proportional response to 1 / amplitude.

[0069] These techniques can be further enhanced by considering the difference or ratio (or other comparison results) between the frequency of the fundamental excitation and frequencies far from the fundamental excitation (e.g., where the frequency of the primary system is much lower than the resonant frequency of the secondary system). This amplifies the viscoelastic response while retaining the advantages of differential measurements, which can reduce or eliminate common-mode noise or measurement distortion.

[0070] Furthermore, the combined output exhibits monotonicity, complex viscosity, and increased sensitivity compared to techniques that do not combine measurements of multiple frequencies, such as the fundamental excitation frequency and frequencies far from the fundamental excitation.

[0071] When considering the relationship between frequency and viscoelasticity, the frequency of the secondary oscillator depends on the fluid load, primarily due to the fluid storage modulus. Therefore, it can be seen that the frequency of the master oscillator increases with the increase of fluid elasticity.

[0072] This is particularly important when the oscillator employs a geometrically damped element, as described in UK Patent Application No. GB2207881.0 filed on 27 May 2023, and further discussed in this disclosure. For example, the vibration transducer may include one or more elongated members. Figure 4 and Figure 5 The pin in the example shown can be an elongated member. Such an elongated member may be characterized by a width, a half-width equal to half the width, and a length greater than the width, wherein the half-width is less than the propagation depth of the shear wave in the fluid at the vibration frequency of the elongated member, more preferably less than 50% of the propagation depth.

[0073] This provides additional, independent hydroelasticity measurements based on the frequency variation of the master oscillator. This is in Figure 9 displayed in Figure 9 Showing the target When the frequency varies from 1 to 0.25, the frequency is related to... The relationship.

[0074] These techniques can be further applied to multi-frequency characterization, which allows fluids to be identified from the characteristics of combined measurement results obtained at multiple frequencies.

[0075] Specifically, the stiffness, mass, and damping of the secondary resonator system are influenced by the elasticity, density, and viscosity of the fluid, respectively. The modulation of the oscillator's stiffness, mass, and damping by the fluid alters the response of the resonant element. This response also varies at different frequencies. Therefore, significant variations in measured amplitude, frequency, and loss factor can be observed for different fluids at different primary excitation frequencies. Many fluids (e.g., polymer melts) can be identified by their density and viscoelasticity. By plotting the frequency response of polymers (e.g., its relationship to amplitude, frequency, and loss factor), their characteristics can be correlated with measurements, thereby identifying the material under test.

[0076] Figure 10 Multifrequency characteristic analysis of four different fluids (1 to 4) is shown, including loss factor, amplitude ( The frequency variation (Hz) and the relative viscosity ( / N) were determined at multiple values. Each of the four fluids has a different characteristic profile, varying with the complex viscosity elasticity ( / N). (i.e., viscoelasticity) changes. By using different characteristic curves, the characteristic curve that best matches the measurement results of the loss factor, amplitude, and frequency changes of the unknown fluid can be found, and the unknown fluid can be estimated.

[0077] To gain a deeper understanding of the behaviors discussed above, we can analyze... Figure 7 A simplified spring-mass-damper model is used to illustrate the energy dissipation or loss factor. It is given by the following formula: Equation 2 in: It is the fundamental (or primary) frequency of the vibration. The resonant frequency of this component, It is the stiffness of the main system. It's the quality of the main system. This is the system stiffness. This system quality, It is the fluid damping coefficient. It is fluid damping stiffness. Fluid damping added mass, It is a system constant, and It is the frequency factor, equal to .

[0078] Frequency factor It has a significant impact on the loss factor (or Q factor) measured in response to fluid properties.

[0079] When the vibration frequency of the main system is close to the resonant frequency of the secondary system (i.e., When ), then In this case, the denominator in equation 2 is... The dependence on [something] decreases or even disappears. The loss factor L can be approximated by the following expression: Equation 3

[0080] Figure 11 It is shown that in these cases (i.e., when) hour) and or The curve graph. From Figure 11 It can be seen from this that Follow It increases and then decreases monotonically. Also follow It increases and then monotonically decreases. Therefore, by... equal When operating the vibration transducer under certain conditions, it was found that the loss factor changes monotonically with the damping coefficient of the fluid, while the damping coefficient is... The function of . Furthermore, it was found that the loss factor monotonically changes with the fluid stiffness, while the stiffness is . The dynamic viscosity and storage modulus of the fluid can be determined in this way, either through a suitable lookup table or by obtaining an approximate function through calibration. The monotonicity of this function is important because it means... The measured values ​​allow for determination and / or In addition, regarding The sensitivity is improved because the sensitivity does not depend on and The combination of .

[0081] Although only when When equal to zero, (and its) The secondary interaction will disappear from Equation 2, but when When it approaches zero (i.e., when) and When similar, you can obtain the pair. Substantial independence. Even Not equal to ,if only and Sufficient similarity is sufficient to obtain and and / or The relationship between them is monotonically decreasing. The excitation frequency of the main system (first oscillator) can be close to (e.g., within 50%, 40%, 30%, 20%, 10%, 5%, 2%, or 1%) the natural frequency of the subsystem (second oscillator). The natural frequency of the main system can be configured to be close to the natural frequency of the subsystem (e.g., within 50%, 40%, 30%, 20%, 10%, 5%, 2%, or 1%). Preferably, one or both of the excitation frequency and natural frequency of the main system are within 20% of the natural frequency of the subsystem, more preferably within 10%, even more preferably within 5%, even more preferably within 2%, or even within 1%. On the other hand, it may be advantageous not to operate the main system at a frequency exactly the same as the natural frequency of the subsystem (e.g., not within 0.1%, 0.5%, or 1% of the natural frequency of the subsystem). In the context of this disclosure, Similar to ( The arrangement of ) can be called 'basic incentives'.

[0082] exist When the result is equal to zero, Equation 3 is further simplified for Newtonian fluids. Newtonian fluid, loss factor It can be represented as: Equation 4

[0083] in other words, and There is an inverse relationship between them. This relationship is based on... Figure 11 The manner shown is monotonically decreasing; therefore, as Equation 3 applies to viscoelastic fluids, the fundamental excitation provides the same or better monotonicity advantage for measuring the damping (viscosity) of Newtonian fluids.

[0084] If the vibration frequency of the primary system exceeds the resonant frequency of the secondary system (i.e., ),but ,So ,So In the context of this disclosure, this arrangement is referred to as 'hyperexcitation'. In this case, in Without simplification, the loss factor is given by Equation 2.

[0085] Figure 12 It shows the super-excitation (i.e., hour) and or The curve graph. From Figure 12 It can be seen from this that, with Figure 11 Compared to the basic incentives shown, Presented with and A more complex relationship. (Targeting) or The plotted loss factor has a maximum value, and there are values ​​on both sides of the peak. or It has multiple values. The maximum value is at The case occurs in the frequency factor Similarly, the location used to achieve the maximum value. The value is given by the following expression: Equation 5

[0086] Under hyperexcitation Not following or The fact that the pattern changes monotonically does not mean that it cannot be used for measurement purposes. For example, if or From the approximate value, we can obtain, and then based on... or Determining the approximate value The measured value is located on the peak side. This approximation can originate from measurements obtained using additional measurement techniques, or from the appropriate selection of transducer characteristics (geometry, stiffness, etc.) for a given fluid measurement application to ensure the peak value is on the peak side. It is outside the expected operating range of the fluid properties.

[0087] For low values The expression for the loss factor under over-excitation simplifies to Equation 6 below.

[0088] If the primary system vibrates at a frequency lower than the resonant frequency of the secondary system (i.e., ),but ,So If we further assume... Then the loss factor can be expressed as: Equation 6 in, It is a very large number. In this case, the monotonic characteristics of the loss factor are not affected by fluid elasticity. In the context of this disclosure, this arrangement is referred to as 'sub-excitation'.

[0089] Figure 13 The secondary excitation is shown, which demonstrates and The relationship between them, Follow Monotonically increasing and independent of This configuration is equivalent to a classic single resonator damping. Essentially, the second resonator 'rides' the vibration of the first oscillator, but is not excited independently; the vibration frequency driving the first resonator is much lower than the resonant frequency of the second resonator.

[0090] Based on these equations, the resonator geometries of the primary and secondary systems can be selected for different frequency conditions (whether fundamental excitation, super-excitation, or secondary excitation). It is important to note that... The natural frequency of the secondary resonator varies with fluid mass and stiffness load, which are functions of the resonator shape and fluid density and elasticity. The natural frequency of the secondary resonator is given by the following expression: Equation 7

[0091] For basic incentives Using this arrangement, one can use... Determine the measurement results and / or .

[0092] For hyperexcitation ,in, Greater than 1. For example, It can be greater than 1.5, or greater than 2. Using this arrangement, one can use... Determine the measurement results and / or .

[0093] For this incentive ,in, Less than 1. For example, It can be less than or equal to 0.5 or less than or equal to 0.25. Using this arrangement, one can use... Determine the measurement results .

[0094] The expression for the additional mass of the fluid can be obtained from Equation 7: Equation 8

[0095] Since the increase in mass is proportional to the density of the fluid, for a given calibration constant A, the expression for the density can be obtained as follows: Equation 9.

[0096] In some examples, one or more vibration transducers are used to operate in more than one of these modes, i.e., in more than one of the basic excitation, super-excitation, and sub-excitation modes. In one example, a first vibration transducer is used to operate in a first mode of these modes, while a second vibration transducer is used to operate in a second mode of these modes that differs from the first mode. For example, the first vibration transducer may operate in the basic excitation mode, while the second vibration transducer may operate in the sub-excitation mode. Alternatively, the first vibration transducer may operate in the super-excitation mode, while the second vibration transducer may operate in the sub-excitation mode. In this way, multiple vibration measurements of the fluid (loss factor, Q-factor, frequency, amplitude, etc.) can be obtained. These vibration measurements can be combined to determine the characteristics of the fluid.

[0097] In some examples, the vibration transducer can operate in multiple modes. For instance, the vibration transducer can operate with two or all three of the following: basic excitation, super excitation, and secondary excitation. The vibration transducer can perform a first vibration measurement under one of the basic, super, and secondary excitations, a second vibration measurement under a different one of the basic, super, and secondary excitations, and a third vibration measurement under the remaining one of the basic, super, and secondary excitations. In this way, multiple vibration measurements of the fluid (loss factor, Q-factor, frequency, amplitude, etc.) can be obtained. These vibration measurements can be combined to determine the characteristics of the fluid.

[0098] Combining more than one of the basic, super, and secondary stimuli can allow for efficient or direct determination. and Both.

[0099] For example, using secondary stimuli can be achieved by The measurement results are determined Under basic incentives, Monotonously dependent on and ,but It can be determined separately through secondary excitation, thereby in the known... and In some cases, it can be determined directly through lookup tables, calibrated approximation functions, etc. This also applies to other combinations of basic incentives, super-incentives, and secondary incentives, although the determination... and It may be necessary to solve for the corresponding equations using each combination of techniques or by performing numerical equation-solving techniques (such as iterative methods). A set of equations for each of the different measurement results. For example, both over-excitation and basic excitation can produce... The measurement results can be used to determine whether the two measurements are from different frequencies. The measurement results are substituted into Equation 2 to determine the approximate function through a lookup table. and If the fluid's elasticity is sufficiently low relative to its elasticity (i.e., Δ is sufficiently high), then It can be considered completely independent of fluid stiffness, in which case the secondary excitation and the hyperexcitation together allow for direct determination. Thus, the results of the over-excitation measurement can be used to determine more directly. .

[0100] However, it is not necessary to combine more than one of the basic, super, and secondary excitations to determine material properties, such as or For example, if the elasticity or viscosity of the fluid is known, or can be determined by any other technique known to those skilled in the art (such as a rotational viscometer, falling ball viscometer, capillary viscometer, shear rheometer, or acoustic rheometer), then it is therefore not necessary to determine it through a combination of primary, secondary, and super-excitations as described herein. or Furthermore, according to the technology disclosed herein, only one of the basic stimulus or the super-stimulus may be used.

[0101] Measurements obtained using multiple different excitation modes (basic excitation / secondary excitation / super excitation) can offer additional advantages. In particular, excitation modes can be combined to eliminate common-mode errors (such as noise) in the measurement results.

[0102] As an example, dividing Equation 6 by Equation 3 provides the following expression, where the fundamental excitation frequency is... The excitation frequency is ,in, Less than 0.5: Equation 10 Equation 11 Equation 12 in, At the basic excitation frequency The measurement results obtained below At the secondary excitation frequency The measurement results obtained below, for example, are as follows: ,and It is a certain constant. If different transducers are used to obtain sub-excitation measurement results and super-excitation measurement results, then... The specific value may vary, but any difference will be incorporated into the final constant in Equation 12. middle.

[0103] Therefore, Equation 12 provides a useful expression where the values ​​obtained from the two measured loss factors strongly depend on the... The fluid stiffness-viscosity function is given.

[0104] Furthermore, by performing ratio processing on the measured loss factor, the losses are effectively offset through division. and This method aims to reduce or eliminate any systematic errors or noise present in the measurement results. Such errors or noise can also be reduced by obtaining the ratio of other measurement results (e.g., the loss factors of the secondary and super-excitations, or the loss factors of the basic and super-excitations). Furthermore, this error or noise can be reduced by obtaining the differences between loss factors obtained from different excitations (e.g., the difference between the loss factors of the secondary and basic excitations, the difference between the loss factors of the secondary and super-excitations, or the difference between the loss factors of the super-excitations and the basic excitations). Further improvements in reducing errors or noise can be achieved by obtaining weighted differences—that is, multiplying one or two loss factors by an appropriately chosen scaling factor (e.g., through an optimization process) before obtaining the differences—to reduce or minimize systematic errors or noise.

[0105] Although the above analysis is based on the loss factor, a corresponding equation can also be derived from the Q factor, where the trend will be opposite due to the reciprocal relationship between the loss factor and the Q factor. Other relationships can be determined based on measurements of the system's amplitude and resonant frequency.

[0106] For example, the analysis provides an approximate equation for the natural frequency of the coupled oscillator under sub-excitation and super-excitation: Equation 13 Equation 14 in, The natural frequency under this stimulus, It is the natural frequency under over-excitation, and , , and It is a system constant.

[0107] In both cases, utilizing and The modulation of the frequency is very obvious.

[0108] Figure 14 It is based on the natural frequency under secondary excitation in Equation 13 and and The graph shows the natural frequency as a function of... and The monotonic response, in which Follow and It increases with the increase of.

[0109] Figure 15 It is based on the natural frequency under over-excitation in Equation 14 and and The graph shows the natural frequency as a function of... and The monotonic response, in which Follow and It decreases as it increases.

[0110] therefore, and The measurement results can be determined whether by approximation functions, lookup tables, or by solving equations 13 and 14 together. and .

[0111] Figure 16 It is based on equations 13 and 14. and and The graph shows the natural frequency as a function of... and The monotonic response.

[0112] Due to the basis and Under the influence of secondary and super-excitation changes The inverse phase change, determine (Or its inverse) can offer particular advantages. In particular, it allows these frequency measurements to be combined to eliminate common-mode errors. For example, fluid temperature can have a significant effect on the natural frequency of a transducer vibrating in that fluid. However, for a given variation, the effect of temperature on the natural frequency is... and The directions of frequency change are the same. Under the inverse phase change, if it is determined and If the ratio is such that the effect of temperature change is at least partially offset, then this quantity... It is less sensitive to the effects of common-mode errors, such as temperature variations, than either measurement result alone. Furthermore, because... and Being in opposite phases together increases the likelihood of... and Sensitivity to change. Therefore, in ratio form and The combination provides for and This increases sensitivity and reduces noise by canceling common-mode effects. Regardless of the ratio... still This applies to all of them.

[0113] Another advantage of this method is that it does not require precise knowledge of the natural frequency of the second oscillator. The frequency required for the secondary excitation is much lower than the expected frequency of the secondary oscillator. Similarly, the over-excitation requires a much higher frequency. In practice, it is easy to estimate very rough values ​​for frequencies much higher and much lower than the second oscillator.

[0114] Furthermore, the above analysis is aimed at Figure 7 The specific mass-spring-damper model shown is based on... Figure 6 The analysis of the specific arrangement shown is a simplification that ignores any mechanical damping of the oscillator itself and any continuous medium mechanics of the oscillator, instead treating the oscillator as a point mass connected via springs. Those skilled in the art will recognize that the technology of this disclosure is not inseparable from the specific equations corresponding to that particular model, but rather represents a broader trend or behavior of mechanically coupled multi-oscillating transducers of other designs and configurations. This analysis can be further extended to transducers comprising three or more oscillators (according to the technology of this disclosure), where a third oscillator may be coupled to a master oscillator in parallel with the second oscillator (where spring and mass characteristics may be combined with the characteristics of the second oscillator to produce the same equations as described above), or the third oscillator may be coupled to the second oscillator, which may produce a more complex frequency response, but allows for the same general concepts of basic excitation, super-excitation, and sub-excitation as described above for each of the second and third oscillators.

[0115] As previously mentioned, it may be advantageous to use a resonator in the form of an elongated member, as described in UK Patent Application No. GB2207881.0 filed on May 27, 2023, and further described below, because the radial / geometric radiation properties produce a high damping value. and high fluid stiffness value At the same time, the contact area with the fluid is small. A small contact area with the fluid is particularly beneficial in applications where the vibrating transducer is placed in a flowing fluid, because it reduces the amount of material adhering to the fluid contact surface, which allows the transducer to detect changes in the characteristics of the flowing fluid more quickly.

[0116] Between different fluid materials The natural variations in fluid density and elasticity produce different loss responses that vary from material to material. For each material, this results in a characteristic response that can be used to identify the material being tested. This is especially true for polymers (e.g., polymer melts) that are characterized by varying density and elastic properties.

[0117] Figure 17 and Figure 18 The diagram shows the loss factor curves for two different materials under overexcitation. It can be seen that the curves are not identical. Based only on a small number of measurements of the loss factor at different frequencies (e.g., multiple overexcitation frequencies, or a combination of the overexcitation frequency and the fundamental excitation frequency), it is possible to determine which of the two loss factor curves represents which material, thus identifying which of the two different materials corresponds to the tested material, or estimating the relative amount of each material in the tested sample.

[0118] In practice, a material's loss factor curve can be characterized by one or more values, such as the location of the peak of the loss factor curve, or the ratio of that peak location to another material property, such as elasticity or density. Users can obtain such characteristic or characterization values ​​for each of several different materials and compare measurements from the tested fluid with a stored dataset of characteristic values ​​for each of the multiple materials to identify the tested material. The result can correspond precisely to one of the stored values, indicating that the material is a specific material, or it can be a mixture of two stored values, indicating a mixture of materials, with the exact value indicating the relative amount of material in the mixture.

[0119] In a configuration according to the present disclosure, the vibration transducer includes a shaft and a plurality of elongated members. If the vibration transducer includes a hammer, the elongated members may be connected to the vibration transducer at the hammer. Alternatively or additionally, the vibration transducer may include elongated members connected to the shaft. The plurality of elongated members are spaced apart around the circumference of the shaft or hammer and extend outward from the shaft or hammer in a completely radial direction, a direction having radial and axial components, or a completely axial direction (not collinear with the longitudinal axis of the shaft / hammer). The plurality of elongated members may be uniformly distributed around the circumference, which may mitigate or avoid any disturbance of the center of mass relative to the longitudinal axis, or may be non-uniformly distributed around the circumference. The plurality of elongated members may be connected to the shaft or hammer at the same axial location along the length of the shaft or hammer, or may be connected at different axial locations, for example, in a helical pattern around the outer surface of the shaft or hammer.

[0120] If multiple elongated members extend from the shaft or hammer in a fully axial or partially axial direction, the elongated members may include spaced supports from the outer surface of the shaft or hammer to provide radial offset to the elongated members. Alternatively, multiple elongated members may extend from the ends of the shaft or hammer, such as being circularly distributed around a longitudinal axis and extending from the ends of the shaft or hammer. The ends of the shaft or hammer may be flat, curved, conical, or may have certain other shapes.

[0121] The width and half-width of the slender member allow for geometric damping (monopole behavior) to occur around the slender member during the vibration of the vibratory transducer. The vibration of the vibratory transducer may be a torsional vibration about the longitudinal axis of the shaft.

[0122] Alternatively, the geometry of one or more elongated members can be defined in such a way that the geometry is independent of geometric damping (monopole behavior), which can be specifically applied based on the characteristics of the fluid (i.e., its shear wave penetration depth). For example, the width or diameter of one or more elongated members can be between 0.1 mm and 5 mm, preferably between 0.2 mm and 4 mm, more preferably between 0.3 mm and 3 mm, more preferably between 0.5 mm and 3 mm, and even more preferably between 0.8 mm and 3 mm. For example, a particularly preferred diameter / width ratio can be between approximately 1 mm and 2 mm (e.g., between 0.9 mm and 2.2 mm if 'approximately' means within ±10% of each end of the range). Alternatively or additionally, the aspect ratio (length to width ratio) of the elongated members can be greater than 3:1, greater than 5:1, greater than 10:1, or even greater than 20:1. Therefore, by way of example only, the width or diameter of the slender component can be 1 mm and the length can be 10 mm; or the width or diameter can be 2 mm and the length can be 15 mm. This dimension can be applied to a variety of fluids of interest.

[0123] A vibration transducer may include two or more elongated members, such as three, four, five, six, seven, eight, nine, ten or more elongated members. The elongated members may have a constant cross-section along their length (such as cylindrical elongated members or elongated members with square / rectangular, rounded square / rectangular (e.g., hyperelliptical), triangular or elliptical cross-sections), or may have varying cross-sectional shapes or dimensions along their length, such as: i) a cone whose cross-sectional area decreases linearly with increasing distance from the axis or vibrating hammer, or ii) a size or shape that changes stepwise with increasing distance from the axis or vibrating hammer (e.g., size decreases stepwise).

[0124] In one particular configuration, the vibration transducer includes a shaft configured for torsional vibration, having a proximal end (where the vibration is driven) and a distal end. At or near the distal end of the shaft (e.g., closer to the distal end than the proximal end, or within the last quarter, tenth, or twentieth of the fluid contact length of the shaft), a plurality of elongated members extend radially outward along the length of the shaft at a common axial location. Eight elongated members are uniformly distributed around the circumference of the shaft in 45° increments. In another particular configuration, a vibratory hammer is present at the distal end of the shaft, and eight elongated members extend radially outward from the hammer. Other configurations include more or fewer elongated members, uniformly or non-uniformly distributed around the shaft / hammer. For example, one configuration includes six elongated members uniformly distributed around the circumference of the shaft.

[0125] In another specific configuration, the vibration transducer includes a shaft and a plurality of elongated members axially aligned with, but not collinear with, the longitudinal axis of the shaft. A vibratory hammer is located at the distal end of the shaft. The hammer is in the form of a cylinder coaxial with the longitudinal axis of the shaft, but with a radius larger than the radius of the shaft. The plurality of elongated members extend axially outward from the end of the hammer, each connected to the end of the hammer with the same radial offset from the longitudinal axis, and are uniformly distributed around the longitudinal axis. The plurality of elongated members includes eight elongated members uniformly distributed around the longitudinal axis in 45° increments. The vibration transducer is configured to torsional vibration around the longitudinal axis. Other configurations include more or fewer elongated members, uniformly or non-uniformly distributed around the longitudinal axis. For example, one configuration includes six elongated members uniformly distributed around the longitudinal axis.

[0126] According to the technology disclosed herein, in this configuration, the shaft / vibrating hammer can represent the first oscillator, while the elongated member (together) can represent the second oscillator.

[0127] The following explanations cover geometric damping and slender members employing geometric damping, first considering purely viscous fluids and then viscoelastic fluids.

[0128] For a purely viscous fluid, the propagation depth of the shear wave is given by the following expression: Equation 15

[0129] The reduction in wave amplitude caused by viscosity generates shear stress at the vibrating surface. The shear stress It is the rate of change of velocity at the surface (i.e., the shear rate). ) and fluid viscosity The product of is given by the following expression: Equation 16

[0130] Shear rate at the oscillating surface caused by wave attenuation The following expression can be obtained by differentiating the wave velocity expression with respect to the distance from the surface and evaluating the expression at the surface: Equation 17 in, It is the shear velocity at the oscillating surface.

[0131] The shear rate caused by viscosity decay is proportional to the square root of the frequency, the square root of the density, and the square root of the reciprocal of the viscosity.

[0132] Therefore, the shear stress at the surface (which is the product of the viscosity and shear rate at the surface) is nonlinear: Equation 18

[0133] In addition to viscous effects, fluids can also exhibit elastic behavior, which depends on the storage modulus. . The presence of this will reduce the loss tangent. .

[0134] For purely viscous fluids, As elastic behavior increases, fluid losses decrease, allowing waves to propagate further within the fluid. Considering elasticity, the propagation depth is given by: Equation 19 in, This is the amount by which the propagation depth is scaled due to the elastic behavior of the fluid. This amount is also equal to... .

[0135] For purely viscous fluids, Equal to 90°, therefore by (or equivalently, The given scaling factor is 1, and the pure viscous propagation depth is restored. Therefore, even for fluids exhibiting little or no viscoelasticity, it is appropriate to use this expression to refer to the viscoelastic propagation depth. For angles less than 90°... The value of is greater than 1, so the propagation depth will increase relative to the pure viscous propagation depth.

[0136] The shear rate at the oscillating surface, caused by both viscosity and elasticity, is given by the following expression: Equation 20

[0137] The shear stress at the oscillating surface, caused by both viscosity and elasticity, is given by the following expression: Equation 21

[0138] Shear stress is a nonlinear function of fluid viscosity, fluid density, frequency, and storage modulus (via the loss tangent). With elasticity... Increase Decrease From the maximum value It begins to decrease, and and Both decrease, therefore the damped shear stress decreases with elasticity. The viscosity increases while the viscosity decreases. This explains why viscoelastic fluids exhibit reduced damping compared to Newtonian fluids with 'similar' viscosities.

[0139] Figure 19 It shows the radius of Shear waves propagate radially across a curved surface in a viscoelastic fluid. Although viscoelastic fluids exhibit relatively low losses over short distances, Figure 19 This shows that as the radial distance increases, energy is distributed over the increasing circumferential length because the potential energy of each wave crest must be preserved. Therefore, the amplitude will decrease. Figure 19 The equipotential energy lines 510 are shown. The distribution of energy along the increasing circumferential length results in a decrease in energy per unit volume, and therefore a decrease in the peak height. This amplitude decay, caused by geometric considerations, behaves similarly to damping, although the amplitude decay itself does not dissipate energy.

[0140] Changes in altitude cause a decrease in speed, and this decrease in speed is related to... The proportion, and this change in velocity, produces the shear rate. The combination of shear rate and viscosity generates shear stress. This shear stress has a component in phase with the surface velocity, which causes energy dissipation. This effect is referred to as 'geometric damping' in this paper.

[0141] If the oscillation is not on a planar surface but has a radius of... By examining the surface of the cylinder, one can obtain its position relative to the central axis of the cylinder. An expression for the velocity of the radial shear wave, and an expression relating to this expression. Differentiating, we obtain the radial shear rate: Equation 22 in, It is the shear rate at the surface. It is by The given phase adjustment angle is equal to ,in, It is the wave number of the propagating wave (i.e., in It is the wavelength of the propagating wave.

[0142] Shear stress at the surface of the cylinder, where Then it is given by the following expression: Equation 23

[0143] item This is the in-phase shear gradient. For any degree of viscoelasticity, this component of the shear rate is in phase with the velocity. This is the inverse shear gradient. The shear rate of this component is... Inverted, It depends on the degree of viscoelasticity. The phase adjustment angle represents the angle between shear stress and velocity. Shear stress in phase with velocity dissipates energy.

[0144] For much smaller of The value of is dominated by the in-phase component, and the dependence of shear rate on viscosity, density, frequency, and storage modulus decreases or even disappears (through ). , it is (function). If and Compared to the values ​​that can be ignored, the shear stress at the cylindrical surface is given by the following expression: Equation 24

[0145] For much larger of The value of is dominated by the inverse component, and the shear rate gradually becomes more dependent on the nonlinear functions of viscosity, density, frequency, and storage modulus. If and Compared to the values ​​that can be ignored, the shear stress at the cylindrical surface is given by the following expression: Equation 25

[0146] The critical value is Because this means The intersection of values, at which point, due to the item The resulting shear stress becomes greater than that due to the term This induces shear stress. According to the technique described herein, this can be considered the beginning of geometric damping.

[0147] when At this point, the dependence of shear stress on the nonlinear function of viscosity, density, frequency, and storage modulus further decreases. It can be considered that if the cylinder radius is less than half the viscoelastic propagation depth, geometric damping begins to dominate; that is, in... In other words, ,in, This can be understood as limiting the range within which geometric damping can be assumed to be dominant and defining the radius of the cylinder that limits the damping behavior.

[0148] To measure the physical properties of a fluid, parameters can be selected to provide fluid loading factors (such as fluid damping factors). Stiffness load factor and inertial load factor The linearity is improved. If The expression for the fluid viscosity at which geometric damping begins to occur is given by the following equation: Equation 26 in, .

[0149] For example, given a radius For 2mm in a purely viscous fluid ( A cylindrical element vibrating at a frequency of 5 kHz in a [structure], with a density of [amount]. For a fluid with a density of 1000 kg / m³, then in Pa... Choose an appropriate fluid viscosity in units of s. The value is given by the following formula:

[0150] For the geometric damping that begins to dominate (i.e., in In this case, the required viscosity is four times higher, that is: .

[0151] Similarly, geometric damping can be utilized by selecting the radius and / or frequency of the vibrating element for a given viscosity and density operating range, depending on the operational requirements.

[0152] Figure 21 A graph showing the damping factor of heavy mineral oil measured at a frequency of 5 kHz using a vibrating cylinder with a radius of 2 mm and the fluid density is presented. The damping factor, at 1000 kg / m³, was measured at a range of viscosity values ​​(obtained by applying heat to heavy mineral oil). The measured damping factor was obtained through... Figure 21 The solid line indicated by 'A' represents the damping. The graph also shows the case where the damping is described by non-geometric damping (i.e., and The curve of the damping factor calculated (compared to the case where it is negligible). The line at... Figure 21 The value is indicated by 'B'. Furthermore, the diagram also shows the case where damping is described by geometric damping (i.e., and The curve of the damping factor calculated (compared to the case where it is negligible). The line at... Figure 21 The middle is indicated by 'C'.

[0153] Figure 21 This indicates that when the viscosity is relatively low (i.e., below about 60 Pa·s), the radius of the vibrating element is larger than the viscous penetration depth, and the shear rate is a nonlinear function of viscosity. At viscosities above about 60 Pa·s, shear wave attenuation begins to be described by geometric damping, and the damping factor gradually becomes linear.

[0154] Figure 21 Three regions are identified. The first region, indicated by reference numeral 570, is a non-linear region and covers areas below... The viscosity value is 62 Pa·s (as determined above). The second region, indicated by reference numeral 580, is a linear transition region and encompasses the... and Viscosities between 250 Pa·s (as determined above). The third region, indicated by reference numeral 590, is a completely linear region and covers viscosity values ​​above [missing value]. The viscosity value. Operating in the second region 580 provides improved linearity compared to operating in the first region 570. Operating in the third region 590 provides improved linearity compared to operating in the second region 580.

[0155] For a vibrating cylinder with a sufficiently large radius so that geometric damping is negligible, the fluid damping factor is... Stiffness load factor and inertial load factor The expression is given by the following expression: Equation 27 Equation 28 Equation 29

[0156] In these expressions, due to the parentheses containing these terms (or quantities that are functions of these terms, such as...) and its impact (dependence), each factor is on , or It exhibits non-linear dependence.

[0157] If the radius of the vibrating cylinder is small enough that non-geometric damping can be neglected, then , and The expression for is given by the following formula: Equation 30 Equation 31 Equation 32

[0158] These expressions show that, when non-geometric damping is negligible, the fluid damping factor... Stiffness load factor and inertial load factor No longer with , or It exhibits no non-linear dependence. Quantity , and respectively with , and They are directly proportional, where the proportionality constant depends only on the geometric parameters.

[0159] Improving the linearity of these fluid load factors may be advantageous. Mechanical systems may have damping. Stiffness and inertia These factors determine the system's vibration frequency using the following equation. And Q factor: Equation 33 Equation 34

[0160] When the system vibrates in air or a vacuum, these mechanical factors can be expressed as , and When the system vibrates the fluid, the fluid's physical properties will be affected by the amount of... , and To 'load' these factors.

[0161] Considering fluid loads, the overall values ​​of the system's damping factor, stiffness factor, and inertia factor can be expressed as: Equation 35 Equation 36 Equation 37

[0162] , and The overall value is related to the above equations for frequency and Q factor, which are easy to measure. The physical properties of the fluid can be based on... , and The contribution to vibrational behavior is determined. As discussed below, the techniques disclosed herein can provide... , and With regard to physical properties such as density Viscosity and energy storage modulus A simple linear relationship between them.

[0163] In these expressions, It is the fluid contact surface area of ​​the cylindrical component. It is the 'radius of gyration' of the element, equal to the radius of the cylindrical element when it undergoes torsional vibration about its axis. .

[0164] When considering the effect of moment of inertia on the rotational motion of an object, the radius of gyration refers to the radial distance to a point where the moment of inertia is the same as the actual mass distribution of the object if all the mass of the object is concentrated. The term 'radius of gyration' in this disclosure is a generalization of the concept to take into account torsional factors other than moment of inertia.

[0165] In damping factor In this case, the radius of gyration represents the radial distance to a point. If the damping is concentrated at that point, then that point will have the same damping effect as the actual damping effect of the object.

[0166] Stiffness load factor In this case, the radius of gyration represents the radial distance to a point. If the stiffness load is concentrated at that point, then that point will have the same stiffness load effect as the actual stiffness load effect of the object.

[0167] In inertial load factor In this case, the radius of gyration represents the radial distance to a point. If the inertial load is concentrated at that point, then that point will have the same inertial load effect as the actual inertial load effect of the object.

[0168] Therefore, the radius of gyration, as defined more generally in this disclosure, represents a convenient measure of the radial effect of these load factors. The radius of gyration will be defined by the specific geometry of the cylindrical element, but it is generally assumed that the radius of gyration has upper and lower limits defined by the maximum and minimum radial extent of the cylindrical element from the axis of rotation, and that when the cylindrical element vibrates torsionally about its axis, the radius of gyration is equal to the radius of the cylindrical element. Because all surface loads occur at the cylindrical surface, all surface loads are at a distance from the axis. Place.

[0169] Figure 20 The radius is shown The first cylinder 520 rotates to twist about a longitudinal axis 25 passing through its center. The cylinder has a length about its axis of rotation. The length is long enough such that the area of ​​its end portion ( The area of ​​the curved side is smaller than the area of ​​the curved side. ), and among them, ,and Damping factor Stiffness load factor and inertial load factor It can be written as: Equation 38 Equation 39 Equation 40

[0170] While geometric damping induced by radial wave propagation has advantages due to its dependence on geometric parameters rather than fluid properties, the conditions for geometric damping necessitate the use of cylindrical elements with small radii, resulting in a smaller effective surface area. Small values ​​in the damping factor, stiffness factor, and inertial load factor contribute to this. This means that even at high viscosity, the damping factor, elastic factor, or inertial load factor from torsional vibrations are very small.

[0171] Figure 20 A second cylinder 530 with the same dimensions as the first cylinder 520 is also shown, wherein the second cylinder 530 is larger than... offset radius The second cylinder 530 is offset perpendicularly to the axis 525 of the first cylinder 520. The second cylinder 530 also undergoes torsional vibration about the axis 525 of the first cylinder 520. This results in a radius of gyration... from (The distance from the cylinder surface to the axis 525) is changed to The effect of (radial offset of the cylinder as a whole).

[0172] If the above is the damping factor Stiffness load factor and inertial load factor If the provided equation holds under geometric damping (i.e., non-geometric damping is negligible), then the equation can be expressed as: Equation 41 Equation 42 Equation 43

[0173] if Greater than By causing the vibration of the cylindrical element to deviate from the axis, the load factor will be amplified. and The square of the ratio, that is, the magnification factor is .exist In this case, the loading factor is amplified. ,Right now, and The ratio to the fourth power.

[0174] However, these equations hold only when the cylindrical element has geometric damping. By shifting the cylindrical element, it no longer undergoes pure torsional vibration, but rather transverse vibration at the displacement distance. These load factor equations no longer apply automatically because, under transverse vibration, the cylindrical element may form a dipole wave field rather than a monopole wave field.

[0175] Figure 22 This illustrates the generation of a dipole wave field by a cylindrical element under transverse vibration. In the dipole wave field, there is a 180° phase difference between the wave fields on each side of the cylindrical element. The formation of the dipole wave field presents a problem because the resulting wave is a pressure (P) wave rather than a shear (S) wave. The hydrodynamics of pressure waves differs from that of shear waves, therefore the relationships previously defined for shear waves no longer apply.

[0176] For example, a different damping factor is defined for shear waves compared to pressure waves. For shear waves, the shear rate and the stress generated by the shear rate result in a relatively well-defined and controllable damped wave. In contrast, pressure waves follow what is called 'secondary damping,' where the damping force is proportional to the square of the velocity. This produces a damping factor of the following form: Equation 44 in, It is a constant. It is velocity. In other words, the damping factor changes unfavorably with vibration velocity.

[0177] However, if the Reynolds number remains low, a monopole wave field can be maintained. The Reynolds number represents the ratio between inertial forces and viscous forces. As the Reynolds number decreases, the viscous force increases relative to the inertial force.

[0178] Figure 23Laminar flow around a cylinder vibrating in a left-right direction perpendicular to its axis is illustrated. In laminar flow, the force between the two sides of the cylinder becomes shear force, and thus shear waves propagate due to transverse vibration. Without being bound by theory, it is assumed that laminar flow makes the inertial force sufficiently small relative to the viscous force, such that the wave field is primarily or at least partially defined by shear waves generated from the upper and lower portions of the cylinder's cross-section (i.e., perpendicular to the axis and the direction of vibration). Therefore, as the Reynolds number decreases, the degree to which the wave field exhibits a dipole shape decreases, while the degree to which the wave field exhibits a monopole shape increases. Low Reynolds numbers recover part of the shear wave field, which remains in phase throughout its propagation space. The advantages of geometric damping are retained, along with the advantage of an increased load factor due to deflecting the element off-axis.

[0179] Advantageously, because relatively low Reynolds numbers are easily achieved at small scales, cylindrical elements with relative axis displacement can achieve a relatively high degree of scaling up with minimal increase in size and weight. In some embodiments of the technology disclosed herein, fluid load factors comparable to those of larger and heavier vibrating elements can be achieved.

[0180] It is further recognized that relatively low Reynolds numbers can be readily achieved for almost all fluids of interest, regardless of their physical properties. Submicron needle-like structures on a vibrating substrate can form the same radial displacement elements discussed above and obtain the same geometric damping benefits. Some implementations may feature multiple cylindrical or quasi-cylindrical elements (such as pins and columns) formed through micro- and nano-fabrication processes, allowing the micro-surface to exhibit a high fluid loading factor.

[0181] It is further recognized that low Reynolds numbers may result in the wavefield being only partially confined by shear waves. Therefore, the expression for the load factor under geometrically damped conditions may differ from the expressions above, but it may be proportional to these expressions, with the proportionality constant depending on the degree to which the wavefield is confined by shear waves. The proportionality constant is introduced in the following expressions. If the wave field is completely defined by shear waves, then The value is 1, and if 50% of the wave field is confined by shear waves, then The value is 0.5, which may be a reasonable assumption in practice: Equation 45 Equation 46 Equation 47

[0182] If we assume If the expression is 0.5, then the above expression simplifies to: Equation 48 Equation 49 Equation 50

[0183] In the context of this disclosure, a 'low' Reynolds number means a Reynolds number low enough to result in laminar flow, and the flow, due to vibration, is characterized to some extent by a shear wave field and, at least to some extent, by the advantage of geometric damping. It is recognized that the transition from laminar to turbulent flow occurs within a range of Reynolds number values, and the precise extent to which this transition occurs depends on the geometry. Lower Reynolds numbers are more likely to result in flow behavior with a partial shear wave field than higher Reynolds numbers. Without being limited to theory, it is considered that the degree of development of the shear wave field and some of the advantages of the techniques of this disclosure obtained thereby depend on the Reynolds number. For example, a Reynolds number of 1000 may exhibit some degree of laminar-like flow and produce a shear wave field to some extent. A Reynolds number of 100 may exhibit even higher degrees of laminar-like flow and produce a shear wave field to even higher degrees. A Reynolds number of 10 may exhibit even higher degrees of laminar-like flow and produce a shear wave field to even higher degrees. A Reynolds number of 1 may exhibit even higher degrees of laminar-like flow and produce a shear wave field to even higher degrees. Generally speaking, a lower Reynolds number may be preferred, but it should be recognized that other technical considerations must be weighed when achieving the lowest possible Reynolds number.

[0184] Provided that the geometric damping condition is met, the propagation depth of the wave is determined by the geometry of the cylindrical element, especially its radius.

[0185] Given the foregoing discussion of geometric damping, the surface of the radiator or detector can be the surface of or comprise an elongated member. Such an elongated member may be characterized by a width, a half-width equal to half the width, and a length greater than the width, wherein the half-width is less than the propagation depth of the shear wave in the fluid at the vibration frequency, more preferably less than 50% of the propagation depth. This elongated member may be non-collinear or offset from the vibration axis (such as a torsional vibration axis). During vibration, the fluid flow around the elongated member can be laminar.

[0186] In some embodiments, the half-width of the elongated member is less than 75% of the propagation depth, optionally less than 60%, optionally less than 50%, optionally less than 40%, optionally less than 25%, optionally less than 10%, optionally less than 5%, optionally less than 2%, optionally less than 1%, or optionally less than 0.5%.

[0187] In some embodiments, the elongated member has a substantially or completely circular cross-section along 50%, 70%, 90%, or 100% of its length. Optionally, the roundness of the cross-section of the elongated member along 50%, 70%, 90%, or 100% of its length is in the range of 0.75 to 1, optionally in the range of 0.8 to 1, optionally in the range of 0.85 to 1, optionally in the range of 0.9 to 1, optionally in the range of 0.95 to 1, more preferably in the range of 0.9 to 1, optionally in the range of 0.95 to 1, wherein the roundness of the cross-sectional shape is determined by... Calculation, where It is the convex area of ​​the cross-sectional shape, and It is the circumference of the convex shape of the cross-section.

[0188] In some embodiments, the half-width of the elongated member, calculated at a point along its length, is based on the convex perimeter or convex area of ​​the cross-section of the elongated member along its length at that point. Optionally, the half-width is the convex perimeter based on the shape of the cross-section, expressed by an expression. Calculated. Alternatively, the half-width can be the convex area based on the shape of the cross-section via an expression. Calculated. If the slender member has a circular cross-section, both expressions yield the radius of the circle, therefore the half-width of the circular cross-section is the radius of the circle.

[0189] In some embodiments, the elongated member has a constant cross-section for more than 50%, more than 60%, more than 70%, more than 80%, more than 90%, or 100% of its length.

[0190] In some embodiments, the elongated member has a constant cross-section only along less than 50%, less than 40%, less than 30%, less than 20%, or less than 10% of its length, or has a continuously varying cross-section along its length.

[0191] In some embodiments, the area of ​​the cross-section increases or decreases monotonically along the length of the elongated member.

[0192] In some embodiments, the elongated member is straight.

[0193] In some embodiments, the elongated member is symmetrical about its length axis.

[0194] In some embodiments, the elongated member is not straight. For example, the elongated member may include a closed loop.

[0195] In some embodiments, the elongated member includes one of the following: a cylinder, a cone, a frustum of a cone, a torus, and an arcuate portion of the torus.

[0196] In some embodiments, the half-width of the elongated member that is less than the propagation depth is the maximum half-width along the length of the elongated member.

[0197] In some embodiments, the half-width of the elongated member less than the propagation depth is the average half-width along the length of the elongated member. Optionally, the average half-width is calculated as the arithmetic mean of the half-widths along the length of the elongated member, or as the average half-width calculated as twice the volume of the elongated member divided by the surface area of ​​the elongated member.

[0198] In some embodiments, the width of the elongated member is greater than 0.5 mm, and / or greater than 1 mm, and / or greater than 2 mm, and / or greater than 5 mm, and / or greater than 10 mm, and / or greater than 20 mm, and / or greater than 50 mm.

[0199] In some embodiments, the length of the elongated member is greater than a multiple of half the width of the elongated member (half the width is half the width of the elongated member), and wherein the multiple is one of the following: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 45, or 50. In other words, the length of the elongated member can be greater than a multiple of the width of the elongated member, wherein the multiple is one of the following: 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10, 12.5, 15, 17.5, 20, 22.5, and 25.

[0200] In some embodiments, the width of the elongated member is between 1 nm and 500 nm. This embodiment can be described as a 'nanoscale' or nanoscale embodiment. In some other embodiments, the width of the elongated member is between 500 nm and 500 μm. This embodiment can be described as a 'micrometer-scale' or micrometer-scale embodiment. A suitably sized device (which can be a nanometer-scale or micrometer-scale device) can vibrate at a lower frequency to advantageously measure the fluid properties of low-viscosity fluids (such as less than 1 mPa·s), or it can vibrate at a higher frequency to advantageously measure the fluid properties of low-viscosity fluids (such as less than 1 mPa·s), because at such a small scale, the width of the elongated member is still small relative to the propagation depth at such a high frequency.

[0201] In some embodiments, the vibratory transducer element includes a shaft having a longitudinal axis, wherein an elongated member is connected to the shaft, and wherein the elongated member is not collinear with the longitudinal axis of the shaft. Optionally, during vibration of the vibratory transducer element at a vibration frequency, the fluid flow around the elongated member is laminar. Alternatively or additionally, the Reynolds number Re of the fluid flow around the elongated member is less than 1, wherein the Reynolds number is equal to... ,in, It is the viscosity of the fluid. It is the density of the fluid. It is half the width of the slender member, and It is the maximum (vibrational) velocity of the elongated member relative to the fluid during the vibration of the vibrating transducer, wherein, optionally, the Reynolds number is less than 1000, or less than 300, or less than 100, or less than 30, or less than 10, or less than 3, or less than 1, or less than 0.9, or less than 0.8, or less than 0.75, or less than 0.7, or less than 0.6, or less than 0.5, or less than 0.4, or less than 0.3, or less than 0.25, or less than 0.2, or less than 0.1. Alternatively or additionally, the elongated member may have a first end and a second end, wherein one or both of the first end and the second end are spaced apart from the longitudinal axis of the shaft by an offset distance greater than half the width of the elongated member, wherein, optionally, the offset distance is greater than a multiple of the width, and the multiple is 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 30, or 50. Alternatively or additionally, the vibration transducer element may include a plurality of elongated members connected to a shaft, each elongated member being non-collinear with the axis of the shaft, each elongated member having a half-width less than the propagation depth of the shear wave in the fluid at the vibration frequency, and wherein, optionally, the half-width of a first elongated member of the plurality of elongated members differs from the half-width of a second elongated member of the plurality of elongated members, and wherein, optionally, two, three, four, five or more elongated members of the plurality of elongated members may uniquely have different half-widths. Alternatively or additionally, the elongated member may include a first end and a second end, wherein the elongated member is connected to the shaft at the first end, and optionally also at the second end. Alternatively or additionally, the shaft may include a vibrating hammer, and the elongated member may be connected to the shaft at the vibrating hammer.

[0202] Nevertheless, the techniques disclosed herein do not require the use of elongated members exhibiting geometric damping as described herein and in GB2207881.0, filed May 27, 2023. For example, the secondary oscillator (subsystem) may instead comprise any system configured to vibrate and resonate within a fluid, including all such vibrating devices known in the art, including but not limited to: torsion discs, torsion pendulums, tuning forks, and cantilever beams.

[0203] According to the technique described herein, a vibratory transducer can be used to determine the physical properties of a fluid by vibrating the transducer at a vibrational frequency in the fluid and determining a quantity indicating the degree of damping based on the vibration. For example, to measure viscosity, the Q-factor of the vibration can be determined. The Q-factor is a dimensionless parameter indicating the damping level of the resonator, where the damping level is a function of viscosity. In particular, it indicates the degree of underdamping of the resonator. In a frequency response curve, a high Q-factor provides a high and narrow peak at the resonant frequency, while a low Q-factor provides a low and wide peak. Since the peak width varies with damping, the Q-factor can be defined as the ratio of the resonant frequency to the resonant bandwidth. Equation 51 in, Resonant frequency (Unit: radians per second), and Full width at half maximum (FWHM) is the bandwidth where the power of the vibration is greater than half of the maximum value (or equivalently, the amplitude of the vibration is greater than the maximum amplitude at resonance divided by √2), i.e., the bandwidth between 3 dB points. Fluid viscosity is a function of the Q factor.

[0204] It is important to note that measuring viscosity at the vibration frequency or its corresponding frequency may involve amplitude measurements at more than one frequency to estimate the Q factor, but only a single viscosity measurement is obtained at the frequency corresponding to the resonant frequency. For example, the bandwidth can be determined based on the frequency required to reduce the amplitude to 1 / √2 times the maximum amplitude at resonance. As a non-limiting example, the frequency required to reduce the amplitude to 1 / √2 times the maximum amplitude at resonance can be determined by performing a frequency sweep near the resonant frequency, but those skilled in the art will recognize that the 3dB point frequency can be identified by various other techniques.

[0205] Another method to determine the Q factor is to measure the amplitude of the vibration at a series of frequencies near the resonant frequency and fit the frequency and amplitude values ​​(or their logarithms) to a parabola using the least squares method. The 3dB point can then be obtained as the solution to the quadratic equation of the best-fit parabola based on the measurement results.

[0206] Another method for determining the Q-factor is through logarithmic decay. By stopping the drive of the transducer and measuring the decay of the vibration, the Q-factor can be determined by monitoring the time series of the vibration and calculating the natural logarithm of the ratio of two consecutive peaks A1 and A2 using the following expression: Equation 52

[0207] As discussed above, the loss factor is the reciprocal of the Q factor, and therefore can be easily determined based on the methods described above.

[0208] According to the technology of this disclosure, a means for causing one or more vibration transducers to vibrate may include an electronic device configured to provide a control signal to the one or more vibration transducers to cause the one or more vibration transducers to vibrate in a fluid in a manner according to the technology of this disclosure.

[0209] According to the technology disclosed herein, an apparatus for determining the material properties of a viscoelastic fluid based on the vibration of one or more vibrating transducers may include an electronic device configured to record and process measurements of the vibration of the one or more vibrating transducers to determine the material properties.

[0210] The device for vibrating one or more vibrating transducers and the device for determining the material properties of a viscoelastic fluid based on one or more vibrating transducers can be the same electronic device (i.e., a single electronic device causes vibration and determines material properties) or different electronic devices.

[0211] Figure 24 A flowchart is shown corresponding to a method for determining one or more material properties of a viscoelastic fluid according to the techniques of this disclosure.

[0212] In the first step 610, the method includes vibrating a vibrating transducer in a viscoelastic fluid, the vibrating transducer including a plurality of oscillators, the plurality of oscillators including a first oscillator and a second oscillator, wherein the first oscillator is coupled to the second oscillator such that vibration of the first oscillator causes the second oscillator to vibrate relative to the first oscillator in the viscoelastic fluid.

[0213] In the second step 620, the method includes performing one or more measurements indicating the frequency response of the coupled vibration of the first oscillator and the second oscillator, the results of which include one or more of the following: resonant frequency, vibration amplitude, loss factor, and Q factor.

[0214] In the third step 630, the method includes determining one or more material properties of the viscoelastic fluid based on one or more measurements indicating the frequency response of the coupled vibrations of the first oscillator and the second oscillator, wherein the material properties include one or more of the following: density indication, viscosity indication, and elasticity indication.

[0215] This method can be performed using an apparatus according to the technology of this disclosure. Such an apparatus includes: one or more vibration transducers, each of which includes a plurality of oscillators, the plurality of oscillators including a first oscillator and a second oscillator for contacting a viscoelastic fluid, wherein the first oscillator is coupled to the second oscillator such that vibration of the first oscillator causes the second oscillator to vibrate relative to the first oscillator in the viscoelastic fluid; and a controller configured to: cause the one or more vibration transducers to vibrate in the viscoelastic fluid; obtain one or more measurements indicative of the frequency response of the coupled vibration of the first and second oscillators, the one or more measurements including one or more of the following: resonant frequency, vibration amplitude, loss factor, and Q factor; and determine one or more material properties of the viscoelastic fluid based on the one or more measurements indicative of the frequency response of the coupled vibration of the first and second oscillators, wherein the material properties include one or more of the following: density indication, viscosity indication, and elasticity indication. The controller may be implemented as an electronic device (such as a general-purpose computer) or using special-purpose circuitry (such as an application-specific integrated circuit or a field-programmable gate array), or using some combination of the above methods.

[0216] In the context of this disclosure, when one frequency is within a percentage of another frequency, that frequency can be higher or lower than the other frequency, and within a percentage of the other frequency; for example, for frequency and ,if exist If it is within 20%, then .

[0217] Those skilled in the art will further recognize that the various illustrative logic blocks, configurations, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or a combination of both. To clearly illustrate this interchangeability between hardware and software, various illustrative components, blocks, configurations, modules, circuits, and steps have been described above in general terms of their functionality. Whether such functionality is implemented as hardware or software depends on the specific application and the design constraints imposed on the system as a whole. Those skilled in the art can implement the described functionality in different ways for each specific application, but such implementation decisions should not be construed as departing from the scope of this disclosure.

[0218] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be embodied directly in hardware, in a software module executed by a processor, or in a combination of both. The software module can reside in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, removable disks, compressed optical disc read-only memory (CD-ROM), or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read information from and write information to the storage medium. Alternatively, the storage medium can be a component of the processor. The processor and storage medium can reside in an application-specific integrated circuit (ASIC). The ASIC can reside in a computing device or user terminal. Alternatively, the processor and storage medium can reside as discrete components in a computing device or user terminal.

Claims

1. A method for determining one or more material properties of a viscoelastic fluid, the method comprising: One or more vibratory transducers are vibrated in the viscoelastic fluid, each of the one or more vibratory transducers including a plurality of oscillators, the plurality of oscillators including a first oscillator and a second oscillator, wherein the first oscillator is coupled to the second oscillator such that vibration of the first oscillator causes the second oscillator to vibrate relative to the first oscillator in the viscoelastic fluid. Obtain one or more measurement results indicating the frequency response of the coupled vibration of the first oscillator and the second oscillator, the one or more measurement results including one or more of the following: resonant frequency, vibration amplitude, loss factor and Q factor; One or more material properties of the viscoelastic fluid are determined based on the frequency response of the coupled vibrations of the first oscillator and the second oscillator, wherein the material properties include one or more of the following: density indication, viscosity indication, and elasticity indication.

2. The method according to claim 2, wherein, Vibrating the one or more vibration transducers includes causing a first oscillator of the vibration transducer to vibrate at a frequency within 20% (optionally, within 10%) of the natural frequency of a second oscillator of the vibration transducer.

3. The method according to claim 1 or 2, wherein, Vibrating the one or more vibration transducers includes causing a first oscillator of the vibration transducer to vibrate at a frequency exceeding 150% (optionally, exceeding 200%) of the natural frequency of a second oscillator of the vibration transducer.

4. The method according to any of the preceding claims, in, Vibrating the one or more vibrating transducers includes vibrating a first oscillator of the vibrating transducer at a first frequency within 20% (optionally, within 10%) of the natural frequency of the second oscillator of the vibrating transducer, or vibrating the first oscillator of the vibrating transducer at a first frequency less than 50% of the natural frequency of the second oscillator of the vibrating transducer. The vibration of the one or more vibrating transducers includes causing a first oscillator of the vibrating transducer to vibrate at a second frequency exceeding 150% (optionally, exceeding 200%) the natural frequency of a second oscillator of the vibrating transducer. Determining the one or more material properties includes combining the results obtained from measurements at the first frequency with the results obtained from measurements at the second frequency to reduce common-mode error.

5. The method according to claim 4, wherein, Combining the results obtained from measurements at the first driving frequency with the results obtained from measurements at the second driving frequency includes obtaining the difference, weighted difference, or ratio of the results to reduce common-mode error.

6. The method according to claim 5, wherein, The result obtained by combining the measurement results from the first driving frequency with the measurement results from the second driving frequency includes the difference, weighted difference, or ratio of the measurement results for obtaining the resonant frequency.

7. The method according to any one of claims 4 to 6, comprising vibrating the same vibrating transducer at the first frequency and the second frequency.

8. The method according to any one of claims 4 to 6, comprising causing a first vibrating transducer to vibrate at the first frequency and causing a second vibrating transducer to vibrate at the second frequency.

9. The method according to any of the preceding claims, in, The one or more vibration transducers are made to vibrate in the viscoelastic material at multiple frequencies, and corresponding multiple loss factor measurement results are obtained; The method further includes determining the composition of the viscoelastic material based on the measurement results of the multiple loss factors.

10. The method according to claim 9, wherein, Determining the composition of the viscoelastic material includes: determining one or more values ​​indicating the loss factor curve of the viscoelastic material based on the multiple loss factor measurement results, and comparing the one or more values ​​with multiple stored values ​​of multiple different materials.

11. The method according to any of the preceding claims, wherein, The first and second oscillators of the vibration transducer vibrate in one of the following modes: torsional mode, transverse mode, or longitudinal mode, wherein the first oscillator vibrates in a mode different from that of the second oscillator.

12. The method according to claim 11, wherein, The first oscillator vibrates in the torsional mode, while the second oscillator vibrates in the transverse mode.

13. The method according to any of the preceding claims, wherein, The second oscillator of the vibration transducer includes an elongated component.

14. The method according to claim 13, wherein, The elongated member is characterized by its width and length, wherein the width is between 0.1 mm and 5 mm, and wherein the length is at least five times the width.

15. The method according to claim 13, wherein, The elongated member is characterized by a width, a half-width equal to half of the width, and a length greater than the width, wherein the half-width is less than the propagation depth of the shear wave in the fluid at the vibration frequency of the second oscillator, wherein the propagation depth of the shear wave is the distance by which the amplitude of the shear wave propagating in the fluid at the vibration frequency of the second oscillator is reduced by a factor of 1 / e.

16. The method according to any one of claims 13 to 15, wherein, Vibrating the transducer includes vibrating the main oscillator about a longitudinal axis in a torsional mode, wherein the elongated member of the second oscillator has a first end and a second end, wherein one or both of the first end and the second end are spaced apart from the longitudinal axis by an offset distance greater than half the width of the elongated member.

17. The method according to any one of claims 13 to 16, wherein, The elongated member extends in a direction that is substantially parallel or substantially perpendicular to the longitudinal axis of the first oscillator.

18. The method according to any of the preceding claims, wherein, Vibrating the one or more vibrating transducers in the viscoelastic fluid includes: vibrating the one or more vibrating transducers in the flowing viscoelastic fluid.

19. An apparatus for determining one or more material properties of a viscoelastic fluid, the apparatus comprising: One or more vibration transducers, each of the one or more vibration transducers including a plurality of oscillators, the plurality of oscillators including a first oscillator and a second oscillator for contacting the viscoelastic fluid, wherein the first oscillator is coupled to the second oscillator such that vibration of the first oscillator causes vibration of the second oscillator relative to the first oscillator in the viscoelastic fluid; and The controller is configured to: The one or more vibratory transducers are made to vibrate in the viscoelastic fluid; Obtain one or more measurement results indicating the frequency response of the coupled vibration of the first oscillator and the second oscillator, the one or more measurement results including one or more of the following: resonant frequency, vibration amplitude, loss factor and Q factor; One or more material properties of the viscoelastic fluid are determined based on the frequency response of the coupled vibrations of the first oscillator and the second oscillator, wherein the material properties include one or more of the following: density indication, viscosity indication, and elasticity indication.

20. The device according to claim 19, wherein, Vibrating the one or more vibration transducers includes causing a first oscillator of the vibration transducer to vibrate at a frequency within 20% (optionally, within 10%) of the natural frequency of a second oscillator of the vibration transducer.

21. The device according to claim 19 or 20, wherein, Vibrating the one or more vibration transducers includes causing a first oscillator of the vibration transducer to vibrate at a frequency exceeding 150% (optionally, exceeding 200%) of the natural frequency of a second oscillator of the vibration transducer.

22. The device according to any one of claims 19 to 21, in, Vibrating the one or more vibrating transducers includes vibrating a first oscillator of the vibrating transducer at a first frequency within 20% (optionally, within 10%) of the natural frequency of the second oscillator of the vibrating transducer, or vibrating the first oscillator of the vibrating transducer at a first frequency less than 50% of the natural frequency of the second oscillator of the vibrating transducer. The vibration of the one or more vibrating transducers includes causing a first oscillator of the vibrating transducer to vibrate at a second frequency exceeding 150% (optionally, exceeding 200%) the natural frequency of a second oscillator of the vibrating transducer. Determining the one or more material properties includes combining the results obtained from measurements at the first frequency with the results obtained from measurements at the second frequency to reduce common-mode error. Combining the results obtained from measurements at the first driving frequency with the results obtained from measurements at the second driving frequency includes obtaining the difference, weighted difference, or ratio of the results to reduce common-mode error.

23. The device according to claim 22, wherein, The controller is configured to cause the same vibration transducer to vibrate at the first frequency and the second frequency.

24. The device according to claim 22, comprising a plurality of vibration transducers, wherein the plurality of vibration transducers includes a first vibration transducer and a second vibration transducer, wherein, The controller is configured to cause the first vibration transducer to vibrate at the first frequency and the second vibration transducer to vibrate at the second frequency.

25. The device according to any one of claims 19 to 24, in, The controller is configured to cause the one or more vibration transducers to vibrate at multiple frequencies in the viscoelastic material and to obtain corresponding multiple loss factor measurements. The controller is further configured to determine the composition of the viscoelastic material based on the results of the multiple loss factor measurements.

26. The device according to claim 25, wherein, Determining the composition of the viscoelastic material includes: determining one or more values ​​indicating the loss factor curve of the viscoelastic material based on the multiple loss factor measurement results, and comparing the one or more values ​​with multiple stored values ​​of multiple different materials.

27. The device according to any one of claims 19 to 26, wherein, The first oscillator and the second oscillator of the vibration transducer are both configured to vibrate in one of the following modes: torsional mode, transverse mode, or longitudinal mode, wherein the first oscillator is configured to vibrate in a mode different from that of the second oscillator.

28. The device according to any one of claims 19 to 27, wherein, The second oscillator of the vibration transducer includes an elongated component.

29. The device according to claim 28, wherein, The elongated member is characterized by its width and length, wherein the width is between 0.1 mm and 5 mm, and wherein the length is at least five times the width.

30. The device according to claim 28, wherein, The elongated member is characterized by a width, a half-width equal to half of the width, and a length greater than the width, wherein the half-width is less than the propagation depth of the shear wave in the fluid at the vibration frequency of the second oscillator, wherein the propagation depth of the shear wave is the distance by which the amplitude of the shear wave propagating in the fluid at the vibration frequency of the second oscillator is reduced by a factor of 1 / e.

31. The device according to any one of claims 28 to 30, wherein, The vibration transducer is configured to cause the main oscillator to vibrate in a torsional mode about a longitudinal axis, wherein the elongated member of the second oscillator has a first end and a second end, wherein one or both of the first end and the second end are spaced apart from the longitudinal axis by an offset distance greater than half the width of the elongated member.

32. The device according to claim 31, wherein, The elongated member extends in a direction that is substantially parallel or substantially perpendicular to the longitudinal axis of the first oscillator.

33. An apparatus for determining one or more material properties of a viscoelastic fluid, the apparatus comprising: A device for causing one or more vibratory transducers to vibrate in a viscoelastic fluid, each of the one or more vibratory transducers including a plurality of oscillators, the plurality of oscillators including a first oscillator and a second oscillator, wherein the first oscillator is coupled to the second oscillator such that vibration of the first oscillator causes the second oscillator to vibrate in the viscoelastic fluid relative to the first oscillator. A means for obtaining one or more measurement results indicating the frequency response of the coupled vibration of the first oscillator and the second oscillator, the one or more measurement results including one or more of the following: resonant frequency, vibration amplitude, loss factor and Q factor; A means for determining one or more material properties of the viscoelastic fluid based on one or more measurements indicating the frequency response of the coupled vibrations of the first oscillator and the second oscillator, wherein the material properties include one or more of the following: density indication, viscosity indication, and elasticity indication.

Images