Method, apparatus, and non-temporary computer-readable medium for measuring the material properties of viscoelastic fluids using one or more vibration transducers

Abstract

A method for measuring the material properties of a viscoelastic fluid using one or more vibrating transducers, the method comprising: vibrating one or more vibrating transducers within the viscoelastic fluid so as to generate a first wave propagating from a first surface of the one or more vibrating transducers and a second wave propagating from a second surface of the one or more vibrating transducers; during vibration of the one or more vibrating transducers, the first surface and the second surface being spaced apart from and oriented with respect to each other such that the first wave and the second wave combine with each other to produce a final constructive or destructive interference; and determining the material properties of the viscoelastic fluid based on the vibration of the one or more vibrating transducers within the viscoelastic fluid.

Description

Technical Field

[0001] The present disclosure relates to the attenuation of vibrations in a fluid, including the use of attenuation to obtain measurements of the physical and rheological properties of materials, such as the measurement of viscosity. Background

[0002] The physical and rheological properties of a fluid can be measured by applying a vibration stimulus to the fluid and observing the mechanical response of the fluid. From the observed mechanical response of the fluid (e.g., the degree of attenuation and / or stiffness, and / or the resonance frequency), measurements of fluid properties such as viscosity, density, storage modulus, loss modulus, and loss tangent can be obtained.

[0003] As an example, the degree of attenuation may be determined from the amplitude of the vibration or a change in amplitude, the resonance frequency or a change in resonance frequency, the attenuation rate of the vibration, or the quality (Q) factor, or the loss factor which is the reciprocal of the quality factor.

[0004] A resonance viscometer measures viscosity by determining the attenuation effect of a viscous fluid on a mechanical oscillator immersed in the fluid. When viscosity is present, the shear stress on the oscillator surface increases. The shear stress generates an attenuation force, and energy dissipates from the oscillator. In the case of a mechanical oscillator operating in a resonant state, this causes a decrease in the Q factor at resonance. Thus, the Q factor is an inverse indicator of viscosity. The loss factor is the reciprocal of the Q factor, and thus the loss factor increases as the viscosity increases. Conventionally, resonance viscometers have been shown to function properly for purely viscous fluids and slightly viscoelastic fluids (non-Newtonian fluids) with a tan Δ (i.e., loss tangent) greater than 1 (i.e., their loss factors effectively change in accordance with the viscosity of the fluid).

[0005] The loss tangent is represented by the following equation. tan Δ = ωμ’ / G’, where ω is the angular frequency of the vibration, μ’ is the dynamic viscosity of the fluid, and G’ is the storage modulus of the fluid.

[0006] Newtonian fluids are purely viscous, i.e., they have no elastic behavior. There is no storage modulus. The loss tangent tanΔ is infinite. Examples of such fluids are water, aqueous solutions, sugar syrups, alcohols, most pure oils, most hydrocarbons, and gases.

[0007] Non-Newtonian fluids may be viscoelastic, in which case tanΔ < ∞. Examples of viscoelastic fluids include blood, suspensions, emulsions, and most synthetic materials. Strongly viscoelastic fluids may have tanΔ < 1. Examples of strongly viscoelastic fluids include liquid polymers, polymer melts, rubber solutions, synthetic oils, detergents, and foods. Overview

[0008] According to a first aspect, a method for measuring the material properties of a viscoelastic fluid using one or more vibrating transducers is described, the method comprising: vibrating one or more vibrating transducers within the viscoelastic fluid so as to generate a first wave propagating from a first surface of the one or more vibrating transducers and a second wave propagating from a second surface of the one or more vibrating transducers, wherein during vibration of the one or more vibrating transducers, the first surface and the second surface are spaced apart from and oriented relative to each other such that the first wave and the second wave combine with each other to produce a final constructive or destructive interference at one or both of the first surface and the second surface; determining the material properties of the viscoelastic fluid based on the vibration of the one or more vibrating transducers within the viscoelastic fluid; and including.

[0009] According to a further aspect, a non-transitory computer-readable medium storing instructions is provided, the instructions causing one or more processors of a system comprising one or more vibrating transducers to perform the above method when executed by the one or more processors.

[0010] According to a further aspect, an apparatus for measuring the material properties of a viscoelastic fluid using one or more vibrating transducers is described, the apparatus comprising: One or more oscillating transducers, comprising a first surface and a second surface, Means for causing the one or more oscillating transducers to oscillate such that when oscillated in a viscoelastic fluid, a first wave propagating from the first surface of the one or more oscillating transducers is generated and a second wave propagating from the second surface of the one or more oscillating transducers is generated, and during the oscillation of the one or more oscillating transducers, the first wave and the second wave combine with each other to cause final constructive or destructive interference on one or both of the first surface and the second surface, wherein the first surface and the second surface are spaced apart from each other and oriented, Means for determining the material properties of the viscoelastic fluid, including final constructive or destructive interference, based on the oscillation of the one or more oscillating transducers in the viscoelastic fluid Comprising.

Brief Description of the Drawings

[0011] The present invention will be described in more detail by way of example only with reference to the accompanying drawings.

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[0012] Figure 1 shows a shear wave generated from the oscillating surface of a fluid and is presented as a graph of velocity V against distance x from the surface. The amplitude of the fluid velocity decays as the distance x from the surface increases. The velocity at the surface is V 0 is.

[0013] The degree of change in velocity with respect to distance x represents the velocity gradient and is also known as the shear velocity.

Number

[0014] The velocity gradient or shear velocity at the oscillating surface is important in determining the damping force generated at the oscillating surface via the shear stress τ and is expressed as follows.

Number

[0015] "Work done" occurs due to the shear stress and the oscillatory displacement of the surface, leading to the dissipation of energy. Since the Q factor can be understood to represent the ratio of the energy lost to the energy stored in the oscillation of the resonator, as the shear stress increases, the energy dissipation increases, the Q factor decreases, and the loss factor, which is the reciprocal of the Q factor, increases. Therefore, the measured loss factor or Q factor indicates the degree of viscosity. However, it also depends on the shear velocity at the surface.

[0016] The propagation depth of the shear wave is the distance at which the amplitude of the shear wave decreases to a factor of 1 / e of the initial amplitude (where e is the base of the natural logarithm and 1 / e is approximately 0.37). This value is sometimes referred to as the "penetration depth" or "skin depth".

[0017] The shear velocity at the surface varies inversely with the propagation depth.

Number

[0018] Propagation depth x 0 may be expressed as follows.

Number

[0019] The propagation depth depends strongly on viscosity and elasticity through the loss angle Δ. The propagation depth also depends on frequency and density, but these are relatively invariant.

[0020] When the elasticity is high, the shear rate is unfavorably distorted. As the elasticity increases, the propagation depth becomes longer, and thus the shear rate decreases. This causes a change in the loss coefficient (or Q factor) for estimating viscosity. This means that significant errors can occur when measuring viscosity, especially in the case of highly non-Newtonian fluids.

[0021] Figure 2 shows a simple model representing a viscoelastic fluid as a spring and damper system. The apparent viscosity μ * has the unit of Pa·S and depends on the dynamic viscosity μ’ (unit of Pa·S), the storage modulus G’ representing elasticity (unit of Pa), and the angular frequency ω (unit of s-1), and is expressed by the following equation.

Number

[0022] The loss modulus G’’ has the unit of Pa and is the product of the dynamic viscosity μ’ and the angular frequency ω.

[0023] The loss tangent is expressed as follows.

Number

[0024] The techniques of the present disclosure utilize the fact that the propagation depth of shear waves depends on the viscosity and elasticity of the fluid. The two surfaces are separated by a gap that allows waves to transition between the primary vibrating surface used as a detector and the secondary vibrating surface used as an irradiator. The primary surface is irradiated by the secondary surface. These surfaces can be (e.g., rigidly) connected to the same oscillator / resonator or can be separate oscillators / resonators.

[0025] The effective or dominant shear rate at the detector surface is modified by the waves radiated from the irradiating surface. The extent to which the shear rate is modified depends on the irradiation intensity and the relative phase between the incident wave near the detector and the shear wave radiated from the detector.

[0026] The irradiation intensity or amplitude of the irradiating shear wave at the detector varies based on the propagation depth and the distance between the primary and secondary surfaces. The phase of the irradiating shear wave at the detector depends on the wavelength of the shear wave in the fluid and the distance between the primary and secondary surfaces. Both the irradiation intensity and the relative phase vary with the dynamic viscosity μ’ and the storage modulus G’. The combination of the shear wave radiated from the detector and the shear wave irradiated at the detector can cause constructive or destructive interference.

[0027] The final destructive interference at the detector occurs when the relative phase between the shear waves at the detector is such that the instantaneous velocity of the shear waves has opposite signs and leads to a lower effective shear rate (e.g., 5% lower, 10% lower, 20% lower, 30% lower, 40% lower, or 50% lower) than that experienced in the absence of the irradiating shear wave.

[0028] The final constructive interference at the detector occurs when the relative phase between the shear waves at the detector is such that the instantaneous velocity of the shear waves has the same sign and results in a higher effective shear rate (e.g., 5% higher, 10% higher, 20% higher, 30% higher, 40% higher, or 50% higher) than that experienced in the absence of the irradiating shear wave.

[0029] In the detector, the shear wave radiated from the detector in the detector may be assumed to have the same velocity as the detector itself.

[0030] In some configurations, each of the pair of vibration planes may function as both a detector and an irradiator with respect to each other. Thus, final constructive or destructive interference due to the combination of shear waves may occur in either or both of the vibration planes.

[0031] The shear rate of the fluid in the detector resulting from interference affects the Q factor (or loss factor). Destructive interference in the detector results in a lower Q factor and thus a higher loss factor. Constructive interference in the detector results in a higher Q factor and thus a lower loss factor. Thus, this change in the Q factor (or loss factor) is related to the viscosity (due to μ’) and elasticity (due to G’) of the fluid.

[0032] An element underlying the techniques of the present disclosure is that the propagation depth of the shear wave depends on the elasticity of the fluid. This is explained by rewriting Equation 4 as the product of the skin depth for viscosity only and the elastic component.

Equation

[0033] Figure 3 is a graph of F(Δ) plotted against Δ (in degrees), where F(Δ) is the elastic component of x in Equation 7 0 and

Equation

[0034] The quantity F(Δ) is plotted to represent the effect of elasticity on the propagation depth. The quantity F(Δ) becomes 1 when Δ is equal to 90°, i.e., for a purely viscous fluid where tanΔ → ∞. For a slightly viscoelastic fluid with 1 < tanΔ < ∞ (i.e., in the range 45° < Δ < 90°), the plotted quantity F(Δ) remains approximately 1. This means that the propagation depth of the shear wave in a slightly viscoelastic fluid can potentially be reasonably approximated as the propagation depth of a shear wave with only viscosity. However, as Δ decreases, the plotted quantity increases at an increasing rate. As Δ decreases, the propagation depth of a shear wave with only viscosity becomes an increasingly inaccurate approximation of the propagation depth of the shear wave. As Δ approaches 0, the plotted quantity F(Δ) approaches infinity. Therefore, for a more viscoelastic fluid such as tanΔ < 1, the effect of viscoelasticity on the propagation depth of the shear wave becomes more important, and it may become more important to consider the effect of viscoelasticity when measuring fluid properties.

[0035] From Equation 7, it can be seen that for a fluid with a relatively low value of μ’ and a relatively low value of G’, the penetration depth of the shear wave is relatively low compared to a fluid with a relatively high value of μ’ and a relatively high value of G’.

[0036] Figure 4 shows the shear wave velocity field generated by the primary vibrating surface 10 (i.e., the detector) and the secondary vibrating surface 20 (i.e., the irradiator). The surfaces vibrate in phase synchronously with each other, the surfaces are separated by a gap distance, and the gap distance is filled with a first viscoelastic fluid 30 having a relatively low μ’ and a relatively low G’. The primary vibrating surface 10 generates a shear wave 12 that propagates a certain distance into the first viscoelastic fluid 30. The secondary vibrating surface 22 also generates a shear wave 22 that propagates a certain distance into the first viscoelastic fluid 30. The relatively low μ’ and relatively low G’ mean that the shear waves 12, 22 do not cross the gap between the primary vibrating surface 10 and the secondary vibrating surface 20, so the shear waves 12, 22 do not interfere with each other. The shear waves 12, 22 decay without any interference occurring.

[0037] FIG. 5 shows a shear wave velocity field generated by the same primary vibration surface 10 and secondary vibration surface 20 separated by the same gap as in FIG. 4, and the primary vibration surface and the secondary vibration surface vibrate together in synchronization in the same manner as shown in FIG. 4. However, in FIG. 5, the viscoelastic fluid 32 filling the gap has a relatively high μ' and a relatively high G'. The relatively high μ' and the relatively high G' mean that the shear waves 12, 22 spread across the gap between the primary vibration surface 10 and the secondary vibration surface 20. The shear waves 12, 22 may interfere with each other at the primary vibration surface and the secondary vibration surface. This means that the effective shear velocity at the primary vibration surface 10 (i.e., the detector) is affected by the shear wave 22 generated at the secondary vibration surface 20 (i.e., the irradiator).

[0038] In order to increase the propagation depth, it is not necessarily required that both μ' and G' be high. For example, a long propagation depth may be achieved by having either μ' or G' be high.

[0039] To cause interference to affect the shear velocity at the detector surface, for a given range of μ' and G', the parameters of the arrangement shown in FIGS. 4 and 5 can be selected. Such parameters include one or more of i) the gap distance, ii) the frequency, iii) the surface radius, and iv) the surface shape.

[0040] Returning to FIG. 1, the velocity of the traveling plane wave may be expressed as follows. v(x,t)=V 0 e -αx e i(ωt-βx) Equation 8 In the above equation, α is the attenuation coefficient, equal to 1 / X 0 and β is the wavelength coefficient, equal to 2π / λ, where λ is the wavelength.

[0041] For the shear wave of the viscoelastic fluid, α and β are expressed by the following equations.

Equation

[0042] The amplitude of the velocity vibration decreases as α = 1 / x with the distance from the generation surface. 0 Only the phase of the velocity vibration changes with the distance from the generation surface according to the wavelength coefficient β. Both α and β depend on the fluid and determine the degree of interference of the velocity field and thus the degree to which the effective shear velocity at the detection surface is modified.

[0043] In the previous explanations, it was assumed that the plane vibration surface vibrates in the plane and shear waves are generated. However, shear waves may also be generated from a non-planar surface. For example, shear waves may be generated from a concave or convex surface that undergoes torsional vibration.

[0044] Figure 6 shows the propagation of shear waves from a surface with a radius of curvature R that undergoes torsional vibration.

[0045] In the case of a convex surface, the traveling wave velocity may be expressed as follows.

Equation

[0046] In this equation, the phase of the wave changes with the distance X in the same way as before according to the wavelength coefficient β. However, the amplitude of the wave changes differently. The amplitude is not only affected by the attenuation coefficient α but also by geometric considerations that as the distance from the generation surface increases, the energy of the wave spreads over an increasingly large area. Therefore, the amplitude changes according to (R / (R + X))e -αX and varies accordingly.

[0047] In the case of a concave surface, the traveling wave velocity may be expressed as follows.

Equation

[0048] Similar to the convex case, the phase change of the wave due to distance depends on β. The amplitude is affected by α and by the geometric terms, but the geometric terms are different in the concave case. The geometric terms explain that as the distance from the generation surface increases, the energy of the wave converges into an increasingly narrow region. Therefore, the amplitude changes according to |R / (R-X)|e -αX and varies accordingly.

[0049] Figure 7 shows an arrangement in which a concave surface 42 is provided on the vibrating transducer 40. The concave surface 42 has a spherical indentation on the surface of the vibrating transducer. The vibrating transducer 40 torsional vibrates about the axis of rotation 44. The axis of rotation 44 extends through the center of the concave surface 42. While the vibrating transducer torsional vibrates about the axis of rotation 44, shear wave "rays" 46 extend from all positions of the concave surface 42, and the shear wave lateral velocity at each starting position of the concave surface 42 of each ray 46 coincides with the velocity of the starting position of the concave surface 42 due to the non-slip state. Due to the spherical profile of the concave surface, this means having a constant radius of curvature, but all rays 46 converge at a single position defined by the radius of curvature and the surface normal direction from the concave surface 42.

[0050] The specific angular position around the axis of rotation 44 of the starting point of the ray 46 defines the direction of the velocity of the concave surface 42 at the starting point of the ray 46. For any two points on the concave surface 42 having the same longitudinal position along the axis of rotation 44, the magnitude of the surface velocity is equal, but the direction and phase depend on the angular offset of the two points about the axis of rotation 44.

[0051] When the two starting points of the ray 46 are shifted from each other by 180° about the axis of rotation 44 on the concave surface 42, the phases of the shear waves of the ray 46 are shifted from each other by 180°.

[0052] Under these conditions, the propagation wave velocity is represented by the following formula.

Equation

[0053] Under these conditions, the concave surface provides not only a focusing effect but also an amplitude inversion effect due to the geometric term (R / (R - x)). The amplitude inversion depends on whether the distance X is greater than or less than the radius of curvature, and the radius of curvature determines the sign of this geometric term.

[0054] The example shown in FIG. 7 represents a simple shape of a depression with a profile of a sphere of constant curvature symmetric about the axis of rotation. Any diffusion effect of the generated shear wave is ignored. In practice, the depression may not be perfectly smooth, or the radius of curvature may not be constant, or the depression may not be symmetric about the axis of rotation. Therefore, in practice, the focus of the shear wave is not a single point in space but a focal region. However, when the depression is concave and rotates in the fluid about the axis of the fluid extending outward through the surface of the depression, and the part of the surface depression far from the axis of rotation on the opposite side of the axis of rotation directs the wave toward the axis of rotation, a focal region is formed, and amplitude inversion may occur behind the focal region.

[0055] Therefore, regardless of whether it is realized by the phase difference due to the distance between the detector and the irradiator or by the amplitude inversion due to the focusing effect, at the detector, when the shear waves from the irradiator and the detector have opposite signs, final destructive interference occurs. At the detector, the shear wave radiated from the detector at the detector may be assumed to have the same velocity as the detector itself.

[0056] FIG. 8 shows a configuration in which a smooth concave depression extends in a ring shape around the axis of rotation (shown in cross-section). In this configuration, since all the "rays" that focus together are in the same phase with each other, it is considered that no amplitude inversion occurs within or behind the focal region. At each point within or behind the focus, all the rays come from the same angular position around the axis of rotation.

[0057] Figure 9 shows a configuration in which a smooth concave depression rotates angularly about the axis of rotation. The concave depression has a certain curvature but is not a perfect sphere. In particular, shear waves are generated in the direction of the axis of rotation, and there is no surface that coincides with the axis of rotation. Amplitude inversion is considered to occur only in the region where the shear waves from both sides of the axis of rotation overlap, which corresponds to phase inversion. Away from this region, since there are no shear waves in the direction of the axis, amplitude inversion along the axis does not occur. Also, since all shear waves in such a region are in the same phase, amplitude inversion does not occur in the shear wave path behind the focus.

[0058] Figure 10 shows a configuration in which a spherical smooth concave depression rotates about the axis of the fluid. The axis extends through the concave depression, but the axis of rotation does not coincide with the center of the concave depression. Neither the axial center of the concave depression nor the resulting focus passes through this axis. Even when rotating about this axis, since the amplitudes of the waves on both sides of the axis of rotation do not match, the shear waves do not converge to the same extent as shown in Figure 7. However, it is considered that some amplitude inversion may occur behind the focus. By bringing the axis of rotation closer to the center of the depression and adjusting it to extend through the focus, the amplitude matching is improved.

[0059] Figure 11 shows a configuration in which the depression is formed from a plurality of conical portions. The cross-section in the lateral direction passing through the axis of rotation shows that the depression is axisymmetric and that the profile of the depression is partially linear. In this configuration, some degree of focusing is possible, but it cannot focus as well as a continuous smooth profile such as the configuration in Figure 7. However, it is still considered that at least some degree of amplitude inversion occurs at the focus or behind the focus.

[0060] Generally, to achieve amplitude inversion behind the focus of the depression, the depression region is symmetric about the axis of rotation. For efficient focusing, the concave depression preferably has a smooth cross-section in the lateral direction. The concave depression is preferably spherical, i.e., having a constant radius of curvature (when viewed in the lateral cross-section), such that all generated shear waves converge to a single point. In some embodiments, the concave depression may have other cross-sectional profiles, such as elliptical or parabolic, depending on the requirements of the application.

[0061] As shown in these examples, by combining amplitude inversion and focusing, it becomes possible to place a detector surface, such as an elongated member or a plane, in the region of amplitude inversion. When the elongated member rotates with the shear wave generation surface of the depression, the shear waves radiated from the detector surface destructively interfere with the shear waves radiated from the depression. The interference waves are amplified by the focusing of the shear waves, and since the detector is placed within the interference focus zone, the final destructive interference gain is high.

[0062] If amplitude inversion is not performed, it is necessary to place the detector surface at a distance determined by β from the generation surface in order to experience destructive interference with the shear waves radiated from the generation surface, where β varies depending on the properties of the fluid Δ, ρ, and μ' and the vibration frequency ω.

[0063] However, using a concave shear wave generation surface that generates shear waves with a phase shift on both sides of the axis of rotation may create a region of phase shift where destructive interference occurs, which is independent of β and thus advantageously independent of μ' or Δ.

[0064] Returning to the arrangement shown in FIG. 5, consider the effect of the interference of the shear waves 12, 22 on the apparent shear velocity of the detector surface.

[0065] The velocity of the shear wave 22 generated from the secondary vibration surface 20 at the position of the gap may be expressed as follows. ν s =A s cos(ωs t - φ s ) Equation 14 In the above equation, A s represents the amplitude change term of the shear wave 22, ω s represents the vibration frequency on the secondary vibration surface 20, and φ s represents the phase of the shear wave 22 at that position.

[0066] The velocity of the shear wave 12 generated from the primary vibration surface 20 at the same position in the gap may be expressed as follows. ν p = A p cos(ω p t - φ p ) Equation 15 In the above equation, A p represents the amplitude change term of the shear wave 12, ω p represents the vibration frequency on the primary vibration surface 10, and φ s represents the phase of the shear wave 12 at that position.

[0067] The linear combination of the shear waves 10 and 12 at that position is expressed as follows. ν p + ν s = A p cos(ω p t - φ p ) + A s cos(ω s t - φ s ) Equation 16

[0068] The shear velocity at that position is expressed as follows.

Number

[0069] Depending on the relative amplitudes and phases of the two waves, destructive interference (leading to a decrease in the Q factor) or constructive interference (leading to an increase in the Q factor) may occur.

[0070] The amplitude is determined by the attenuation coefficient α of the fluid and the radius of curvature of the surface. The phase is determined by the wavelength coefficient β and the propagation distance. As shown in Equations 9 and 10, both α and β depend on the fluid properties.

[0071] The inventors recognized that a properly designed system can provide a measured value of the Q factor (or the loss factor, which is the reciprocal of the Q factor) that varies monotonically with the increase in μ’ and G’. This is desirably achieved by having the phase and amplitude conspire to generate increasing destructive interference for increasing μ’ and G’, resulting in a proportionally increasing loss over that range.

[0072] As explained above, the measured loss factor or Q factor indicates the degree of viscosity but also depends on the shear rate at the surface. The shear rate is affected by other coefficients including the elasticity of the fluid, and the relationship between the loss factor or Q factor and viscosity becomes increasingly non-linear and even non-monotonic. The techniques of the present disclosure may employ increasing destructive interference with μ’ and G’ to provide a monotonic relationship between the Q factor or loss factor and the measured value of μ’ or G’, or any other material property that may be obtained from the measured value of μ’ or G’.

[0073] In the case of a measurement device, it is desirable for the output signal to vary linearly and monotonically with the measurement variable over the target range. If the output signal does not vary linearly and varies monotonically over the target range, a numerical approximation such as a curve fitting technique like non-linear regression using a non-linear function such as a non-linear polynomial may still be used to directly convert such an output signal into an estimated value of the measurement variable. If the output signal is not monotonic with respect to the measurement variable over the target range, it becomes more difficult to determine an estimated value of the measurement variable. For example, if multiple values of μ’ produce the same output signal (e.g., loss factor or Q factor), that value of the output signal does not deterministically indicate μ’. Thus, it is advantageous to have a monotonic relationship between the measurement variable and the output signal (e.g., loss factor or Q factor).

[0074] In the techniques of the present disclosure, the gap dimension and the vibration frequency are selected for a given fluid property, and the changes in the wave coefficients α and β monotonically change the loss coefficient or the Q factor together with μ' and G'.

[0075] Before directly describing specific embodiments according to the techniques of the present disclosure, it is useful to present some general points regarding the techniques of the present disclosure, and the embodiments may comply with one or more of the following points in any combination. ● An architecture including an architecture that supports phase and amplitude can be set for one or both of destructive interference and constructive interference. ● Promoting destructive interference may be advantageous to achieve a more useful monotonic behavior of the Q factor or the loss factor measured for changing material properties. ● Each of the pair of vibration surfaces may function as both a detector and an irradiator with respect to each other. ● In a simple architecture, both the primary vibration surface and the secondary vibration surface may be part of the same resonator or vibrator, but it is not necessary to arrange the primary vibration surface and the secondary vibration surface in that way. ● The resonator surface can be designed such that the relative phase of the vibration is zero or has a defined phase offset. ● Shear waves generated from a convex irradiator may have a greater amplitude loss with distance than a planar or concave irradiator due to geometric considerations of the diffused wave (i.e., radial attenuation or geometric attenuation as described below). ● Shear waves generated from a concave irradiator may converge to a certain distance according to the radius of curvature of the irradiator surface, and the amplitude at the focus may increase. ● In some configurations, shear waves with a phase shift from the opposite side of the convex irradiator may interfere destructively, causing an amplitude inversion in the shear wave field behind the focus. ● Vibration pins or ring monopole detectors may enable an effective arrangement at the focus of a convex irradiator because they concentrate the velocity field over a short distance due to radial (geometric) attenuation. ● In practice, determining the loss coefficient may be more useful than determining the Q factor (the reciprocal of the loss coefficient). ● The wave characteristics and the gap distance (surface separation) may be selected such that the measured loss coefficient increases monotonically with the increase of μ’ and G’. ● The operating frequency is arbitrary. However, in many practical implementations, frequencies in the range of 100 Hz to 100 kHz, preferably 200 Hz to 10 kHz, more preferably 300 Hz to 5 kHz, even more preferably 500 Hz to 2 kHz, for example, frequencies around 1 kHz (e.g., + / - 10%) are used. ● The Q factor (or the loss coefficient) may be used to measure the shear stress. However, the techniques of the present disclosure are not limited thereto and may include, as an alternative, the measurement of shear stress by direct torque measurement. The use of constructive and destructive interferences described herein may provide the same advantages regardless of whether the Q factor or the loss coefficient is measured. ● The techniques of the present disclosure are presented in the context of shear waves, but the same principle applies to vibrations from a surface that generates pressure waves (sound waves or P waves) that interfere constructively or destructively. However, note that since such waves have a longer wavelength than shear waves, vibrations at a fairly high frequency are required, otherwise the size of the system needs to be increased to account for the longer wavelength. ● The techniques of the present disclosure may be advantageously implemented using a torsional vibration device to generate shear waves. However, the vibration surface may be provided by the surface of a mechanical vibrator that vibrates in the plane, i.e., in a lateral or longitudinal vibration mode, in addition to or instead of the torsional mode.

[0076] Figure 12 shows the configuration of a vibration transducer according to the techniques of the present disclosure, where a plurality (in this case, four) of elongated members 52, such as pins, extend vertically outward from a flat disk base 50. The flat disk base 50 is configured to vibrate in a plane, i.e., to vibrate planar in a direction perpendicular to the normal of the plane, or to torsional vibrate about an axis parallel to the normal of the plane. Optionally, the elongated member may be the elongated member described below and in UK Patent Application No. 2207881.0 filed on May 27, 2022, which is incorporated herein by reference. Such an elongated member is characterized by a width, a half-width equal to half of the width, and a length longer than the width, and the half-width is smaller than the propagation depth of the shear wave of the fluid at the vibration frequency, and more preferably less than 50% of the propagation depth. The propagation depth of the shear wave may be 1 / α, where α is given by Equation 9. During vibration, the fluid flow around the elongated member may be laminar flow.

[0077] In this configuration, the flat disk base 50 may be understood as an irradiator, and the elongated member 52 may be understood as a detector.

[0078] In a certain configuration, the flat disk base 50 may be configured to torsional vibrate about the longitudinal axis of the base rather than laterally.

[0079] Figure 13 shows the shear wave 54 generated by the flat base 50 and the shear wave 56 generated by the elongated member 52. Due to the geometric attenuation described below, the shear wave 56 generated by the elongated member has a shape as shown in Figure 8, and the amplitude of the shear wave rapidly attenuates due to geometric considerations. Assuming that the elongated member 52 is sufficiently rigid and the bending vibration of the elongated member 52 at the operating frequency is negligibly small, the elongated member 52 vibrates in phase with the flat disk base 50. The shear wave 54 generated by the flat disk base 50 changes in value as the distance from the flat disk base 50 increases according to β.

[0080] FIG. 14 further shows the phase change of the shear wave 54 generated by the flat base 50 along the length of the elongated member 52. In the first range marked C in FIG. 9, the shear wave 54 generated by the flat base 50 is in phase with the movement of the elongated member 52, and thus in phase with any shear wave 56 generated from that portion of the elongated member 52. In this region, constructive interference occurs between the shear wave 54 generated by the flat base 50 and the shear wave 56 generated by the elongated member 52. In the second range marked D in FIG. 9, the shear wave 54 generated by the flat base 50 is out of phase with the movement of the elongated member 52, and thus also out of phase with any shear wave 56 generated from that portion of the elongated member 52. In this region, destructive interference occurs between the shear wave 54 generated by the flat base 50 and the shear wave 56 generated by the elongated member 52. As described above, in practice, destructive interference may be preferred. In the arrangement shown in FIG. 9, adjacent to the base of the elongated member 52, the constructive interference in region C in contact with the flat base 50 may provide only a slight destructive interference gain.

[0081] FIG. 15 shows the configuration of a vibration transducer according to the techniques of the present disclosure, where a plurality (in this case four) of elongated members 62, such as pins, extend vertically outward from a flat disk base 60. Further, the distal ends of the elongated members 62 are attached to a ring member 63. The ring member 63 surrounds an axis that is perpendicular or substantially perpendicular to the flat base 60. Since each of the elongated members 63 has the same or similar length, around the ring member 63, each portion of the ring member 63 is at approximately the same distance from the flat base 60. Optionally, both the ring member 63 and the elongated members 62 may optionally have a width that is narrow enough to provide the geometric attenuation described below. The flat disk base 60 is configured to vibrate in a plane, i.e., to vibrate planar in a direction perpendicular to the normal of the plane, or to torsional vibrate about an axis parallel to the normal of the plane.

[0082] In this configuration, the flat disk base 60 may be understood as an irradiator, the elongated member 62 may be understood as a detector, and the ring member 63 may also be understood as a detector.

[0083] The shear waves generated by the movement of the elongated member 62 interact with the shear waves 64 generated by the movement of the flat disk base 60 in the same way as shown in FIGS. 7 to 9. However, in this configuration, there is a possibility that the final destructive interference, that is, the amount of effective interference considering the contributions of constructive interference and destructive interference, may increase.

[0084] In one configuration, the flat disk base 60 may be configured to torsional vibrate about the longitudinal axis of the base rather than laterally.

[0085] FIG. 16 shows the ring member 63 of the shear wave 64 generated by the movement of the flat base 60. The ring member 63 is connected to the elongated member 63, and it is assumed that the elongated member 63 is rigid so that the elongated member 63 moves in phase with the flat base 60 and the ring member 63 moves in phase with the flat base 60. Since the entire ring member 63 is disposed at a position away from the flat base 60, the shear wave 64 generated by the movement of the flat base is out of phase with the ring member 63 at the position of the ring member 63, and thus is out of phase with any shear wave generated from the movement of the ring member 63. Therefore, destructive interference occurs between the shear wave 64 generated by the flat base 60 and the shear wave generated by the ring member 63. Therefore, the elongated member 62 may provide only a small amount of final destructive interference, but adding the ring member 63 improves the amount of final destructive interference when the shear wave generated by the movement of the flat base 60 is out of phase with the flat base 60 and thus the ring member 63 is disposed at a position out of phase with the ring member 63.

[0086] FIG. 17 shows the configuration of a vibration transducer according to the techniques of the present disclosure, in which a plurality (in this case four) of elongated members 72, such as pins, extend radially outward from a shaft 70 having a circular cross-section and are configured to torsionally vibrate about the longitudinal axis of the shaft 70. Optionally, the elongated members 72 can optionally have a width that is narrow enough to provide geometric damping, as described below.

[0087] In this configuration, the cylindrical outer surface facing radially of the shaft 70 may be understood as an irradiator, and the elongated members 72 may be understood as detectors.

[0088] FIG. 18 shows various shear waves generated by the movement of the elements of this configuration. Due to the torsional vibration of the shaft, a shear wave 74 extending radially outward from the cylindrical surface of the shaft 70 is generated. As explained above in connection with Equation 11, as the distance from the shaft 70 increases, the amplitude of the shear wave 74 is affected not only by the attenuation coefficient but also by geometric considerations. The elongated members 72 move in phase with the shaft 70 and generate shear waves 76 from their movement in the fluid. At several positions along the length of the elongated members 72, the movement of the elongated members is in phase with the amplitude of the shear wave 74 generated from the shaft 70. At other positions along the length of the elongated members 72, the movement of the elongated members is out of phase with the amplitude of the shear wave 74 generated from the shaft 70.

[0089] Figure 19 shows a position where the amplitude of the shear wave 74 generated from the cylindrical surface of the shaft 70 and extending radially outward from the shaft 70 is in phase with the movement of the shaft 70, and thus the movement of the elongated member 72. In the region closest to the base of the elongated member 72 where the elongated member 72 is connected to the shaft 70, the amplitude of the shear wave 74 is in phase with the movement of the elongated member 72, and thus in phase with the shear wave generated by the movement of the elongated member 72, and it can be seen that constructive interference occurs in this part of the elongated member 72. In the next adjacent region further away from the shaft 70, the amplitude of the shear wave 74 is out of phase with the movement of the elongated member 72, and thus out of phase with the shear wave generated by the movement of the elongated member 72, so destructive interference occurs in this part of the elongated member 72. Due to the constructive region at the base of the elongated member 72, the final destructive interference gain is small. Compared with the arrangements shown in FIGS. 12 - 18, the irradiation surface is convex, and due to geometric considerations, the attenuation becomes even greater as the radial distance increases.

[0090] Figure 20 shows the configuration of a vibration transducer according to the technique of the present disclosure based on the configuration shown in FIGS. 17 - 19, where the distal end of the elongated member 73 is connected to the ring member 73. The ring member 73 may optionally have a width narrow enough to provide geometric attenuation.

[0091] Figure 21 shows the position of the ring member 73 in a region where the shear wave 74 generated by the movement of the shaft 70 is out of phase with the movement of the shaft 70, and thus out of phase with the movement of the ring member 73. The shear wave generated by the movement of the ring member 73 is out of phase with the shear wave 74 generated by the movement of the shaft 70 at this distance radially outward from the shaft 70, so destructive interference occurs. The irradiated outer surface of the shaft 70 is convex, and thus the shear wave 74 undergoes additional geometric attenuation depending on the radial distance. However, as shown in FIG. 21, since the ring member 73 detector is arranged only in the destructive interference region, the final destructive interference gain may be high.

[0092] FIG. 22 shows the configuration of a vibration transducer according to the technique of the present disclosure based on FIG. 15, where the vibration is torsion and the shear wave is generated from the concave surface. In particular, the base 80 is cylindrical in shape configured to torsionally vibrate about the longitudinal axis of the base 80. At one end of the cylindrical base 80, there are four elongated members 82 extending outward from the base, and the elongated members 82 are aligned with the longitudinal axis of the cylindrical base 80. A ring member 83 is connected to the distal end of the elongated member 82. A concave groove 88 is provided at the end of the base 80, and the concave groove 88 extends circularly around the longitudinal axis of the base 80 that is concentric with the outer cylindrical surface of the base 80. The elongated members 82 are connected to the end of the base 80 within the concave groove 88. In this example, the concave groove has a constant radius of curvature across the entire groove cross-section. However, other examples may have grooves with cross-sectional profiles other than circular, such as elliptical or parabolic cross-sectional profiles. However, the concave surface or groove in the context of the present disclosure need not be smooth and may include a surface or groove having a partially linear profile, or a groove surface with a mixture of flat and curved portions. As an example, a groove with a V-shaped cross-sectional profile may be mentioned.

[0093] FIG. 23 shows a cross-section through the end of the base 80 and shows the ring member 83. The elongated members 82 are not shown. Due to the torsional vibration about the longitudinal axis within the fluid of the base 80, shear waves are generated from within the concave groove 88 and including from the end of the base 80. The shear waves are generated in a direction perpendicular to the surface. The shear waves generated from the surface within the concave groove 88 are focused in a region offset from the base 80 as shown by the ray 85 representing the propagation direction of the shear waves from the generation surface within the concave groove 88. The circular cross-section of the concave groove 88 leads to a shallow focus region. At distances beyond the focus region, the resulting amplitude of the shear waves is not thought to invert as explained above in relation to Equation 12. This is because all the shear waves that converge together are in the same phase.

[0094] FIG. 23 shows the position of the ring member 83 that is separated from the base 80 beyond the focus region. The shear wave indicated by the ray 85 is considered not to cause an amplitude inversion with respect to the movement of the base 80 beyond the focus region 89.

[0095] FIG. 24 shows an arrangement that can be exemplified by a “sheave wheel” irradiator and a ring detector according to the techniques of the present disclosure. FIG. 24 shows a side view of the fluid contact element of the vibration transducer on the left side and an axial view of the same transducer on the right side. The vibration transducer includes a shaft 97 configured to torsional vibrate about a longitudinal axis. The shaft 97 includes a bob 90 along the length of the shaft 97, and the bob 90 has a cylindrical shape that coincides with the axis of the shaft 97. A concave groove 98 having a circular profile extends circumferentially around the outer cylindrical surface of the bob 90. The bob 90 including the concave groove 98 has the shape of a sheave wheel. There are a plurality of elongated members 92 that extend radially outward from the concave groove 98, and the elongated members 92 are connected at their distal ends to a ring member 93 that surrounds the bob 90 around the concave groove 98. The surface of the concave groove 98 functions as an irradiator for the ring member 93 that functions as a detector.

[0096] The ray 95 represents a shear wave radiated from the surface of the concave groove 98. Due to the radius of curvature of the concave groove 98, the shear wave radiated from the concave groove 98 converges in an intermediate region between the concave groove 98 and the ring member 93.

[0097] Figure 25 shows an arrangement that can be exemplified by a "semi - pulley" irradiator and a ring detector according to the techniques of the present disclosure. Figure 25 shows a side view of the fluid - contact element of the vibrating transducer on the left side and an axial view of the same transducer on the right side. The vibrating transducer comprises a shaft 107 configured to torsional - vibrate about a longitudinal axis. The shaft 107 includes a bob 100 along the length of the shaft 107, and the bob 100 has a cylindrical shape that coincides with the axis of the shaft 97. The bob 100 includes a concave groove 108, and the concave groove 108 represents that the diameter of the bob 100 narrows from a maximum value to a minimum value. The concave groove 108 has a circular profile (constant radius of curvature). The bob 100 including the concave groove 108 has the shape of a semi - pulley. There are a plurality of elongated members 102 extending radially outward from the concave groove 108, and the elongated members 92 are connected at their distal ends to a ring member 103 that surrounds the bob 100 around the concave groove 108. The surface of the concave groove 108 functions as an irradiator for the ring member 103 that functions as a detector.

[0098] Ray 105 represents a shear wave radiated from the surface of the concave groove 108. Due to the radius of curvature of the concave groove 108, the shear wave radiated from the concave groove 108 converges in the intermediate region between the concave groove 108 and the ring member 103.

[0099] Figure 26 shows an arrangement according to the techniques of the present disclosure, in which a base or bob 110 on a shaft 117 is provided with a concave groove 118 that extends circularly around the shaft 117. A ring member 113 extends circumferentially around the shaft 117 (connected to the shaft by elongated members not shown) and is disposed at a position axially offset from the bob 110. The shaft 117 and the bob 117 torsional - vibrate about the longitudinal axis of the shaft. The ring member 113 is disposed closer to the bob 110 than the focal region 119 indicated by the ray 115 radiated from the concave groove 118. This means that the amplitude of the interference shear wave from the concave groove 118 irradiator received by the ring member 113 detector increases, and the influence of the interference becomes greater.

[0100] Figure 27 shows the same arrangement as in Figure 26, except that, according to the technique of the present disclosure, the ring member 123 is disposed farther from the irradiator than the focal region 129.

[0101] Figure 28 shows an arrangement in which, according to the technique of the present disclosure, two bobs 130, 131 are disposed at a constant distance from each other on a torsional vibration shaft 137. The first bob 130 is provided with a circularly extending concave groove 138a around the shaft 137 on the side facing axially the second bob 131 on the side facing axially the first bob 130. The second bob is provided with a circularly extending concave groove 138b around the shaft 137 on the side facing axially the first bob 130 on the side facing axially the second bob 131. The shear waves radiated from the concave groove 138a of the first bob 130 converge in the region between the two bobs 130, 131 and invert beyond the focal region. The shear waves radiated from the concave groove 138b of the second bob 131 converge in the region between the two bobs 130, 131.

[0102] Figure 29 shows an arrangement in which, according to the technique of the present disclosure, two opposing disks 140, 141 are attached to a shaft 147 and configured to torsional vibrate. The first surface 144 of the first disk 140 faces the second surface 146 of the second disk 141. Shear waves propagating beyond the gap distance between the first surface 144 and the second surface 146 may interfere constructively or destructively with each other.

[0103] Figure 30 shows an arrangement in which, according to the technique of the present disclosure, a disk 151 extending circumferentially around a bob 150 is provided on the bob 150 of a torsional vibration shaft 157. The outermost radius range of the disk 151 is larger than the outermost radius range of the bob 150. During torsional vibration of the shaft 157, shear waves are radiated radially from the outer cylindrical surface 154 of the bob 150. Further, shear waves are radiated axially from the surface 156 facing axially the disk. Such shear waves may interfere constructively or destructively with each other.

[0104] Figure 31 shows that, according to the technique of the present disclosure, two bobs 160 are arranged apart from each other on the torsional vibration shaft 167. There is a disk 161 axially aligned with the bobs 160 and the shaft 167 between the two bobs 160. The outermost radius range of the disk 11 is larger than the outermost radius range of any of the bobs 160. During the torsional vibration of the shaft 167, shear waves are radiated radially from the outer cylindrical surface 164 of the bob 160. Further, shear waves are radiated axially from the surface 166 facing the axial direction of the disk. Such shear waves may interfere with each other constructively or destructively. Compared with the arrangement shown in FIG. 30, the arrangement shown in FIG. 31 may improve destructive interference. This is because the diameter of the bob 160 detector adjacent to the disk 161 irradiator is significantly reduced, and the contribution effect of constructive interference from this region is significantly reduced.

[0105] Figures 32 and 33 show an arrangement according to the technique of the present disclosure, which is similar to the arrangement shown in FIGS. 26 and 27, except that the ring members 173, 183 are arranged on shafts 174, 184 different from the shafts 177, 187 on which the bobs are arranged. The shafts are configured to torsional vibrate together to achieve shear wave interference as required.

[0106] Figure 34 shows an arrangement in which two bobs 190, 191 are arranged at a constant distance from each other on different torsional vibration shafts 194, 197, respectively, according to the technique of the present disclosure. The first bob 190 causes the shaft 137 to torsional vibrate at positions separated from each other. The first bob 190 attached to the shaft 197 is provided with a concave groove 198a that extends circularly around the side facing the axial direction of the first bob 190 on the side facing the second bob 191 in the axial direction. The second bob attached to the shaft 194 is provided with a concave groove 198b that extends circularly around the side facing the axial direction of the second bob 191 on the side facing the first bob 190 in the axial direction. The shear waves radiated from the concave groove 198a of the first bob 190 converge in the region between the two bobs 190, 191. The shear waves radiated from the concave groove 198b of the second bob 191 converge in the region between the two bobs 190, 191.

[0107] Figure 35 shows an arrangement according to the technique of the present disclosure in which two opposing disks 200, 201 are attached to respective shafts 207, 208 and configured to torsional vibrate. The first surface 204 of the first disk 200 faces the second surface 206 of the second disk 201. Shear waves propagating across the gap distance between the first surface 204 and the second surface 206 may interfere with each other constructively or destructively.

[0108] Figure 36 shows an arrangement in which, according to the techniques of the present disclosure, a first bob 210 is disposed on a first torsional vibration shaft 217 and a second bob 211 is disposed on a second torsional vibration shaft 218. The shafts 217, 218 are axially aligned and vibrate about the same axis. There is a gap between the two bobs 210, 211. The outermost radius range of the first bob 210 is larger than the outermost radius range of the second bob 211. During torsional vibration of the shaft 218, shear waves are radiated radially from the outer cylindrical surface 216 of the second bob 201. Further, the shear waves are radiated axially from the surface 214 facing axially of the first bob 201 across the gap between the first bob 210 and the second bob 211. Such shear waves may interfere constructively or destructively with each other. Since there is a gap between the first bob 210 and the second bob 211, the contribution of constructive interference is reduced, advantageously allowing final destructive interference.

[0109] Figure 37 shows a vibration transducer in which two elongated members 320a, 320b are connected to a second axial portion of a bob 314. The two elongated members 320a, 320b are cylindrical and have a constant same radius along the lengths of the two elongated members 320a, 320b. The first elongated member 320a is disposed around the bob 314 and diametrically opposite the other elongated member 320b. Each elongated member 320a, 320b extends outward from the bob 314 in a radial direction perpendicular to the axis 312 of the shaft 310. Either or both of the first elongated member 320a and the second elongated member 320b may provide a surface where constructive or destructive interference may occur with waves radiated from the conical surface of the bob 314.

[0110] FIG. 38 shows a vibration transducer in which two elongated members 320a, 320b are connected to a third axial portion of the bob 314. Each elongated member 320a, 320b is parallel to the axis 312 of the shaft 310 but is aligned along its respective axis that is radially offset from the axis 312 of the shaft 310. The two elongated members 320a, 320b are cylindrical and have the same constant radius along the lengths of the two elongated members 320a, 320b. The first elongated member 320a is disposed diametrically opposite the other elongated member 320b around the third axial portion of the bob 314. Either or both of the first elongated member 320a and the second elongated member 320b may provide a surface where constructive or destructive interference may occur with waves radiated from the conical surface of the bob 314 or with waves radiated from each other.

[0111] FIG. 39 shows a vibration transducer in which two elongated members 340a, 340b are connected to a second axial portion of the bob 314. The two elongated members 340a, 340b are conical. The first elongated member 340a is disposed diametrically opposite the other elongated member 340b around the bob 314. Each elongated member 340a, 340b extends outwardly from the bob 314 in a radial direction perpendicular to the axis 312 of the shaft 310. Each elongated member 340a, 340b has a maximum radius at its proximal end and is connected to the second axial portion of the bob 314 at its proximal end. Either or both of the first elongated member 340a and the second elongated member 340b may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314.

[0112] FIG. 40 shows a vibration transducer in which four elongated members 340a, 340b, 340c, 340d are connected to a second axial portion of the bob 314. The four elongated members 340a, 340b, 340c, 340d are conical. The first elongated member 340a is disposed around the bob 314 and diametrically opposed to the second elongated member 340b, but is in the same axial position as the second elongated member 340b along the axis 312. The third elongated member 340c is disposed around the bob 314 and diametrically opposed to the fourth elongated member 340d, but is in the same axial position as the fourth elongated member 340d along the axis 312. The first elongated member 320a and the second elongated member 320b are axially spaced from the third elongated member 340c and the fourth elongated member 340d, respectively, along the axis 312. Each elongated member 340a, 340b, 340c, 340d has a maximum radius at its proximal end and is connected to the second axial portion of the bob 314 at the proximal end. Any or all of the first through fourth elongated members 340a, 340b, 340c, 340d may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314 or with waves radiated from each other.

[0113] FIG. 41 shows a vibration transducer in which two elongated members 360a, 360b are connected to a second axial portion of the bob 314. The two elongated members 360a, 360b each have a semi - annular shape. The first elongated member 360a is curved and is connected to the bob 314 at two axially spaced positions, and has a circular cross - section along a curved axis passing through the elongated member 360a. The second elongated member 360b is curved and is connected to the bob 314 at two axially spaced positions that are diametrically opposite around the bob from the positions where the first elongated member 360a is connected to the bob 314. The second elongated member also has a circular cross - section along a curved axis passing through the elongated member 360b. Either or both of the first elongated member 360a and the second elongated member 360b may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314, either in a substantially radially - aligned base portion close to the surface of the bob 314 or in a substantially axially - aligned "loop" portion far from the surface of the bob 314.

[0114] FIG. 42 shows a vibration transducer in which four elongated members 320a, 320b, 320c, 320d are connected to a second axial portion of the bob 314. Each of the four elongated members 320a, 320b, 320c, 320d is cylindrical with the same constant radius and extends radially from the bob 314 from positions distributed along the circumference of the second axial portion at 90° from adjacent elongated members. The distal ends of each of the four elongated members 320a, 320b, 320c, 320d are connected to a fifth elongated member 324 having an annular or ring shape that surrounds the bob 314. Any or all of the first through fourth elongated members 320a, 320b, 320c, 320d, or the fifth elongated member 324 having an annular or ring shape, may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314 or with waves radiated from each other.

[0115] Figure 43 shows a vibration transducer in which four elongated members 320a, 320b, 320c, and 320d are connected to a second axial portion of the bobbin 314. The four elongated members 320a, 320b, 320c, and 320d are cylindrical, but have different radii. The first elongated member 320a has the largest radius. The second elongated member 320b has a radius smaller than the radius of the first elongated member 320a. The third elongated member 320c has a radius smaller than the radius of the second elongated member 320b. The fourth elongated member 320d has a radius smaller than the radius of the third elongated member 320c. The first elongated member 320a and the second elongated member 320b each extend radially outward from respective positions that are axially offset from each other from the second axial portion of the bobbin 314 but have the same circumferential position at other points. The third elongated member 320c and the fourth elongated member 320d each extend radially outward from respective positions that are axially offset from each other from the second axial portion of the bobbin 314 but have the same circumferential position at other points. The first elongated member 320a and the second elongated member 320b are arranged at an interval of 90° from the third elongated member 320c and the fourth elongated member 320d along the circumference of the bobbin 314. Any or all of the first to fourth elongated members 320a, 320b, 320c, and 320d may provide a surface where constructive interference or destructive interference may occur with waves radiated from the cylindrical surface of the bobbin 314 or with waves radiated from each other.

[0116] Figure 44 shows a vibration transducer in which eight elongated members 370a, 370b, 370c, 370d, 370e, 370f, 370g, and 370h are connected to the bobbin 314.

[0117] The first elongated member 370a is connected to a third axial portion of the bobbin 314 and has a conical shape extending in a direction oblique to the axis 312 of the shaft 310. The first elongated member 370a may provide a surface where constructive interference or destructive interference may occur with waves radiated from the conical surface of the bobbin 314.

[0118] The second elongated member 370b is connected to the second axial portion of the bob 314 and extends radially outward from the bob 314 from the proximal end of the second elongated member 370b. The second elongated member 370b is not linear and two linear portions are connected at a right angle to form an "L"-shaped member. The distal portion of the second elongated member 370b extends in a direction parallel to the axis 312. Either or both of the proximal and distal portions of the second elongated member 370b may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314 or with waves radiated from each other.

[0119] The third elongated member 370c is connected to the second axial portion of the bob 314 and has a "T"-shaped configuration. The proximal portion of the third elongated member 370c is connected to the bob 314 and extends radially outward from the bob 314. The distal portion of the third elongated member 370c is connected to the distal end of the proximal portion of the third elongated member 370c and extends in a direction parallel to the axis 312, i.e., a direction perpendicular to the direction of the proximal portion. Either or both of the proximal and distal portions of the third elongated member 370c may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314 or with waves radiated from each other or from any other elongated member.

[0120] The fourth elongated member 370d is connected to the second axial portion of the bob 314 and includes a proximal portion and a distal portion. The proximal portion is connected to the bob 314 and extends obliquely with respect to the axis 312 of the shaft 310. The end of the distal portion is connected to the distal end of the proximal portion and the distal portion extends in a direction parallel to the axis 312. Either or both of the proximal and distal portions of the fourth elongated member 370d may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314 or with waves radiated from each other or from any other elongated member.

[0121] The fifth elongate member 370e is connected to the second axial portion of the bob 314. The fifth elongate member 370e is not straight and extends outward in a wide radial direction from the bob 314, but has a wide circular cross-section along the length of the fifth elongate member 370e. The fifth elongate member 370e may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314 or with waves radiated from any other elongate member.

[0122] The sixth elongate member 370f is connected to the second axial portion of the bob 314 and extends radially outward from the bob 314. A further elongate member is connected to the distal end of the sixth elongate member 370f, and this further elongate member has the shape of a closed loop, specifically an annular body. Either or both of the proximal and distal portions of the fifth elongate member 370e may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314 or with waves radiated from each other or from any other elongate member.

[0123] The seventh elongate member 370g is connected to the second axial portion of the bob 314 and extends radially outward from the bob 314. A further elongate member is connected to the distal end of the seventh elongate member 370g, and this further elongate member is curved circumferentially about an arc concentric with the circumference of the second axial portion of the bob 314. Either or both of the proximal and distal portions of the seventh elongate member 370g may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the bob 314 or with waves radiated from each other or from any other elongate member.

[0124] The eighth elongated member 370h is connected to the third axial portion of the bob 314 and includes a proximal portion and a distal portion. The proximal portion is connected to the bob 314 and extends outward from the surface of the third axial portion in an oblique direction with respect to the axis 312 of the shaft 310. The end of the distal portion is connected to the distal end of the proximal portion, and the distal portion extends in a direction parallel to the axis 312. Either or both of the proximal and distal portions of the eighth elongated member 370g may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical or conical surface of the bob 314, or from each other, or from waves radiated from any other elongated member.

[0125] Note that some embodiments may include only a subset of the elongated members shown in FIGS. 37-44, such as one or more of the numerous and diverse elongated members shown in FIG. 44. The skilled reader will recognize, in particular, that FIG. 44 shows a wide range of possible elongated members in a single device and that not all of the elongated members shown in FIG. 44 need to be included in an actual implementation.

[0126] FIG. 45 shows a partial configuration of a vibration transducer according to the techniques of the present disclosure, in which elongated members 420a, 420b, 420c, 420d, 420e, 420f are connected to a shaft or bob 400 configured to torsionally vibrate about axis 412. The elongated members 420a, 420b, 420c, 420d, 420e, 420f are cylindrical. The first elongated member 420a and the second elongated member 420b each extend radially outward from respective positions that are axially offset from each other and have the same circumferential position from the shaft of the bob 400. The third elongated member 420c and the fourth elongated member 420d each extend radially outward from respective positions that are axially offset from each other and have the same circumferential position from the shaft of the bob 400. The fifth elongated member 420e and the sixth elongated member 420f each extend radially outward from respective positions that are axially offset from each other and have the same circumferential position from the shaft of the bob 400. The first elongated member 420a and the second elongated member 420b are arranged at an interval of 45° from the third elongated member 420c and the fourth elongated member 420d along the circumference of the shaft or bob 400. The fifth elongated member 420a and the sixth elongated member 420b are arranged at an interval of 45° from the third elongated member 420c and the fourth elongated member 420d along the circumference of the shaft or bob 400, and at an interval of 90° from the first elongated member 420a and the second elongated member 420b. Any or all of the first through sixth elongated members 420a, 420b, 420c, 420d, 420e, 420f may provide a surface where constructive or destructive interference may occur with waves radiated from the cylindrical surface of the shaft or bob 400 or with waves radiated from other members among the elongated members.

[0127] Furthermore, pairs of adjacent elongated members, such as the first elongated member 420a and the second elongated member 420b, are axially spaced from each other such that shear waves radiated therefrom destructively interfere. The shear wave radiated from the first elongated member 420a is out of phase with the shear wave radiated from the second elongated member 420b in the vicinity of the second elongated member 420b. The shear wave radiated from the second elongated member 420b is out of phase with the shear wave radiated from the first elongated member 420a in the vicinity of the first elongated member 420a. The first elongated member and the second elongated member may function as mutual radiators and detectors. Similar destructive interference may occur between shear waves radiated between the third elongated member 420c and the fourth elongated member 420d, and between shear waves radiated between the fifth elongated member 420e and the sixth elongated member 420f. According to the techniques of the present disclosure, similar destructive interference (or constructive interference, if desired) may occur between any coupled pair of elongated members, depending on their shape and shear wave propagation characteristics (such as propagation depth, wavelength, etc.).

[0128] In another configuration according to the techniques of the present disclosure (optionally, final constructive interference or destructive interference may occur due to vibration), the vibration transducer includes a shaft and a plurality of elongated members. If the vibration transducer includes a bobbin, the elongated members may be connected to the vibration transducer at the bobbin. Alternatively or additionally, the vibration transducer may include elongated members connected to the vibration transducer at the shaft. The plurality of elongated members are spaced along the circumference of the shaft or bobbin and extend completely radially outward from the shaft or bobbin, or in a direction having a radial component and an axial component, or completely axially (not on the same straight line as the longitudinal axis of the shaft / bobbin). The plurality of elongated members may be evenly distributed along the circumference, thereby reducing or avoiding the disturbance of the center of mass with respect to the longitudinal axis, but may also be unevenly distributed along the circumference. The plurality of elongated members may be connected to the shaft or bobbin at the same axial position along the length of the shaft or bobbin, for example, in a helical pattern around the outer surface of the shaft or bobbin, or may be connected at different axial positions.

[0129] When the plurality of elongated members extend completely or partially axially from the shaft or bobbin, the elongated members may include a spacer from the outer surface of the shaft or bobbin to provide a radial offset to the elongated members. Alternatively, the plurality of elongated members may be circularly distributed around the longitudinal axis and may extend from the end of the shaft or bobbin, such as extending from the end of the shaft or bobbin. The end of the shaft or bobbin may be flat, curved, conical, or have some other profile.

[0130] The elongated members may have a width and a half-width such that geometric attenuation (monopole behavior) may occur around the elongated members during vibration of the vibration transducer. The vibration of the vibration transducer may be twisted about the longitudinal axis of the shaft.

[0131] The vibration transducer may comprise two or more elongated members, such as 3, 4, 5, 6, 7, 8, 9, 10 or more elongated members. The elongated members may have a constant cross-section (such as a cylindrical elongated member, or a square / rectangular, rounded square / rectangular (e.g., super-elliptical shape), triangular, or elliptical cross-section) along the length of the elongated member, or may have a cross-sectional shape or size that varies along their length, such as i) a cone with a linearly decreasing cross-sectional area as the distance from the shaft or bob increases, or ii) one where the size or shape changes stepwise (e.g., the size decreases stepwise) as the distance from the shaft or bob increases.

[0132] In a particular configuration, the vibration transducer comprises a shaft configured for torsional vibration, the shaft having a proximal end where the vibration is driven and a distal end. At the distal end of the shaft, or near the distal end of the shaft (e.g., closer to the distal end than the proximal end, or within the last quarter, or within the last tenth, or within the last twentieth of the fluid contact length of the shaft), a plurality of elongated members extend radially outward from the shaft at a common axial position along the length of the shaft. Eight elongated members are evenly distributed at 45° intervals along the circumference of the shaft. In another particular configuration, the bob is at the distal end of the shaft and eight elongated members extend radially outward from the bob. Other configurations comprise more or fewer elongated members evenly or unevenly distributed around the shaft / bob. For example, one configuration comprises six elongated members evenly distributed along the circumference of the shaft.

[0133] In another specific configuration, the vibrating transducer includes a shaft and a plurality of elongated members that are aligned axially with the longitudinal axis of the shaft but not on the same straight line as the longitudinal axis of the shaft. There is a bob at the distal end of the shaft. The bob has the shape of a cylinder coaxial with the longitudinal axis of the shaft, but the radius is larger than that of the shaft. The plurality of elongated members extend axially outward from the end of the bob, each being connected to the end of the bob with the same radial offset from the longitudinal axis and evenly distributed around the longitudinal axis. The plurality of elongated members comprises eight elongated members evenly distributed at 45° intervals around the longitudinal axis. The vibrating transducer is configured to torsional vibrate about the longitudinal axis. Other configurations include more or fewer elongated members, which may be evenly or unevenly distributed around the longitudinal axis. For example, one configuration includes six elongated members evenly distributed around the longitudinal axis.

[0134] Figures 46 and 47 show configurations according to the techniques of the present disclosure that employ advantageous modularity.

[0135] Figure 46 shows a cross-section of segment 440 of a vibrating transducer through the axis of torsional vibration, with an axially symmetric flange extending outward from the shaft, a convex surface 444 provided on one axial side of the flange, and a detector surface 442 (shown as a rectangle in cross-section for example only) provided on the other side of the flange. This segment 440 may be axially aligned with other identical or similar segments such that the convex surface 444 generates a focused shear wave at the detector of an adjacent segment and the detector 442 can receive the focused shear wave from the convex surface of an adjacent segment.

[0136] Figure 47 shows a cross-section of a vibration transducer configured such that four segments 440a, 440b, 440c, and 440d, identical to the segments shown in Figure 46, are aligned adjacent to each other in the axial direction and twist and vibrate about a common axis. The convex surface 444a of the first segment 440a provides a focused shear wave to the detector surface 442b of the second segment 440b. The convex surface 444b of the second segment 440b provides a focused shear wave to the detector surface 442c of the third segment 440c. The convex surface 444c of the third segment 440c provides a focused shear wave to the detector surface 442d of the fourth segment 440d. A modular configuration of repeating segments as shown in Figure 47 may provide advantages in the manufacture and design of vibration transducers tailored to specific operating requirements. In particular, the sensitivity of the transducer may be altered by increasing or decreasing the number of segments without changing the shape of the segments.

[0137] Both the radiator surface and the detector surface may be the surfaces of elongated members that can employ geometric attenuation.

[0138] Some explanations of geometric attenuation and elongated members that employ geometric attenuation are given below. Here, first, a purely viscous fluid is considered, and then a viscoelastic fluid is considered.

[0139] From Figure 1 and Equation 7, for a purely viscous fluid, the propagation depth of the shear wave is represented by the following equation.

Equation

[0140] Due to the decrease in the amplitude of the wave caused by viscosity, a shear stress τ sμ is generated on the vibration surface, which is the rate of change of the surface velocity (i.e., the shear rate

Equation

Equation

[0141] on the oscillating surface caused by wave attenuation and the viscosity μ’ of the fluid, and is represented by the following equation.

Equation

Equation

[0142] The shear rate due to viscous attenuation is proportional to the square root of the frequency, proportional to the square root of the density, and proportional to the square root of the reciprocal of the viscosity.

[0143] Therefore, the shear stress at the surface (the product of the surface viscosity and the shear rate) is non-linear.

Equation

[0144] In addition to the viscous effect, the fluid may exhibit elastic behavior, which depends on the storage modulus G’. The presence of G’ reduces the loss tangent tanΔ.

[0145] As described above, in the case of a purely viscous fluid, tanΔ = ∞. As the elastic behavior increases, the loss of the fluid decreases, and the wave can propagate further into the fluid. Considering elasticity, the propagation depth is represented by Equation 7, and in this equation, 1 / (sin(Δ / 2)√(2sinΔ)) is the quantity that scales the propagation depth according to the elastic behavior of the fluid. This quantity is also equal to 1 / √(sinΔ(1 - cosΔ)).

[0146] In the case of a purely viscous fluid, since Δ is equal to 90°,

Equation

[0147] The shear rate on the vibration surface due to both viscosity and elasticity is represented by the following equation.

Equation

[0148] The shear stress on the vibration surface due to both viscosity and elasticity is represented by the following equation.

Equation

[0149] The shear stress is a non-linear function of the fluid viscosity, fluid density, frequency, and storage modulus (by loss tangent). As the elastic G’ increases, tanΔ decreases, Δ decreases from its maximum value of π / 2, and both sinΔ and sinΔ / 2 decrease, so the damping shear stress decreases as the elastic G’ increases. This explains why viscoelastic fluids exhibit reduced damping compared to Newtonian fluids of “similar” viscosity.

[0150] Figure 48 shows a shear wave propagating radially through a viscoelastic fluid from a curved surface with radius R. The viscoelastic fluid has relatively little loss over short distances, but Figure 48 shows that as the radial distance increases, the peak position energy of each wave needs to be maintained, and the amplitude decreases as it spreads over the increasing circumference (2πr) where the energy increases. A line 510 of constant position energy is shown in Figure 48. As the energy is dispersed over the increasing circumference, the energy per unit volume decreases, and thus the peak height also decreases. This attenuation of the amplitude due to geometric considerations appears to be similar to attenuation, although it does not itself dissipate energy.

[0151] The change in height causes a decrease in velocity proportional to 1 / r, and this change in velocity causes

Number

[0152] Instead of the plane vibrating as in Figure 1, when a cylindrical surface of radius R vibrates, an equation for the velocity of the radial shear wave at a position r from the central axis of the cylinder may be obtained, and it may be differentiated with respect to r to obtain the radial shear rate.

Number

[0153] Next, the shear stress r = R on the cylindrical surface is represented by the following equation. [Number]

[0154] 1 / R ’ The term is the in-phase shear gradient. The shear rate of this component is in phase with the velocity regardless of the degree of viscoelasticity. 1 / δ μG’ The term is the out-of-phase shear gradient. The shear rate of this component is phase-shifted by φ, which depends on the degree of viscoelasticity. The phase adjustment angle represents the angle between the shear stress and the velocity. The shear stress that is in phase with the velocity dissipates energy.

[0155] When the value of R is much smaller than δ μG’ , the in-phase part becomes dominant, and the shear rate decreases its dependence on viscosity, density, frequency, and the storage modulus (through tanΔ / 2, which is a function of G''), or becomes even more independent. 1 / δ μG’ When 1 / δ is negligible compared to 1 / R, the shear stress on the cylindrical surface is represented by the following equation. [Number]

[0156] When the value of R is much larger than δ μG’ , the out-of-phase part becomes dominant, and the shear rate increasingly depends on the non-linear function of viscosity, density, frequency, and the storage modulus. When 1 / R is 1 / δ μG’When it can be ignored compared to, the shear stress on the cylindrical surface is expressed by the following equation.

Equation

[0157] The critical value of R is R onset =δ μG’ and this represents the intersection point of the value of R at which the shear stress due to the 1 / R ’ term becomes larger than the shear stress due to the 1 / δ μG’ term. According to the techniques described in this specification, this may be considered the beginning of geometric attenuation.

[0158] R < δ μG’ In the case of, the dependence of the shear stress on the non - linear function of viscosity, density, frequency, and storage modulus further decreases. When the radius of the cylinder is less than half of the visco - elastic propagation depth, it may be considered that geometric attenuation begins to dominate, that is, R < R onset / 2. In other words, R geo = <R onset / 2, and in this equation, R geo is understood to be the radius of the cylinder that defines the region where geometric attenuation is assumed to be dominant and the attenuation behavior can be defined.

[0159] In the measurement of the physical properties of a fluid, parameters such as the fluid attenuation coefficient C F and the stiffness load coefficient K F and the inertia load coefficient J F that improve the linearity of the fluid load coefficient can be selected. When R = δ μG’ , the equation for the viscosity of the fluid at which the beginning of geometric attenuation occurs is expressed as follows.

Equation

[0160] For example, a cylindrical element having a radius R of 2 mm is vibrating in a purely viscous fluid (sin(Δ / 2)√(2sinΔ)=1) at a frequency of 5 kHz, and the fluid has a density ρ of 1000 kg / m 3 ³. When appropriate selection of the fluid viscosity in Pa·S units is made, R = R onset is expressed as follows. μ’ onset = 2 2 ·π·5000·1000 = 62

[0161] For geometric attenuation to start becoming dominant (i.e., R geo = R onset / 2), the required viscosity becomes 4 times higher, i.e., as follows. μ’ geo =(2·2) 2 ·π·5000·1000 = 250

[0162] Similarly, the radius of the vibrating element and / or the vibration frequency can be selected to utilize geometric attenuation for a given viscosity and density operating range according to the operating requirements.

[0163] Figure 50 shows a graph of the attenuation coefficient of a heavy mineral oil measured at a frequency of 5 kHz using a vibrating cylinder with a radius of 2 mm. The density ρ of the fluid is 1000 kg / m³, and the attenuation coefficient is measured over a range of viscosity values (obtained by heating the heavy mineral oil). The measured attenuation coefficient is shown by the solid line indicated by "A" in Figure 4. The graph also shows a plot of the calculated attenuation coefficient when the attenuation is described by non-geometric attenuation, i.e., when 1 / R is negligible compared to 1 / δ μG’ . This line is indicated by "B" in Figure 4. The graph also shows a plot of the calculated attenuation coefficient when the attenuation is described by geometric attenuation, i.e., when 1 / δ μG’ is negligible compared to 1 / R. This line is indicated by "C" in Figure 4.

[0164] Figure 50 shows that while the viscosity is relatively low, i.e., less than about 60 Pa·S, the radius of the vibrating element is larger than the viscous penetration depth and the shear rate is a non-linear function of the viscosity. When the viscosity exceeds about 60 Pa·S, the attenuation of the shear wave begins to be explained by geometric attenuation and it can be seen that the attenuation coefficient becomes increasingly linear.

[0165] Figure 4 shows three regions. The first region, indicated by reference numeral 570, is the non-linear region and covers viscosity values less than μ onset (62 Pa·S determined above). The second region, indicated by reference numeral 580, is the linear transition region and covers viscosity values between μ onset and μ geo (250 Pa·S determined above). The third region, indicated by reference numeral 590, is the fully linear region and covers viscosity values greater than μ geo . When operating in the second region 580, the linearity is improved compared to when operating in the first region 570. When operating in the third region 590, the linearity is improved compared to when operating in the second region 580.

[0166] For a vibrating cylindrical tube with a radius that is sufficiently wide such that geometric attenuation can be neglected, the fluid attenuation coefficient C F , the stiffness loading coefficient K F , and the inertia loading coefficient J F are expressed by the following equations.

Equation

[0167] In these equations, since these terms (or quantities that are functions of these terms, such as Δ and the dependence of Δ on G’) are present within the parentheses, each of the coefficients has a non-linear dependence on μ’, G’, or ρ.

[0168] When the radius of the vibrating cylindrical tube is sufficiently small such that non-geometric attenuation can be neglected, C F , K F , and J FThe formula is expressed as follows.

Number

[0169] From these formulas, when non-geometric attenuation can be ignored, the fluid attenuation coefficient C F , the stiffness load coefficient K F , and the inertia load coefficient J F are found to no longer have non-linear dependence on μ’, G’, or ρ. Each of C F , K F , and J F is directly proportional to μ’, G’, and ρ respectively, and the proportionality constants depend only on geometric parameters.

[0170] It may be advantageous to improve the linearity of these fluid load coefficients. A mechanical system may have attenuation C, stiffness K, and inertia J. These determine the vibration frequency ω and Q factor of the system through the following equations.

Number

[0171] When the system is vibrating in air or in a vacuum, these mechanical coefficients can be designated as C 0 , K 0 , and J 0 . When the system is vibrating in a fluid, due to the physical properties of the fluid, these coefficients are each "loaded" by the amounts of C F , K F , and J F .

[0172] The overall values of the attenuation, stiffness, and inertia coefficients of the system considering fluid loading may be expressed as follows. C = C 0 + C F Equation 37 K = K 0 + K F Equation 38 J = J 0 + JF Formula 39

[0173] The overall values of C, K, and J are related to the above formulas of the easily measurable frequency and Q factor. The physical properties of the fluid are C F , K F , and J F may be determined based on their contributions to the vibration behavior. As will be described below, the techniques of the present disclosure may provide a simple linear relationship between C F , K F , and J F and the physical properties of interest such as the density ρ, viscosity μ', and storage modulus G'.

[0174] In these formulas, A is the fluid contact surface area of the cylindrical element, and R G is the "radius of gyration" of the element, which is equal to the radius R of the cylindrical element when the cylindrical element twists and vibrates about its axis.

[0175] When considering the influence of the moment of inertia on the rotational motion of an object, the radius of gyration is the radial distance to the point that has the same moment of inertia as the actual mass distribution of the object if all the mass of the object were concentrated there. The term "radius of gyration" in the present disclosure generalizes this concept to account for torsional coefficients other than the moment of inertia.

[0176] For the damping coefficient C F , the radius of gyration represents the radial distance to the point that has the same damping effect as the actual damping effect of the object if the damping were concentrated at that point.

[0177] For the stiffness load coefficient K F , the radius of gyration represents the radial distance to the point that has the same stiffness load effect as the actual stiffness load effect of the object if the stiffness load were concentrated at that point.

[0178] For the inertia load coefficient K F , the radius of gyration represents the radial distance to the point that has the same inertia load effect as the actual inertia load effect of the object if the inertia load were concentrated at that point.

[0179] Thus, the radius of rotation more generally defined in the present disclosure represents a convenient measure of the radial influence of these load factors. The radius of rotation is defined by the particular shape of the cylindrical element, but generally has upper and lower limits defined by the maximum and minimum radius ranges of the cylindrical element from the axis of rotation. When the cylindrical element torsional oscillates about its axis, all surface loads occur on the cylindrical surface and are all at a distance R from the axis, and thus are assumed to be equal to the radius R of the cylindrical element.

[0180] Figure 49 shows a first cylinder 520 of radius R torsional rotating about a longitudinal axis 25 passing through the center of the cylinder. The cylinder has a length l that rotates about the axis, and since the length of the cylinder is long enough, the area of the end (πR 2 ) is small compared to the area of the curved side (2πRl), R << δ μG’ , and when R = R G , the damping coefficient C F , the stiffness load coefficient K F , and the inertia load coefficient J F may be expressed as follows. C F = A R μ’ = (2πR 2 l)μ’ Equation 40 K F = A R G’ = (2πR 2 l)G’ Equation 41 J F = A R 3 ρ = (2πR 4 l)ρ Equation 42

[0181] Geometric attenuation due to the propagation of radio waves provides an advantage because it depends on geometric parameters rather than fluid properties, but the conditions for geometric attenuation recommend the use of cylindrical elements with small radii, resulting in a small active surface area. A smaller R 2· term in the damping, stiffness, and inertia load coefficients means that the damping, elastic, or inertia load coefficients due to torsional vibration are small even when the viscosity is high.

[0182] FIG. 49 also shows a second cylinder 530 having the same size as the first cylinder 520, and the second cylinder 530 is offset vertically by an offset radius R greater than R from the axis of the axis 525 of the first cylinder 520 0 only. The second cylinder 530 also torsional vibrates about the axis 525 of the first cylinder 520. As a result, the radius of rotation R G is changed from R (the distance from the cylindrical surface to the axis 525) to R 0 (the radius offset of the entire cylinder).

[0183] Damping coefficient C F , stiffness load coefficient K F , inertia load coefficient J F For the equations shown above, when geometric damping holds (that is, when non-geometric damping can be ignored), the equations may be expressed as follows. [Number]

[0184] R 0 When R is greater than R, by offsetting the vibration of the cylindrical element from the axis, the load coefficient is the square of the ratio of R 0 to R, that is, (R 0 / R) 2 only amplified. In the case of J F , the load coefficient is (R 0 / R) 4 , that is, the fourth power of the ratio of R 0 to R only amplified.

[0185] However, these equations hold only under the geometric damping of the cylindrical element. By offsetting the cylindrical element, pure torsional vibration no longer occurs, and instead vibrates laterally at the offset distance. These equations for the load coefficients are not automatically applicable because the cylindrical element may form a bipolar wave field rather than a monopole wave field under lateral vibration.

[0186] Figure 51 shows a cylindrical element in which a bipolar wave field occurs under lateral vibration. In the case of a bipolar wave field, there is a 180° phase difference between the wave fields on both sides of the cylindrical element. The formation of a bipolar wave field is problematic because the resulting wave is a pressure wave (P) rather than a shear wave (S). The hydrodynamics of pressure waves is different from that of shear waves, and the relationships previously defined for shear waves are no longer applicable.

[0187] For example, the attenuation coefficient is defined differently for shear waves and pressure waves. In the case of shear waves, it is relatively clearly defined by the shear velocity and the stress generated by the shear velocity, resulting in a controllable attenuated wave. In contrast, pressure waves follow a phenomenon known as "secondary attenuation," where the attenuation force is proportional to the square of the velocity. As a result, the attenuation coefficient is as follows. C quadratic =b·ν Equation 46 In the above equation, b is a constant and ν is the velocity. In other words, the attenuation coefficient changes unhelpfully according to the vibration velocity.

[0188] However, if the Reynolds number is kept low, a monopole wave field may be maintained. The Reynolds number represents the ratio between the inertial force and the viscous force. As the Reynolds number decreases, the viscous force becomes larger relative to the inertial force.

[0189] Figure 52 shows the laminar flow around a cylinder vibrating in the left - right direction perpendicular to the axis of the cylinder. In laminar flow, the forces on both sides of the cylinder become shear, and thus shear waves propagate as a result of lateral vibration. Without intending to be bound by theory, it is considered that due to laminar flow, the inertial force becomes sufficiently lower than the viscous force, and the wave field is mainly, or at least partially, defined by the shear waves generated from the upper and lower parts of the cylinder cross - section, that is, perpendicular to the axis and the direction of vibration. As a result, as the Reynolds number decreases, the degree to which the wave field has a dipole shape decreases, and the degree to which the wave field has a monopole shape increases. At low Reynolds numbers, a partially shear wave field with the same phase is restored throughout the propagation space. The advantage of geometric attenuation is retained, and there is also an advantage that the load factor gain increases by offsetting the element from the axis.

[0190] Since a cylindrical element offset from the axis can be easily achieved at a relatively low Reynolds number with a short length scale, it is advantageous that a relatively high amplification factor can be achieved with little increase in size and weight. In some implementations of the techniques of the present disclosure, a fluid loading coefficient equivalent to that of a much larger and heavier vibrating element may be achieved.

[0191] Regardless of physical properties, it is further recognized that relatively low Reynolds numbers can be easily achieved with microscale and nanoscale devices for almost all fluids of interest. The submicron needle structure of the vibrating substrate may form elements offset in the same radial direction as described above and achieve the same advantages of geometric attenuation. In some implementations, a plurality of cylindrical elements or elements shaped like cylinders, such as pins and spikes formed by a microfabrication process or a nanofabrication process, may be featured, which may also make it possible to achieve a high fluid loading coefficient on a small surface.

[0192] It is further recognized that at low Reynolds numbers, the wave field may be only partially defined by shear waves, so the equations for the loading coefficient under geometric attenuation conditions may not be the same as the above equations, but may be proportional to those equations, and the proportionality constant may vary depending on the extent to which the wave field is defined by shear waves. In the following equations, a proportionality constant h is introduced. When the wave field is completely defined by shear waves, the value of h has a value of 1. When the wave field is 50% defined by shear waves, the value of h has a value of 0.5, which is a reasonable assumption in practice. C F =h(2πlR 0 2 )μ’ Equation 47 K F =h(2πlR 0 2 )G’ Equation 48 J F =h(2πlR 0 4 )ρ Equation 49

[0193] Assuming h is 0.5, the above equation is simplified as follows. C F = h(πlR 0 2 )μ’ Equation 50 K F = h(πlR 0 2 )G’ Equation 51 J F = h(πlR 0 4 )ρ Equation 52

[0194] In the context of the present disclosure, the meaning of "low" Reynolds number is that the Reynolds number is low enough to obtain laminar flow, and the flow due to vibration may be characterized to some extent by a shear wave field, and at least some advantages of geometric attenuation are provided. The transition from laminar flow to turbulent flow occurs over a range of Reynolds numbers, and it is recognized that the exact range in which the transition from laminar flow to turbulent flow occurs depends on the shape. When the Reynolds number is low, there is a higher probability that the flow behavior resulting in a partial shear wave field will occur compared to when the Reynolds number is high. Without intending to be bound by theory, it is considered that the degree to which the shear wave field develops, and thus the degree to which some advantages of the techniques of the present disclosure are obtained, depends on the Reynolds number. For example, when the Reynolds number is 1000, a flow such as a certain degree of laminar flow may occur, and a certain degree of shear wave field may occur. When the Reynolds number is 100, the flow such as laminar flow becomes larger, and the shear wave field also becomes larger. When the Reynolds number is 10, the flow such as laminar flow becomes larger, and the shear wave field also becomes larger. When the Reynolds number is 1, the flow such as laminar flow becomes larger, and the shear wave field also becomes larger. Generally, it may be desirable for the Reynolds number to be low, but the reader will recognize that in order to achieve the lowest possible Reynolds number, it is necessary to balance other technical considerations.

[0195] When the geometric attenuation condition is satisfied, the propagation depth of the wave is determined by the shape of the cylindrical element, specifically the radius of the cylindrical element.

[0196] Considering the above discussion regarding geometric attenuation, the radiator surface or the detector surface may be the surface of an elongated member or may include an elongated member. Such an elongated member may be characterized by a width, a half-width equal to half of the width, and a length longer than the width, where the half-width is less than the propagation depth of the shear wave of the fluid at the vibration frequency, and more preferably less than 50% of the propagation depth. Such an elongated member may be non-collinear with the vibration axis, such as the axis of the torsional vibration, and may be offset from the vibration axis. During vibration, the flow of the fluid around the elongated member may be laminar.

[0197] In some embodiments, the half-width of the elongated member is less than 75%, 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% of the propagation depth.

[0198] In some embodiments, the elongated member has a substantially or completely circular cross-section along 50%, 70%, 90%, or 100% of the length of the elongated member. Optionally, the elongated member has a circularity 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 along 50%, 70%, 90%, or 100% of the length of the elongated member, and the circularity of the cross-sectional shape is 4πA / p 2 is calculated by this formula, where A is the convex area of the cross-sectional shape and p is the convex perimeter of the cross-sectional shape.

[0199] In some embodiments, the half-width of the elongated member calculated at a point along the length of the elongated member is based on the convex perimeter or convex area of the cross-section of the elongated member at a point along the length of the elongated member. Optionally, the half-width is calculated by the formula p / 2π based on the convex perimeter of the cross-sectional shape. Alternatively, the half-width may be calculated based on the convex area of the cross-sectional shape by the formula √(A / π). When the elongated member has a circular cross-section, both of these formulas yield the radius of the circle, so the half-width of the circular cross-section is the radius of the circle.

[0200] In some embodiments, the elongated member has a constant cross-section along more than 50%, more than 60%, more than 70%, more than 80%, more than 90%, or 100% of the length of the elongated member.

[0201] 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%, less than 10% of the length of the elongated member, or the cross-section varies continuously along the length of the elongated member.

[0202] In some embodiments, the cross-section increases or decreases monotonically along the length of the elongated member.

[0203] In some embodiments, the elongated member is straight.

[0204] In some embodiments, the elongated member is axisymmetric along the length of the elongated member.

[0205] In some embodiments, the elongated member is not straight. For example, the elongated member may comprise a closed loop.

[0206] In some embodiments, the elongated member comprises one of a cylinder, a cone, a frustum of a cone, a toroid, and an arc portion of a toroid.

[0207] 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.

[0208] In some embodiments, the half-width of the elongated member that is 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 is the average half-width calculated by dividing twice the volume of the elongated member by the surface area of the elongated member.

[0209] 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.

[0210] In some embodiments, the length of the elongated member is greater than a multiple of the half-width of the elongated member (where the half-width is half of the width of the elongated member), and the multiple is one of 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 is greater than a multiple of the width of the elongated member, and the multiple is one of 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.

[0211] In some embodiments, the width of the elongated member is between 1 nm and 500 nm. Such embodiments may be described as "nanoscale" or nanoscopic-scale embodiments. In some other embodiments, the width of the elongated member is between 500 nm and 500 μm. Such embodiments may be described as "microscale" or microscopic-scale embodiments. A device of appropriate dimensions, which may be a nanoscale or microscale device, may vibrate at low frequencies to advantageously measure the fluid properties of a low-viscosity fluid, such as less than 1 mPa·S, and may also vibrate at high frequencies to advantageously measure the fluid properties of a low-viscosity fluid, such as less than 1 mPa·S, because at such small scales, the width of the elongated member may still be small compared to the propagation depth at such high frequencies.

[0212] In some embodiments, the oscillating transducer element comprises a shaft having a longitudinal axis, the elongate member is connected to the shaft, and the elongate member is not collinear with the longitudinal axis of the shaft. Optionally, while the oscillating transducer element is oscillating at the oscillation frequency, the fluid flow around the elongate member is laminar. Alternatively or additionally, the Reynolds number Re of the fluid flow around the elongate member is less than 1, the Reynolds number is equal to 2Rνρ / μ, where μ is the viscosity of the fluid, ρ is the density of the fluid, R is the half-width of the elongate member, ν is the maximum (oscillation) velocity of the elongate member with respect to the fluid during oscillation of the oscillating transducer, and 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 elongate member may have a first end and a second end, and one or both of the first end and the second end are offset from the longitudinal axis of the shaft by an offset distance greater than the half-width of the elongate member, and 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 oscillating transducer element comprises a plurality of elongate members connected to the shaft, each elongate member is not collinear with the axis of the shaft, each elongate member has a half-width less than the propagation depth of the shear wave of the fluid at the oscillation frequency, and optionally, the half-width of the first elongate member among the plurality of elongate members is different from the half-width of the second elongate member among the plurality of elongate members, and optionally, two, three, four, five, or more of the plurality of elongate members may have uniquely different half-widths. Alternatively or additionally, the elongate member may comprise a first end and a second end, the elongate member is connected to the shaft at the first end, and optionally, is also connected to the shaft at the second end. Alternatively or additionally, the shaft may comprise a bobbin, and the elongate member may be connected to the shaft at the bobbin.

[0213] The vibration transducer according to the techniques described herein may be used to determine the physical properties of a fluid by vibrating the vibration transducer at the vibration frequency within the fluid and determining a quantity indicative of the degree of attenuation 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 attenuation level of the resonator, and the attenuation level is a function of viscosity. In particular, it indicates the extent to which the resonator is underdamped. In a plot of the frequency response, a high Q factor results in a high and narrow peak at the resonance frequency, while a low Q factor results in a low and wide peak. Due to the change in the width of the peak due to attenuation, the Q factor can be defined as the ratio of the resonance frequency to the resonance bandwidth.

Number

[0214] The measurement of viscosity at the vibration frequency, or the measurement of viscosity corresponding to the vibration frequency, may include performing amplitude measurements at multiple frequencies to estimate the Q factor, but it should be noted that a single viscosity measurement is obtained at its resonance frequency or a frequency corresponding to a certain resonance frequency. For example, the bandwidth can be determined based on the frequency required to reduce the amplitude to a factor of 1 / √2 of the maximum amplitude at resonance. As a non-limiting example, the frequency required to reduce the amplitude to a factor of 1 / √2 of the maximum amplitude at resonance may be determined by performing a frequency sweep near the resonance frequency, but the skilled reader will recognize that the 3 dB point frequencies can be identified by various other techniques.

[0215] Another method for determining the Q factor is to measure the amplitude of vibration at a series of frequencies near the resonance frequency and fit a parabola to the frequency and amplitude values (or their logarithms) by the least squares method. Then, the 3 dB point can be obtained as the solution of the quadratic equation based on the parabola that best fits the measured values.

[0216] Another method for determining the Q factor is to use logarithmic decrement. By stopping the drive of the transducer and measuring the decay of vibration, the Q factor can be determined by monitoring the time series of vibration and determining the natural logarithm of the ratio of two consecutive peaks A 1 and A 2 by the following formula.

Equation

[0217] As described above, since the loss factor is the reciprocal of the Q factor, it can be easily determined based on the above method.

[0218] FIG. 53 shows a flowchart of a method according to the techniques of the present disclosure. The method includes a first step 610 of vibrating one or more vibration transducers in a viscoelastic fluid to generate a first wave propagating from a first surface of the one or more vibration transducers and a second wave propagating from a second surface of the one or more vibration transducers, wherein during the vibration of the one or more vibration transducers, the first surface and the second surface are spaced apart from each other and oriented such that the first wave and the second wave combine with each other to cause final constructive or destructive interference on one or both of the first surface and the second surface.

[0219] The method includes a second step 620 of determining the material properties of the viscoelastic fluid based on the vibration of the one or more vibration transducers in the viscoelastic fluid.

[0220] According to the techniques of the present disclosure, the means for vibrating one or more vibration transducers may include an electronic device configured to provide a control signal to the one or more vibration transducers in order to vibrate the one or more vibration transducers in a fluid by a method according to the techniques of the present disclosure.

[0221] According to the techniques of the present disclosure, the means for determining the material properties of a viscoelastic fluid based on the vibration of one or more vibration transducers in the viscoelastic fluid may include an electronic device configured to record measured values of the vibration of the one or more vibration transducers and process the measured values in order to determine the material properties.

[0222] The means for vibrating one or more vibration transducers and the means for determining the material properties of a viscoelastic fluid based on the one or more vibration transducers may be the same electronic device (i.e., a single electronic device causes the vibration and determines the material properties), or may be different electronic devices.

[0223] One of ordinary skill in the art will further appreciate that the various illustrative logical blocks, configurations, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, configurations, modules, circuits, and steps are described generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as departing from the scope of the present disclosure.

[0224] The steps of a method or algorithm described in connection with the embodiments disclosed in this specification may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. The software module may 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, a hard disk, a removable disk, a compact 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, which can read information from, and write information to, the storage medium. Alternatively, the storage medium may be integral to the processor. The processor and the storage medium may reside in an application specific integrated circuit (ASIC). The ASIC may reside in a computing device or a user terminal. Alternatively, the processor and the storage medium may reside as discrete components of a computing device or a user terminal.

[0225] The material of the present disclosure may be described by the following numbered aspects. [Aspect 1] A method of measuring the material properties of a viscoelastic fluid using one or more vibrating transducers, ● vibrating one or more vibrating transducers within the viscoelastic fluid to generate a first wave propagating from a first surface of the one or more vibrating transducers and a second wave propagating from a second surface of the one or more vibrating transducers, wherein during vibration of the one or more vibrating transducers, the first surface and the second surface are spaced apart from and oriented with respect to each other such that the first wave and the second wave combine with each other to cause final constructive or destructive interference on one or both of the first surface and the second surface; ●Determining the material properties of the viscoelastic fluid based on the vibration of the one or more vibration transducers in the viscoelastic fluid; A method comprising the same. [Aspect 2] The method according to aspect 1, wherein the first wave and the second wave combine with each other to cause final destructive interference. [Aspect 3] The method according to aspect 1, wherein the first wave and the second wave combine with each other to cause final constructive interference. [Aspect 4] The method according to aspect 1 or aspect 2, wherein the first wave and the second wave are shear waves. [Aspect 5] The method according to any one of aspects 1 to 4, wherein the step of determining the measured value of the material properties of the viscoelastic fluid includes determining the loss coefficient or Q coefficient of the vibration of the one or more vibration transducers in the viscoelastic fluid. [Aspect 6] The method according to aspect 5, wherein the determined loss coefficient or Q coefficient is a monotonic function of the viscosity or storage modulus of the viscoelastic fluid. [Aspect 7] The method according to any one of aspects 1 to 6, wherein tanΔ of the viscoelastic fluid is less than 1, and tanΔ is the loss tangent of the viscoelastic fluid. [Aspect 8] The method according to any one of aspects 1 to 7, wherein one or both of the first surface and the second surface are curved. [Aspect 9] The method according to aspect 8, wherein one or both of the first surface and the second surface are convex. [Aspect 10] The method according to aspect 8 or aspect 9, wherein one or both of the first surface and the second surface are partially or entirely concave. [Aspect 11] The first surface is partially or entirely concave, and the first wave generated from the first surface is configured to converge at the focal distance from the first surface, where i) the second surface is disposed farther from the first surface than the focal distance from the first surface, or ii) the second surface is disposed closer to the first surface than the focal distance from the first surface, or iii) the second surface is disposed at the focal distance from the first surface, the method according to aspect 10. [Aspect 12] The first surface includes a recess configured to focus the first wave, the recess including a first region of the recess and a second region of the recess configured to vibrate out of phase with the first region of the recess to generate a wave out of phase with the wave generated from the first region of the recess, the method according to any one of aspects 1 to 11. [Aspect 13] The step of vibrating the one or more vibration transducers includes torsionally vibrating the recess of the first surface about a vibration axis extending through the recess of the first surface, where i) the first region of the recess and the second region of the recess are disposed on opposite sides of the vibration axis, and / or ii) the recess of the first surface is axially symmetric about the vibration axis, and / or iii) the vibration axis extends through the focal region of the recess, the method according to aspect 12. [Aspect 14] The depth profile of the recess in a transverse cross-section passing through the vibration axis is smooth and preferably has a shape of an arc, a parabolic arc, or an elliptical arc, the method according to aspect 12 or aspect 13. [Aspect 15] The step of vibrating the one or more vibration transducers includes vibrating the first region and the second region of the recess along a path such as a straight path or a circular path, the method according to aspect 12. [Aspect 16] The method according to aspect 15, wherein the first region and the second region of the recess have a constant recess depth profile in the direction of the path. [Aspect 17] The method according to aspect 16, wherein the step of vibrating the one or more vibration transducers includes vibrating the first region and the second region of the recess in the direction of the path. [Aspect 18] The method according to aspect 16 or aspect 17, wherein the depth profile of the first region and the second region of the recess is smooth and preferably has the shape of an arc, a parabolic arc, or an elliptical arc. [Aspect 19] The method according to any one of aspects 1 to 18, wherein one or both of the first surface and the second surface comprise an elongate member. [Aspect 20] The method according to aspect 19, wherein the step of vibrating the one or more vibration transducers in the viscoelastic fluid includes vibrating the one or more vibration transducers through or about the respective vibration axes of the one or more vibration transducers, and the vibration axes are not collinear with at least one elongate member corresponding to the first surface or the second surface. [Aspect 21] The method according to aspect 19 or aspect 20, wherein the step of vibrating the one or more vibration transducers in the viscoelastic fluid includes torsional vibration of the one or more vibration transducers about a common vibration axis. [Aspect 22] The method according to aspect 21, wherein one or both of the first surface and the second surface comprise an elongate member configured in the shape of a ring. [Aspect 23] The method according to aspect 22, wherein the axis passing through the center of the ring is collinear with the common vibration axis. [Aspect 24] The method according to aspect 22 or aspect 23, wherein one or both of the first surface and the second surface are concave and configured to focus waves on the ring. [Aspect 25] The method according to any one of aspects 21 to 24, wherein the first surface comprises an elongated member configured in a ring shape, the first surface being connected to the second surface by one or more support members that offset the first surface from the second surface. [Aspect 26] The method according to aspect 25, wherein the second surface comprises a recess configured to generate a shear wave by torsional vibration about the common vibration axis, and the generated shear wave converges toward the first surface. [Aspect 27] The method according to aspect 19 or aspect 20, wherein the one or more vibration transducers comprise a shaft having a longitudinal axis extending along the shaft, and a plurality of elongated members extending outward from the longitudinal axis and spaced apart from each other, and the step of vibrating the one or more vibration transducers includes torsional vibration of the shaft about the longitudinal axis. [Aspect 28] The method according to aspect 27, wherein the plurality of elongated members are connected to the shaft. [Aspect 28A] The method according to aspect 28, wherein the plurality of elongated members extend completely radially outward from the shaft from the longitudinal axis. [Aspect 29] The method according to aspect 27, wherein the shaft comprises a bob, and the plurality of elongated members are connected to the shaft at the bob. [Aspect 29A] The method according to aspect 29, wherein the plurality of elongated members extend completely radially outward from the bob from the longitudinal axis. [Aspect 29B] The method according to aspect 19 or 20, wherein the one or more vibration transducers comprise a shaft having a longitudinal axis extending along the shaft, and a plurality of elongated members extending in a direction along the longitudinal axis and spaced apart from each other, and the step of vibrating the one or more vibration transducers includes torsional vibration of the shaft about the longitudinal axis. [Aspect 29C] The method according to aspect 29B, wherein none of the plurality of elongated members is on the same straight line as the longitudinal axis of the shaft. [Aspect 29D] The method according to aspect 29B or aspect 29C, wherein some or all of the plurality of elongated members extend axially outward from an end of the shaft. [Aspect 29E] The method according to aspect 29B or aspect 29C, wherein the shaft includes a bobbin, and the plurality of elongated members are connected to the shaft at the bobbin. [Aspect 29F] The method according to aspect 29E, wherein the bobbin is cylindrical and coaxial with the longitudinal axis. [Aspect 29G] The method according to aspect 29E or 29F, wherein the plurality of elongated members extend axially outward from an end of the bobbin. [Aspect 29H] The method according to any one of aspects 29B to 29G, wherein the plurality of elongated members are evenly distributed around the longitudinal axis of the shaft. [Aspect 29I] The method according to any one of aspects 29B to 29H, wherein the plurality of elongated members are respectively arranged at the same radial distance from the longitudinal axis of the shaft. [Aspect 30] The method according to any one of aspects 25 to 29I, wherein the first wave and the second wave are shear waves, and one or both of the first surface and the second surface include an elongated member characterized by a width, a half-width equal to half of the width, and a length longer than the width, and the half-width is smaller than the propagation depth of the shear wave of the fluid at the vibration frequency. [Aspect 31] The method according to aspect 30, wherein the propagation depth is the distance at which the amplitude of the shear wave propagating in the fluid at the vibration frequency decreases to a factor of 1 / e, where e is the base of the natural logarithm. [Aspect 32] The propagation depth of the shear wave propagating in the fluid at the vibration frequency is represented by the following formula: [Number] In the above formula, μ is the viscosity of the fluid, ρ is the density of the fluid, ω is the angular frequency of vibration, Δ varies between 0 and π / 2 (radians), is defined by the loss tangent tanΔ, and tanΔ is equal to the following formula: [Number] The method according to aspect 30 or aspect 31, wherein G' in the above formula is the storage modulus of the fluid. [Aspect 33] The method according to any one of aspects 30 to 32, wherein the half-width is less than 50% of the propagation depth. [Aspect 34] The method according to any one of aspects 30 to 33, wherein the one or more vibration transducers comprise a shaft having a longitudinal axis, an elongated member is connected to the shaft, and the elongated member is not on the same straight line as the longitudinal axis of the shaft. [Aspect 35] The method according to any one of aspects 30 to 34, wherein the shaft comprises a bob, and the elongated member is connected to the shaft at the bob. [Aspect 36] The method according to any one of aspects 30 to 36, wherein the vibration transducer element comprises a plurality of elongated members connected to the shaft, each elongated member is not on the same straight line as the longitudinal axis of the shaft, and each elongated member has a half-width smaller than the propagation depth of the shear wave of the fluid at the vibration frequency. [Aspect 37] The method according to aspect 36, wherein the half-width of the first elongated member among the plurality of elongated members is different from the half-width of the second elongated member among the plurality of elongated members. [Aspect 38] The elongated member has a cross-section having a roundness in the range of 0.75 to 1 along at least 50% of its length, and the roundness of the cross-section is [Number] Calculated by, in the above formula, A is the convex area of the cross section, and p is the convex perimeter of the cross section, the method according to any one of Aspects 30 to 37. [Aspect 39] The method according to any one of Aspects 30 to 38, wherein the elongated member has a constant cross section along at least 90% of its length or has a constant cross section along 10% or less of its length. [Aspect 40] The method according to any one of Aspects 30 to 39, wherein the elongated member is linear or non-linear, or includes one of a cylinder, a cone, a frustum of a cone, an annular body, and an arc portion of an annular body. [Aspect 41] The method according to any one of Aspects 30 to 40, wherein the step of vibrating the vibration transducer includes vibrating the vibration transducer using a vibratory rotational motion and / or a vibratory linear motion and / or a vibratory curvilinear motion. [Aspect 42] The method according to Aspect 41, wherein the elongated member is linear, and the step of vibrating the vibration transducer includes vibrating the elongated member by a vibratory rotational motion about an axis along the length of the elongated member. [Aspect 43] The method according to any one of Aspects 30 to 42, wherein the length of the elongated member is greater than twice the width of the elongated member. [Aspect 44] The half-width of the elongated member is greater than 0.5 mm, the viscosity of the fluid is greater than 100 Pa·s, the density of the fluid is 500 kg / m 3 ~1500 kg / m 3 and the frequency of the vibration is less than 10 kHz, the method according to any one of Aspects 30 to 43. [Aspect 45] The method according to any one of Aspects 35 to 44, wherein the flow of the fluid around the elongated member becomes laminar while the elongated member is vibrating at the vibration frequency. [Aspect 46] The method according to any one of Aspects 35 to 45, wherein the elongated member has a first end and a second end, and one or both of the first end and the second end are separated from the longitudinal axis of the shaft by an offset distance greater than the half-width of the elongated member. [Aspect 47] While the one or more vibration transducers are vibrating in the fluid at the vibration 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. The Reynolds number is expressed as follows: [Equation] In the above formula, μ' is the viscosity of the fluid, ρ is the density of the fluid, R is the half-width of the elongated member, and ν is the maximum velocity of the elongated member with respect to the fluid during the vibration of the one or more vibration transducers. The method according to any one of Aspects 35 to 46. [Aspect 48] The method according to any one of Aspects 30 to 34, wherein the elongated member is ring-shaped. [Aspect 49] The step of vibrating the one or more vibration transducers includes vibrating the one or more vibration transducers at the vibration frequency. The vibration frequency is between 100 Hz and 100 kHz, preferably between 200 Hz and 10 kHz, more preferably between 300 Hz and 5 kHz, more preferably between 500 Hz and 2 kHz, even more preferably between 700 Hz and 1300 Hz, and even more preferably 1 kHz or an approximation thereof, for example within 100 Hz of 1 kHz, preferably within 50 Hz of 1 kHz. The method according to any one of Aspects 1 to 48. [Aspect 50] The method according to any one of Aspects 1 to 49, wherein the one or more vibration transducers perform torsional vibration about a common axis. [Aspect 51] The step of determining the material properties of the viscoelastic fluid based on the measurement of the vibration includes determining one or more of viscosity, viscoelasticity, density, fluid stiffness, loss tangent, storage modulus, loss modulus, and yield stress, according to any one of Aspects 1 to 50. [Aspect 52] The step of determining the material properties of the viscoelastic fluid based on the vibration of the one or more vibration transducers within the viscoelastic fluid includes determining a quantity indicative of the degree of attenuation of the fluid at the vibration frequency, according to any one of Aspects 1 to 51. [Aspect 53] The step of determining a quantity indicative of the degree of attenuation of the vibration of the fluid at the vibration frequency includes determining a loss factor or a Q factor, according to the method of Aspect 52. [Aspect 54] The step of determining a quantity indicative of the degree of attenuation of the fluid at the vibration frequency includes determining a first quantity indicative of the degree of attenuation at the vibration frequency, and the method further includes vibrating the vibration transducer at a further vibration frequency and determining a second quantity indicative of the degree of attenuation at the further vibration frequency, and the step of determining the material properties of the fluid further includes determining the viscoelasticity of the fluid based on the quantities indicative of the degree of attenuation at the vibration frequency and at the further vibration frequency, according to the method of Aspect 52 or Aspect 53. [Aspect 55] The step of determining the material properties of the fluid includes determining the density of the fluid based on the measurement of the resonance frequency of the vibration transducer within the fluid, according to the method of Aspect 52 or Aspect 53. [Aspect 56] An apparatus for measuring the material properties of a viscoelastic fluid using one or more vibration transducers, ● the one or more vibration transducers, each having a first surface and a second surface, ● Means for vibrating one or more vibration transducers such that when vibrating in a viscoelastic fluid, a first wave propagating from a first surface of the one or more vibration transducers is generated and a second wave propagating from a second surface of the one or more vibration transducers is generated, and during vibration of the one or more vibration transducers, the first surface and the second surface are spaced apart from each other and oriented such that the first wave and the second wave combine with each other to cause final constructive or destructive interference on one or both of the first surface and the second surface. ● Means for determining a material property of the viscoelastic fluid including the final constructive or destructive interference based on the vibration of the one or more vibration transducers in the viscoelastic fluid. An apparatus comprising the above. [Aspect 57] The apparatus according to aspect 56, wherein the first surface comprises a recess. [Aspect 58] The apparatus according to aspect 56 or aspect 57, wherein the first surface comprises an elongated member. [Aspect 59] The apparatus according to any one of aspects 56 to 58, wherein the second surface comprises an elongated member. [Aspect 60] The apparatus according to any one of aspects 56 to 58, wherein the second surface is flat and optionally, the first surface comprises an elongated member extending outward from the second surface. [Aspect 61] The apparatus according to aspect 60, wherein the first surface comprises an elongated member extending in a direction perpendicular to the second surface. [Aspect 62] The apparatus according to aspect 61, wherein the first surface comprises an elongated member configured in a ring shape. [Aspect 63] The second surface faces radially outward from the axis of the torsional vibration of the vibration transducer on which the second surface is disposed, and is configured to generate a shear wave extending radially outward from the axis of the torsional vibration, and optionally, the first surface comprises an elongated member extending outward from the second surface, the apparatus according to aspect 58. [Aspect 64] The apparatus according to aspect 64, wherein the first surface comprises an elongated member extending in a direction perpendicular to the second surface. [Aspect 65] The apparatus according to aspect 66, wherein the first surface comprises an elongated member extending circumferentially around the second surface or extending in a direction coinciding with the axis of the torsional vibration. [Aspect 66] The second surface comprises a recess configured to generate a wave in the fluid that converges at a focal distance from the second surface, and i) the first surface is disposed farther from the second surface than the focal distance from the second surface, or ii) the first surface is disposed closer to the second surface than the focal distance from the second surface, or iii) the first surface is disposed at the focal distance from the second surface, the apparatus according to any one of aspects 60 to 65. [Aspect 67] The apparatus according to any one of aspects 56 to 71, wherein the first surface comprises an elongated member configured in the shape of a ring and connected to the second surface by one or more support members that offset the first surface from the second surface. [Aspect 68] The apparatus according to aspect 67, wherein the second surface comprises a recess configured to generate a shear wave by torsional vibration about the common vibration axis, and the generated shear wave converges toward the first surface. [Aspect 69] The one or more vibration transducers include a shaft having a longitudinal axis extending along the shaft, and a plurality of elongated members extending outward from the longitudinal axis and spaced apart from each other, and the step of vibrating the one or more vibration transducers includes torsionally vibrating the shaft about the longitudinal axis, the apparatus according to any one of aspects 56 to 66. [Aspect 70] The apparatus according to aspect 69, wherein the plurality of elongated members are connected to the shaft and extend radially outward from the shaft. [Aspect 70A] The apparatus according to aspect 70, wherein the plurality of elongated members extend completely radially outward from the shaft from the longitudinal axis. [Aspect 71] The apparatus according to aspect 69, wherein the shaft includes a bob, and the plurality of elongated members are connected to the shaft at the bob. [Aspect 71A] The apparatus according to aspect 71, wherein the plurality of elongated members extend completely radially outward from the bob from the longitudinal axis. [Aspect 71B] The one or more vibration transducers include a shaft having a longitudinal axis extending along the shaft, and a plurality of elongated members extending in a direction along the longitudinal axis and spaced apart from each other, and vibrating the one or more vibration transducers includes torsionally vibrating the shaft about the longitudinal axis, the apparatus according to any one of aspects 56 to 66. [Aspect 71C] The apparatus according to aspect 71B, wherein none of the plurality of elongated members are on the same straight line as the longitudinal axis of the shaft. [Aspect 71D] The apparatus according to aspect 71B or aspect 71C, wherein some or all of the plurality of elongated members extend axially outward from an end of the shaft. [Aspect 71E] The apparatus according to aspect 71B or aspect 71C, wherein the shaft comprises a bob, and the plurality of elongated members are connected to the shaft at the bob. [Aspect 71F] The apparatus according to aspect 71E, wherein the bob is cylindrical and coaxial with the longitudinal axis. [Aspect 71G] The apparatus according to aspect 71E or 71F, wherein the plurality of elongated members extend axially outward from an end of the bob. [Aspect 71H] The apparatus according to any one of aspects 71B to 71G, wherein the plurality of elongated members are evenly distributed around the longitudinal axis of the shaft. [Aspect 71I] The apparatus according to any one of aspects 71B to 71H, wherein the plurality of elongated members are respectively arranged at the same radial distance from the longitudinal axis of the shaft. [Aspect 72] The apparatus according to any one of aspects 56 to 71I, wherein one or both of the first surface and the second surface comprise an elongated member characterized by a width, a half-width equal to half of the width, and a length longer than the width, and the half-width is smaller than the propagation depth of the shear wave of the fluid at the vibration frequency. [Aspect 73] The apparatus according to aspect 72, wherein the half-width is less than 50% of the propagation depth. [Aspect 74] The apparatus according to aspect 72 or aspect 73, wherein the one or more vibration transducers comprise a shaft having a longitudinal axis, the elongated member is connected to the shaft, and the elongated member is not on the same straight line as the longitudinal axis of the shaft. [Aspect 75] While the one or more vibration transducers are vibrating in the fluid at the vibration 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, and the Reynolds number is represented as follows:

Equation

[0226] The foregoing description of the disclosed embodiments is provided to enable a person skilled in the art to make or use the disclosed embodiments. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the principles defined herein may be applied to other embodiments without departing from the scope of the disclosure. Accordingly, the present disclosure is not intended to be limited to the embodiments shown herein, but rather should be accorded the widest possible scope consistent with the principles and novel features defined by the appended claims.

Claims

1. A method for measuring the material properties of a viscoelastic fluid using one or more vibration transducers, A step of vibrating one or more vibration transducers in a viscoelastic fluid to generate a first wave propagating from a first surface of one or more vibration transducers and a second wave propagating from a second surface of one or more vibration transducers, wherein the first surface and the second surface are spaced apart from and oriented toward each other such that the first wave and the second wave couple together to produce a final constructive or destructive interference on one or both of the first and second surfaces during the vibration of the one or more vibration transducers. A step of determining the material properties of the viscoelastic fluid based on the vibration of one or more vibration transducers in the viscoelastic fluid. Methods that include...

2. The method according to claim 1, wherein the first wave and the second wave couple to each other to produce a final destructive interference on one or both of the first surface and the second surface.

3. The method according to claim 1, wherein the first wave and the second wave are shear waves.

4. The method according to claim 1, wherein the step of determining a measured value of the material properties of the viscoelastic fluid includes determining the vibration loss coefficient or Q coefficient of the one or more vibration transducers in the viscoelastic fluid.

5. The method according to claim 4, wherein the determined loss coefficient or Q coefficient is a monotonic function of the viscosity or storage modulus of the viscoelastic fluid.

6. The method according to claim 1, wherein the tanΔ of the viscoelastic fluid is less than 1, and tanΔ is the loss tangent of the viscoelastic fluid.

7. The method according to claim 1, wherein one or both of the first surface and the second surface are curved or have a curved portion.

8. The method according to claim 7, wherein one or both of the first surface and the second surface are concave or have a recess, and the first wave is focused at a focal distance from the first surface.

9. The method according to claim 8, wherein the second surface is located at a distance from the first surface greater than the focal distance from the first surface.

10. The recess of the first surface is The first region of the recess and, A second region of the recess is configured to vibrate in phase with respect to the first region of the recess in order to generate a wave that is out of phase with respect to the wave generated from the first region of the recess, The method according to claim 8, comprising:

11. The first surface and the second surface, or one or both, are provided with an elongated member. The step of vibrating one or more vibration transducers in the viscoelastic fluid is The process involves vibrating one or more vibration transducers through or around their vibration axes, wherein the vibration axes are not collinear with the elongated member. The method according to claim 1, including the method described in claim 1.

12. The method according to claim 11, wherein the step of vibrating one or more vibration transducers in the viscoelastic fluid includes torsional vibration of one or more vibration transducers about a common vibration axis, and comprises an elongated member in which one or both of the first surface and the second surface are configured in the shape of a ring, and the axis passing through the center of the ring is collinear with the common vibration axis.

13. The method according to claim 12, wherein the first surface comprises an elongated member configured in the shape of a ring, the first surface being connected to the second surface by one or more support members that offset the first surface from the second surface.

14. The method according to claim 12, wherein the second surface includes a recess configured to generate shear waves by torsional vibrations centered on the common vibration axis, and the generated shear waves converge toward the first surface.

15. The one or more vibration transducers described above A shaft having a vertical axis extending along the shaft, Multiple elongated members extending outward from the aforementioned vertical axis and spaced apart from each other, Equipped with, The method according to claim 11, wherein the step of vibrating one or more vibration transducers includes torsion vibration of the shaft about the vertical axis.

16. The method according to claim 1, wherein the first wave and the second wave are shear waves, and one or both of the first surface and the second surface are elongated members characterized by a width, a half-width equal to half the width, and a length longer than the width, wherein the half-width is smaller than the propagation depth of the shear wave of the fluid at the vibration frequency.

17. The method according to claim 1, wherein the step of vibrating one or more vibration transducers includes vibrating one or more vibration transducers at a vibration frequency, the vibration frequency being between 500 Hz and 2 kHz.

18. An apparatus for measuring the material properties of a viscoelastic fluid using one or more vibration transducers, One or more vibration transducers, each comprising a first surface and a second surface, Means for vibrating one or more vibration transducers such that, when vibrated in a viscoelastic fluid, a first wave propagating from a first surface of one or more vibration transducers is generated, and a second wave propagating from a second surface of one or more vibration transducers is generated, wherein the first surface and the second surface are spaced apart from and oriented toward each other such that, during the vibration of the one or more vibration transducers, the first wave and the second wave couple together to cause a final constructive or destructive interference on one or both of the first and second surfaces. Means for determining the material properties of the viscoelastic fluid, including the final constructive or destructive interference, based on the vibrations of one or more vibration transducers within the viscoelastic fluid. A device equipped with the following features.

19. The apparatus according to claim 18, wherein the first surface comprises an elongated member, a flat surface, and / or a recess configured to generate waves that converge toward the second surface by vibration, and the second surface comprises an elongated member, a flat surface, and / or a recess configured to generate waves that converge toward the first surface by vibration.

20. The first surface and the second surface, or one or both, are provided with an elongated member. Vibrating one or more vibration transducers within the viscoelastic fluid is The process involves vibrating one or more vibration transducers through or around their vibration axes, wherein the vibration axes are not collinear with the elongated member. The apparatus according to claim 18 or claim 19, including the apparatus described in claim 18 or 19.

21. The apparatus according to claim 20, wherein vibrating one or more vibration transducers in the viscoelastic fluid includes torsional vibration of one or more vibration transducers about a common vibration axis, and comprises an elongated member in which one or both of the first surface and the second surface are configured in the shape of a ring, and the axis passing through the center of the ring is collinear with the common vibration axis.

22. The method according to claim 21, wherein the first surface comprises an elongated member configured in the shape of a ring, the first surface being connected to the second surface by one or more support members that offset the first surface from the second surface.

23. The apparatus according to claim 21, wherein the second surface has a recess configured to generate shear waves by torsional vibrations centered on the common vibration axis, and the generated shear waves converge toward the first surface.

24. The one or more vibration transducers described above A shaft having a vertical axis extending along the shaft, Multiple elongated members extending outward from the aforementioned vertical axis and spaced apart from each other, Equipped with, The apparatus according to claim 20, wherein vibrating one or more of the vibration transducers includes torsion vibration of the shaft about the vertical axis.

25. The apparatus according to claim 18 or 19, wherein one or both of the first surface and the second surface comprises an elongated member characterized by a width, a half-width equal to half the width, and a length longer than the width, wherein the half-width of the elongated member is less than the propagation depth of the shear wave of the fluid at the vibration frequency.

26. The apparatus according to claim 18 or 19, wherein the first surface and the second surface are located on the same vibration transducer or on different vibration transducers configured to vibrate at the same frequency.

27. The apparatus according to claim 18 or 19, wherein the first surface and the second surface are configured to vibrate in the same phase as each other or with a phase offset relative to each other.

28. A non-temporary computer-readable medium on which instructions are stored, wherein, when the instructions are executed by one or more processors of a system comprising one or more vibration transducers, the one or more processors cause the one or more processors to perform the method according to any one of claims 1 to 17.

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