Wave interference in rheological measurements

Abstract

A method of measuring a material property of a viscoelastic fluid using one or more vibration transducers, the method comprising: vibrating the one or more vibration transducers in the viscoelastic fluid, the first surface and the second surface are spaced apart and oriented relative to each other such that during vibration of the one or more vibration transducers, the first wave and the second wave combine with each other 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, where the first surface and the second surface are spaced apart and oriented relative to each other such that during vibration of the one or more vibration transducers, the first wave and the second wave combine with each other. To provide net constructive interference or net destructive interference; and determining a material characteristic of the viscoelastic fluid based on the vibration of the one or more vibration transducers in the viscoelastic fluid.

Description

Technical Field

[0001] The present disclosure relates to the damping of vibrations within fluids, including the use of damping to obtain measurements of physical and rheological properties of materials, such as measurements of viscosity. Background Art

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

[0003] For example, the degree of damping may be determined by the amplitude of vibration or changes in amplitude, the resonant frequency or changes in resonant frequency, the rate of vibration attenuation, or the quality (Q) factor, or loss factor, which is the inverse of the quality factor.

[0004] Resonant viscometers measure viscosity by determining the damping effect of a viscous fluid on a mechanical oscillator immersed in the fluid. The presence of viscosity increases the shear stress on the surface of the oscillator. The shear stress creates a damping force that consumes energy from the oscillator. For a mechanical oscillator operating at resonance, this reduces the Q factor at resonance. The Q factor is therefore the inverse of viscosity. The loss factor is the reciprocal of the Q factor, so an increase in viscosity results in an increase in the loss factor. Historically, resonant viscometers have been shown to work well for purely viscous fluids and slightly viscoelastic fluids (non-Newtonian fluids) with tanΔ (i.e., loss tangent) greater than 1 (i.e., their loss factor effectively varies with changes in the viscosity of the fluid).

[0005] The loss tangent is given by the following equation: tanΔ = ωμ′ / G′, where ω is the angular frequency of oscillation, 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 do not have any elastic behavior. There is no storage modulus. The loss tangent tanΔ is infinite. Examples of such fluids are water, aqueous solutions, syrups, alcohols, most pure oils, most hydrocarbons, and gases.

[0007] Non-Newtonian fluids may be viscoelastic, so that tanΔ < ∞. Examples of viscoelastic fluids include blood, suspensions, emulsions, and most synthetic materials. Strongly viscoelastic fluids may be tanΔ < 1. Examples of strongly viscoelastic fluids include liquid polymers, polymer melts, rubber solutions, synthetic oils, detergents, and foods. Summary of the invention

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

[0009] According to another aspect, a non-transitory computer-readable medium is provided having instructions stored thereon, which, when executed by one or more processors of a system including one or more vibration transducers, cause the one or more processors to perform the above method.

[0010] According to another aspect, a device for measuring material properties of a viscoelastic fluid using one or more vibration transducers is described, the device comprising: one or more vibration transducers, the one or more vibration transducers comprising a first surface and a second surface; a component for vibrating the one or more vibration transducers so that when vibrating in the viscoelastic fluid, a first wave propagating from the first surface of the one or more vibration transducers is generated, and a second wave propagating from the second surface of the one or more vibration transducers is generated, wherein the first surface and the second surface are spaced apart and oriented relative to each other so that during vibration of the one or more vibration transducers, the first wave and the second wave combine with each other to provide net constructive interference or destructive interference at one or both of the first surface and the second surface; and a component for determining the material properties of the viscoelastic fluid based on the vibration of the one or more vibration transducers in the viscoelastic fluid including the net constructive interference or destructive interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The invention will now be described in more detail, by way of example only, with reference to the accompanying drawings, in which:

[0012] Figure 1 shows shear waves generated from an oscillating surface in a fluid;

[0013] Figure 2 A simple model of a viscoelastic fluid acting as a spring and damper system is shown;

[0014] Figure 3 is plotted against Δ (in degrees) Graph of

[0015] Figure 4shows the shear wave velocity field generated by the primary oscillating surface (i.e., detector) and the secondary oscillating surface (i.e., radiator) of a first viscoelastic fluid having relatively low μ′ and relatively low G′;

[0016] Figure 5 shows the shear wave velocity field generated by the primary oscillating surface (i.e., the detector) and the secondary oscillating surface (i.e., the radiator) of a second viscoelastic fluid having relatively high μ′ and relatively high G′;

[0017] Figure 6 shows the propagation of a shear wave from a surface having a radius of curvature subjected to torsional vibration; and

[0018] Figure 7 to Figure 47 shows a configuration of a vibration transducer according to the technology of the present disclosure;

[0019] Fig.48 An exemplary elongated member is shown in which geometric damping may occur during vibration thereof;

[0020] Fig.49 Yet another example elongated member in which geometric damping may occur during vibration is shown;

[0021] Fig.50 is a graph of the damping coefficient and the penetration depth relative to the damping coefficient, showing three states of different linearity;

[0022] Fig.51 shows acoustic waves generated by lateral vibration of an elongated member in a fluid;

[0023] Fig.52 shows shear waves generated by lateral vibration of an elongated member during laminar flow; and

[0024] Fig.53 A flow chart showing a method according to the techniques of this disclosure is shown. DETAILED DESCRIPTION

[0025] Figure 1 Shear waves generated from an oscillating surface in a fluid are shown as a graph of velocity V versus distance x from the surface. The magnitude of the fluid velocity decays as the distance x from the surface increases. The velocity at the surface is V 0 .

[0026] The variation of velocity with distance x gives the velocity gradient, also called the shear rate:

[0027]

[0028] The velocity gradient or shear rate at the oscillating surface is important for determining the damping force generated at the oscillating surface via the shear stress τ, which is given by:

[0029]

[0030] The shear stress and the oscillating displacement of the surface produce "work", which results in energy dissipation. Since the Q factor can be understood as representing the ratio of energy stored in the resonator oscillation to the energy lost, an increase in shear stress results in an increase in energy dissipation, which results in a decrease in the Q factor and an increase in its inverse, the loss factor. The measured loss factor or Q factor is therefore an indication of the viscosity. But it also depends on the shear rate at the surface.

[0031] The shear wave propagation depth is the distance a shear wave travels for its amplitude to drop to 1 / e of its starting amplitude (where e is the base of the natural logarithm, 1 / e is approximately 0.37). This value is sometimes referred to as the "penetration depth" or "skin depth."

[0032] The shear rate at the surface is inversely proportional to the propagation depth.

[0033]

[0034] Propagation Depth x 0 can be written as:

[0035]

[0036] where ω is the angular frequency, ρ is the fluid density, and Δ is the loss tangent, also called the loss angle, which depends on ω, μ′, and G′.

[0037] The depth of propagation is highly dependent on viscosity and elasticity through the loss angle Δ. The depth of propagation is also dependent on frequency and density, although frequency and density are relatively constant.

[0038] A high degree of elasticity can adversely distort shear rates. Increasing elasticity extends the propagation depth, which reduces shear rates. This changes the loss factor (or Q factor), from which viscosity can be inferred. This means that significant errors can occur when measuring viscosity, especially in highly non-Newtonian fluids.

[0039] Figure 2 A simple model of a viscoelastic fluid acting as a spring and damper system is shown. The apparent viscosity μ * The unit is Pa·s, which is related to the dynamic viscosity μ′ (in Pa·s), the storage modulus G′ (in Pa) representing elasticity, and the angular frequency ω (in s -1 is a unit) and is given by:

[0040]

[0041] The loss modulus G″ has the unit of Pa and is the product of the dynamic viscosity μ′ and the angular frequency ω.

[0042] The loss tangent is given by:

[0043]

[0044] The disclosed technology exploits the dependence of shear wave propagation depth on fluid viscosity and elasticity. The two surfaces are separated by a gap that allows waves to transition between a primary oscillating surface used as a detector and a secondary oscillating surface used as a radiator. The primary surface is radiated by the secondary surface. These surfaces may be connected (e.g. rigidly) to the same oscillator / resonator, or may be independent oscillators / resonators.

[0045] The effective or principal shear rate at the detector surface is modified by the wave emitted from the radiating surface. The extent to which the shear rate is modified is related to the intensity of the radiation and the relative phase between the incident wave near the detector and the shear wave emitted from the detector.

[0046] The radiation intensity or amplitude of the radiated shear wave at the detector varies as a function of the propagation depth and the distance between the primary and secondary surfaces. The phase of the radiated shear wave at the detector is related to the wavelength of the shear wave in the fluid and the distance between the primary and secondary surfaces. Both the radiation intensity and the relative phase vary as a function of the dynamic viscosity μ' and the storage modulus G'. The combination of the shear wave emitted from the detector and the radiated shear wave at the detector results in interference, either constructive or destructive.

[0047] When the relative phase between the shear waves at the detector is such that the instantaneous velocities of the shear waves have opposite signs, net destructive interference occurs at the detector, resulting in an effective shear rate that is less than the effective shear rate when there are no radiating shear waves (e.g., more than 5% lower, more than 10% lower, more than 20% lower, more than 30% lower, more than 40% lower, or more than 50% lower).

[0048] When the relative phase between the shear waves at the detector is such that the instantaneous velocities of the shear waves have the same sign, net constructive interference occurs at the detector, resulting in an effective shear rate that is greater than the effective shear rate when there are no radiating shear waves (e.g., more than 5% greater, more than 10% greater, more than 20% greater, more than 30% greater, more than 40% greater, or more than 50% greater).

[0049] At the detector, the shear wave emanating from the detector may be assumed to have the same velocity at the detector as the detector itself.

[0050] In some configurations, a pair of oscillating surfaces may each become a detector and radiator for each other. Thus, net constructive or destructive interference may occur at either or both of the oscillating surfaces according to shear wave combining.

[0051] The shear rate of the fluid at the detector caused by interference affects the Q factor (or loss factor). Destructive interference at the detector results in a lower Q factor, which leads to a higher loss factor. Constructive interference at the detector results in a higher Q factor, which leads to a lower loss factor. Thus, the variation of the Q factor (or loss factor) is related to the fluid viscosity (via μ′) and elasticity (via G′).

[0052] One element supporting the disclosed technology is the correlation between the shear wave propagation depth and the fluid elasticity. This is illustrated by rewriting Equation 4 as the product of the purely viscous skin depth and the elastic component:

[0053]

[0054] where tanΔ = ωμ′ / G′ and F(Δ) is the quantity within the parentheses, which is the elastic component.

[0055] Figure 3 is a plot of F(Δ) versus Δ (in degrees), where F(Δ) is the elastic component of x in Equation 7 and is equal to 0 The elastic component of x in Equation 7 and is equal to

[0056] This parameter F(Δ) is plotted because it represents the effect of elasticity on the propagation depth. For Δ equal to 90°, this parameter is 1, which is a purely viscous fluid where tanΔ → ∞. For a mildly viscoelastic fluid where 1 < tanΔ < ∞ (i.e., the range of Δ values is 45° < Δ < 90°), the plotted parameter F(Δ) remains approximately 1. This means that the shear wave propagation depth of a mildly viscoelastic fluid can be reasonably approximated as the purely viscous shear wave propagation depth. However, the plotted parameter increases at an increasing rate as Δ decreases. As Δ decreases, the purely viscous shear wave propagation depth approaches the shear wave propagation depth with increasing inaccuracy. When Δ approaches 0, the plotted parameter F(Δ) will approach infinity. Thus, for more viscoelastic fluids, such as fluids where tanΔ < 1, the effect of viscoelasticity on the shear wave propagation depth is more important, and it may become more important to consider the effect of viscoelasticity when measuring fluid properties.

[0057] Note from Equation 7 that the penetration depth of the shear wave is lower for a fluid with relatively low values of μ′ and relatively low values of G′ compared to a fluid with relatively high values of μ′ and relatively high values of G′.

[0058] Figure 4The shear wave velocity field generated by the primary oscillating surface 10 (i.e., the detector) and the secondary oscillating surface 20 (i.e., the radiator) are shown, which oscillate in phase with each other and are separated by a gap distance filled with a first viscoelastic fluid 30 having a relatively low μ′ and a relatively low G′. The primary oscillating surface 10 generates a shear wave 12, which propagates a distance into the first viscoelastic fluid 30. The secondary oscillating surface 22 generates a shear wave 22, which also propagates a distance into the first viscoelastic fluid 30. The shear waves 12, 22 do not interfere with each other because the relatively low μ′ and the relatively low G′ mean that the shear waves 12, 22 do not pass through the gap between the primary oscillating surface 10 and the secondary oscillating surface 20; they decay without causing any interference.

[0059] Figure 5 Shown by Figure 4 The shear wave velocity field generated by the same primary oscillation surface 10 and the secondary oscillation surface 20 separated by the same gap in the Figure 4 oscillate together in the same synchronous manner as shown. Figure 5 In the embodiment of the present invention, 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 can extend through the gap between the primary oscillation surface 10 and the secondary oscillation surface 20. The shear waves 12, 22 can interfere with each other at the primary oscillation surface and the secondary oscillation surface. This means that the effective shear rate at the primary oscillation surface 10 (i.e., the detector) is affected by the shear wave 22 generated at the secondary oscillation surface 20 (i.e., the radiator).

[0060] To make the propagation depth long, it is not necessary that both μ′ and G′ are high. For example, a long propagation depth can be achieved by only μ′ being high or G′ being high.

[0061] For a given range of μ′ and G′, one can choose Figure 4 and 5 Parameters of the arrangement shown in , to influence the shear rate at the detector surface via interference. These parameters include one or more of the following: i) gap distance, ii) frequency, iii) surface radius, iv) surface shape.

[0062] Back to Figure 1 , the speed of the traveling plane wave can be expressed as:

[0063] v(x,t)=V 0 e -αx e i(ωt-βx) Equation 8

[0064] Where α is the attenuation coefficient, equal to 1 / x 0, β is the wavelength coefficient, equal to 2π / λ, where λ is the wavelength.

[0065] For shear waves in viscoelastic fluids, α and β are given by the following expressions:

[0066]

[0067] The amplitude of the velocity oscillation is α = 1 / x 0 The phase of the velocity oscillations changes with the distance from the original surface according to the wavelength factor β. Both α and β are fluid dependent and determine the degree to which the velocity field is disturbed and therefore the degree to which the effective shear rate at the detection surface is modified.

[0068] The discussion so far has assumed a flat oscillating surface that oscillates in a plane to generate shear waves. However, shear waves can be generated from surfaces that are not flat. For example, shear waves can be generated from a concave or convex surface that is subjected to torsional vibrations.

[0069] Figure 6 The propagation of a shear wave from a surface of radius of curvature R subjected to torsional vibration is shown.

[0070] For a convex surface, the traveling wave velocity can be expressed as:

[0071]

[0072] In this equation, the phase of the wave changes with distance x according to the wavelength factor β, as before. But the amplitude of the wave changes differently. The amplitude is affected not only by the attenuation factor α, but also by geometric factors, because the energy of the wave is spread over a larger and larger area as the distance from the original surface increases. Therefore, the amplitude is calculated according to (R / (R+x))e -αx And changes.

[0073] For a concave surface, the traveling wave velocity can be expressed as:

[0074]

[0075] As with convex surfaces, the phase of the wave changes with distance based on β. The amplitude is affected by α and a geometric term, although the geometric term is different from the concave case. The geometric term accounts for the fact that the energy of the wave is focused into a smaller and smaller area as the distance from the original surface increases. Therefore, the amplitude is determined by |R / (Rx)|e -αx And changes.

[0076] Figure 7An arrangement is shown in which a vibration transducer 40 is provided with a concave surface 42 comprising a spherical recess in the surface of the vibration transducer. The vibration transducer 40 vibrates in a torsional manner about an axis of rotation 44. The axis of rotation 44 extends through the center of the concave surface 42. When the vibration transducer vibrates in a torsional manner about the axis of rotation 44, shear wave "rays" 46 extend from all locations on the concave surface 42, in which case the shear wave transverse velocity of each ray 46 at its corresponding origin location on the concave surface 42 is aligned with the velocity of the origin location on the concave surface 42 due to the no-slip condition. Due to the spherical profile of the concave surface, which means that there is a constant radius of curvature, all rays 46 are focused to a single location defined by the radius of curvature and the surface normal direction of the concave surface 42.

[0077] The particular angular position of the origin of ray 46 about the axis of vibration 44 defines the direction of the velocity of concave surface 42 at that origin. For any two points on concave surface 42 having the same longitudinal position along the axis of rotation 44, the surface velocity is equal in magnitude, but its direction and phase are related to the angular offset of the two points about the axis of rotation 44.

[0078] If the two origins of the rays 46 are offset by 180° relative to each other about the rotation axis 44 on the concave surface 42 , the phases of the shear waves of the rays 46 will be offset by 180° relative to each other.

[0079] Under these conditions, the traveling wave velocity is given by:

[0080]

[0081] Under these conditions, the concave surface provides not only a focusing effect but also an amplitude inversion effect due to the geometric term (R / (Rx))x, which is related to whether the distance is greater than or less than the radius of curvature, which determines the sign of this geometric term.

[0082] Figure 7 The example shown in represents a simple geometry of a groove having a constant curvature spherical profile symmetrical about the axis of rotation. It neglects any propagation effects of the generated shear waves. The actual groove may not be completely smooth, or the radius of curvature may not be constant, or the groove may not be symmetrical about the axis of rotation. In practice, the focus of the shear wave is therefore not a point in space, but a focal region. However, if the groove is concave and rotates in a fluid about an axis in the fluid, the axis extends through the surface of the groove and extends outward from the surface of the groove, so that the surface groove portions spaced from the axis of rotation on opposite sides of the axis of rotation direct the wave towards the axis of rotation, forming a focal region, after which an amplitude reversal may occur.

[0083] Therefore, net destructive interference occurs when the shear waves from the radiator and the detector have opposite signs at the detector, whether this interference is achieved through a phase difference due to the distance between the detector and the radiator or through an amplitude reversal due to focusing effects. At the detector, the shear wave emanating from the detector can be assumed to have the same velocity at the detector as the detector itself.

[0084] Figure 8 A configuration is shown where a smooth concave groove extends annularly around the axis of rotation (shown in cross section). This configuration is not expected to result in amplitude reversals within or behind the focal region because the "rays" that are focused together are all in phase with each other. At every point within or behind the focal point, all rays originate from the same angular position about the axis of rotation.

[0085] Fig. 9 A configuration is shown in which a smooth concave groove is rotated at an angle about the axis of rotation. The concave groove has a constant curvature, but does not provide a complete sphere. In particular, there is no curved surface that produces shear waves in the direction of the axis of rotation and aligned with the axis of rotation. Amplitude reversal is expected to occur only in the region where shear waves on both sides of the axis of rotation are superimposed, which corresponds to a phase reversal. Away from this region, there will be no amplitude reversal along the axis because there are no shear waves in the direction of the axis. There will also be no amplitude reversal in the shear wave path behind the focus because all shear waves in these regions are in phase.

[0086] Fig.10 A configuration of a spherical smooth concave groove rotated about an axis in a fluid is shown. The axis extends through the concave groove, but the axis of rotation is not aligned with the center of the concave groove. It passes neither through the axis of the concave groove nor through the final focus. Rotation about this axis will not focus the shear wave to the same Figure 7 The amplitude matching can be improved by moving the axis of rotation closer to the center of the groove and aligning it to extend through the focal point.

[0087] Fig.11 A configuration is shown where the groove is formed from multiple tapered sections. A transverse section through the axis of rotation (about which the groove is axisymmetric) shows that the profile of the groove is piecewise linear. This configuration will provide some degree of focusing, but it will not be as Figure 7 However, it is still expected that it will cause amplitude reversal at least to some extent at or behind the focus.

[0088] In general, in order to achieve amplitude reversal after the focus of the groove, the concave area should be symmetrical about the rotation axis. For effective focusing, the cross-section of the concave groove should preferably be smooth. Preferably, the concave groove should be spherical, i.e., have a constant radius of curvature (when viewed in cross section) so that all generated shear waves are focused to one point. In some embodiments, the concave groove can have other cross-sectional profiles, such as elliptical or parabolic, depending on the application requirements.

[0089] Amplitude inversion combined with focusing as shown in these examples allows the detector surface (e.g., an elongated member or a planar surface) to be located in the region of amplitude inversion. If the elongated member rotates with the shear wave generating surface in the groove, the shear waves emitted from the detector surface destructively interfere with the shear waves emitted from the groove. The net destructive interference gain is high because the focusing of the shear waves amplifies the interference waves and the detector is located in the interference focal region.

[0090] In the absence of amplitude inversion, it is necessary to position the detector surface at a distance from the generation surface controlled by β in order to experience destructive interference with the shear wave emanating from the generation surface, and this β varies depending on the fluid properties Δ, ρ and μ′ and the vibration frequency ω.

[0091] However, using concave shear wave generating surfaces that generate out-of-phase shear waves on either side of the rotation axis can produce out-of-phase regions in which destructive interference can occur that is unrelated to β and therefore advantageously unrelated to μ′ or Δ.

[0092] Back to Figure 5 The arrangement shown takes into account the effect of the interference of the shear waves 12, 22 on the apparent shear rate at the detector surface.

[0093] The velocity of the shear wave 22 originating from the secondary oscillating surface 20 at the location in the gap can be expressed as:

[0094] v s =A s cos(ω s t-φ S ) Equation 14

[0095] Among them, A s represents the amplitude change term of shear wave 22, ω s represents the oscillation frequency at the secondary oscillation surface 20, φ s represents the phase of the shear wave 22 at this position.

[0096] The velocity of the shear wave 12 originating from the main oscillating surface 20 at the same position in the gap can be expressed as:

[0097] v p =A pcos(ω p t-φ p )Equation 15

[0098] Among them, A p represents the amplitude change term of shear wave 12, ω p represents the oscillation frequency at the main oscillation surface 10, φ p represents the phase of the shear wave 12 at this position.

[0099] The linear combination of shear waves 10, 12 at this location is given by:

[0100] v p +v s =A p cos(ω p t-φ p )+A s cos(ω s t-φ s )Equation 16

[0101] The shear rate at this location is given by:

[0102]

[0103] Depending on the relative amplitude and phase of the two waves, they may experience destructive interference (resulting in a lowered Q factor) or constructive interference (resulting in an increased Q factor).

[0104] The amplitude is determined by the fluid attenuation coefficient α and the surface curvature radius. The phase is determined by the wavelength coefficient β and the propagation distance. As described in Equation 9 and Equation 10, both α and β are related to the fluid properties.

[0105] The inventors have recognized that a properly designed system can provide a measure of the Q factor (or its inverse, the loss factor) that varies monotonically with increasing μ′ and G′. Preferably, the measure is achieved by ensuring that the phase and amplitude together produce destructive interference as μ′ and G′ increase, thereby producing proportionally increasing losses over the entire range.

[0106] As described above, the measured loss factor or Q factor is an indication of viscosity, but it is also related to the shear rate at the surface. The shear rate is affected by other factors including the elasticity of the fluid, resulting in an increasingly non-linear or even non-monotonic relationship between the loss factor or Q factor and viscosity. The disclosed techniques can employ destructive interference that increases with increasing μ' and G' to provide a monotonic relationship between the Q factor or loss factor and a measurement of μ' or G', or any other material property that can be derived from a measurement of μ' or G'.

[0107] Ideally, for a measuring device, the output signal varies linearly and monotonically with the measured variable over a target range. If the output signal does not vary linearly but varies monotonically over a target range, such an output signal can still be directly converted into an estimate of the measured variable via numerical approximation, such as via curve fitting techniques, such as nonlinear regression using nonlinear functions (e.g., nonlinear polynomials). If the output signal is not monotonic with respect to the measured variable over the target range, it becomes more difficult to determine an estimate of the measured variable. For example, if multiple values ​​of μ′ produce the same output signal (e.g., loss factor or Q factor), then that value of the output signal is not conclusive indicative of μ′. Therefore, a monotonic relationship between the measured variable and the output signal (e.g., loss factor or Q factor) is advantageous.

[0108] In the disclosed technique, the gap size and vibration frequency are selected for given fluid properties so that changes in the fluctuation coefficients α and β cause the loss factor or Q factor to vary monotonically with μ′ and G′.

[0109] Before directly describing specific embodiments of the technology according to the present disclosure, it will be helpful to set forth some general points about the technology of the present disclosure, where the embodiments may follow any combination of one or more of the following points:

[0110] • Architectures can be built for either or both destructive and constructive interference, including phase-supported and amplitude-supported architectures.

[0111] • For varying material properties, promoting destructive interference can be beneficial in achieving a more favorable monotonic behavior of the measured Q factor or loss factor.

[0112] • A pair of oscillating surfaces can both be detectors and radiators for each other.

[0113] • Simple structure Both the primary and secondary oscillating surfaces may be part of the same resonator or oscillating body, although the primary and secondary oscillating surfaces need not be so arranged.

[0114] • The resonator surface can be designed to have zero relative phase in its oscillation, or to have a defined phase shift.

[0115] • Shear waves originating from a convex radiator may have higher amplitude losses over distance than a flat or concave radiator due to the geometrical factors of spreading waves (ie radial or geometric damping as described below).

[0116] ● Shear waves originating from a concave radiator can be focused at a certain distance depending on the radius of curvature of the radiator surface, resulting in an increase in amplitude at the focal point.

[0117] • In some configurations, out-of-phase shear waves from opposite sides of a concave radiator can destructively interfere, resulting in an amplitude reversal in the shear wave field behind the focal point.

[0118] • Due to radial (geometric) damping, oscillating pin or ring-shaped monopole detectors focus their velocity field over a shorter distance, which may allow them to be effectively placed at the focus of a concave radiator.

[0119] • In practice, it may be more useful to determine the loss factor than the Q factor (its inverse).

[0120] • The wave characteristics and gap distance (surface spacing) can be selected so that the measured loss factor increases monotonically with increasing μ′ and G′.

[0121] The operating frequency is arbitrary, but many practical implementations will use a frequency in the region of 100 Hz to 100 kHz, preferably 200 Hz to 10 kHz, more preferably 300 Hz to 5 kHz, more preferably 500 Hz to 2 kHz, such as 1 kHz or thereabouts (e.g. + / - 10%).

[0122] While the Q factor (or loss factor) can be used to measure shear stress, the technology of the present disclosure is not limited thereto and can include measuring shear stress via direct torque measurement as an alternative. Whether the Q factor or loss factor is measured, the use of constructive and destructive interference described herein can provide the same benefits.

[0123] The disclosed techniques are presented in the context of shear waves, but the same principles apply to oscillations from surfaces that generate pressure waves (acoustic or P-waves) that interfere constructively or destructively. However, it should be noted that the wavelength of such waves is longer than that of shear waves, and therefore requires oscillations at considerably higher frequencies, or the system size needs to be increased to accommodate the longer wavelength.

[0124] • The disclosed technique may advantageously be implemented by generating shear waves using a torsional vibration device. However, in addition to or instead of a torsional mode, the oscillating surface may alternatively be provided by the surface of a mechanical oscillator vibrating in-plane, ie a lateral or longitudinal vibration mode.

[0125] Fig.12A configuration of a vibration transducer according to the technology of the present disclosure is shown, in which a plurality (four in this example) of elongated members 52 (e.g., pins) extend vertically outward from a flat disc base 50. The flat disc base 50 is configured to vibrate in a plane, i.e., planar in a direction perpendicular to the normal to the plane, or to vibrate in a torsional manner about an axis parallel to the normal to the plane. Optionally, the elongated member may be an elongated member as described below and in UK Application No. 2207881.0 filed on May 27, 2022, which is incorporated by reference into the present disclosure; such an elongated member is characterized by a width, a half-width equal to half the width, and a length greater than the width, wherein the half-width is less than the propagation depth of the shear wave in the fluid at the vibration frequency, more preferably less than 50% of the propagation depth. 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.

[0126] In this configuration, the flat disc base 50 may be understood as a radiator, while the elongated member 52 may be understood as a detector.

[0127] In one configuration, the flat plate base 50 may be configured to vibrate in torsion about the longitudinal axis of the base, rather than laterally.

[0128] Fig.13 The shear wave 54 generated by the flat base 50 and the shear wave 56 generated by the elongated member 52 are shown. Geometric damping, as described below, may cause the shear wave 56 generated by the elongated member to be Figure 8 The form shown, where the shear wave amplitude decays rapidly due to geometric factors. Assuming that the elongated member 52 is sufficiently rigid so that any bending vibration of the elongated member 52 at the operating frequency is negligible, the elongated member 52 vibrates in phase with the flat base 50. The value of the shear wave 54 generated by the flat base 50 varies with increasing distance from the flat base 50 according to β.

[0129] Fig.14 Also shown is the phase variation of the shear wave 54 generated by the flat base 50 along the length of the elongated member 52. Fig. 9 In the first range, marked C in FIG. 5 , the shear waves 54 generated by the flat base 50 are in phase with the motion of the elongated member 52 and are therefore in phase with any shear waves 56 generated from that portion of the elongated member 52. In this region, constructive interference occurs between the shear waves 54 generated by the flat base 50 and the shear waves 56 generated by the elongated member 52. Fig. 9In the second range, marked D in FIG. 5 , the shear waves 54 generated by the flat base 50 are out of phase with the motion of the elongated member 52 and, therefore, out of phase with any shear waves 56 generated from that portion of the elongated member 52. In this region, destructive interference occurs between the shear waves 54 generated by the flat base 50 and the shear waves 56 generated by the elongated member 52. As discussed above, destructive interference may be preferred in practice. Fig. 9 The arrangement shown in may provide only modest destructive interference gain due to constructive interference in a region C adjacent the base of the elongated member 52 where the elongated member 52 contacts the planar base 50 .

[0130] Fig.15 A configuration of a vibration transducer according to the technology of the present disclosure is shown, in which a plurality of (four in this example) elongated members 62 (e.g., pins) extend vertically outward from a flat disc base 60. In addition, the distal ends of the elongated members 62 are attached to an annular member 63. The annular member 63 surrounds an axis that is perpendicular or approximately perpendicular to the flat base 60. Each elongated member 63 has the same or similar length, so that around the annular member 63, each portion of the annular member 63 is approximately the same distance from the flat base 60. Optionally, the annular member 63 and the elongated members 62 may optionally have a sufficiently narrow width to provide geometric damping as described below. The flat disc base 60 is configured to vibrate in a plane, i.e., be planar in a direction perpendicular to the plane normal, or vibrate in a torsional manner around an axis parallel to the plane normal.

[0131] In this configuration, the flat disc base 60 may be understood as a radiator, the elongated member 62 may be understood as a detector, and the annular member 63 may also be understood as a detector.

[0132] The shear waves generated by the movement of the elongated member 62 are Figures 7 to 9 The same manner is shown interacting with the shear waves 64 generated by the motion of the flat plate base 60. However, this configuration can provide a greater amount of net destructive interference, ie, effective interference that takes into account both constructive and destructive interference contributions.

[0133] In one configuration, the flat disc base 60 may be configured to vibrate in torsion about the longitudinal axis of the base, rather than laterally.

[0134] Fig.16The annular member 63 is shown in a shear wave 64 generated by the movement of the flat base 60. The annular member 63 is connected to the elongated member 63, assuming that the elongated member 63 is rigid, so that the elongated member 63 moves in phase with the flat base 60, and the annular member 63 moves in phase with the flat base 60. The entire annular member 63 is located at a distance from the flat base 60 so that the shear wave 64 generated by the movement of the flat base is out of phase with the annular member 63 at the location of the annular member 63, and is therefore out of phase with any shear wave generated by the movement of the annular member 63. Therefore, destructive interference occurs between the shear wave 64 generated by the flat base 60 and any shear wave generated by the annular member 63. Therefore, while the elongated member 62 may provide only a moderate amount of net destructive interference, the addition of the annular member 63 provides an improved amount of net destructive interference when the annular member 63 is located at a position where the shear wave generated by the movement of the flat base 60 is out of phase with the flat base 60, and is therefore out of phase with the annular member 63.

[0135] Fig.17 A configuration of a vibration transducer according to the disclosed technique is shown in which a plurality (four in this example) of elongated members 72 (e.g., pins) extend radially outward from a shaft 70 that is circular in cross-section and is configured to vibrate in torsion about the longitudinal axis of the shaft 70. Optionally, the elongated members 72 may optionally have a sufficiently narrow width to provide geometric damping as described below.

[0136] In this configuration, the radial cylindrical outer surface of the shaft 70 may be understood as a radiator, while the elongated member 72 may be understood as a detector.

[0137] Fig.18 Different shear waves generated by the motion of the elements of this configuration are shown. The torsional vibration of the shaft generates a shear wave 74 that extends radially outward from the cylindrical surface of the shaft 70. As discussed above with respect to 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 factors. The elongated members 72 move in phase with the shaft 70 and generate shear waves 76 through their motion in the fluid. At some locations along the length of the elongated members 72, the motion of the elongated members is in phase with the amplitude of the shear waves 74 generated from the shaft 70. At other locations along the length of the elongated members 72, the motion of the elongated members is out of phase with the amplitude of the shear waves 74 generated from the shaft 70.

[0138] Fig.19The locations 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 therefore in phase with the movement of the slender member 72) are shown. It can be seen that in the region closest to the base of the slender member 72, where the slender member 72 is connected to the shaft 70, the amplitude of the shear wave 74 is in phase with the movement of the slender member 72, and therefore in phase with the shear wave generated by the movement of the slender member 72, resulting in constructive interference at that portion of the slender member 72. In the next adjacent region slightly further from the shaft 70, the amplitude of the shear wave 74 is out of phase with the movement of the slender member 72, and therefore out of phase with the shear wave generated by the movement of the slender member 72, resulting in destructive interference at this portion of the slender member 72. Due to the constructive region at the base of the slender member 72, the net destructive interference gain is moderate. Figures 12 to 18 Compared to the arrangement shown in , the radiating surface is convex, which, due to geometric factors, leads to additional attenuation with increasing radial distance.

[0139] Fig. 20 The configuration of the vibration transducer according to the technology of the present disclosure is shown. Figures 17 to 19 The configuration shown, however, wherein the distal end of the elongated member 73 is connected to the annular member 73. The annular member 73 may optionally have a sufficiently narrow width to provide geometric damping.

[0140] Fig.21 The position of the annular member 73 is shown in a region where the shear wave 74 generated by the motion of the shaft 70 is out of phase with the motion of the shaft 70 and, therefore, with the motion of the annular member 73. At this distance radially outward from the shaft 70, the shear wave 74 generated by the motion of the annular member 73 is out of phase with the shear wave 74 generated by the motion of the shaft 70, resulting in destructive interference. Although the radiating outer surface of the shaft 70 is convex and the shear wave 74 will therefore experience additional geometric attenuation with radial distance, since the annular member 73 detector is only located Fig.21 In the destructive interference region shown, the net destructive interference gain can be high.

[0141] Fig. 22 Shown based on Fig.15The configuration of a vibration transducer according to the technology of the present disclosure, but wherein the vibration is torsional and wherein the shear wave is generated from a concave surface. In particular, the base 80 is in the form of a cylinder configured to vibrate in a torsional manner about its longitudinal axis. At one end of the cylindrical base 80, four elongated members 82 extend outwardly from the base, and the elongated members 82 are aligned with the longitudinal axis of the cylindrical base 80. An annular member 83 is connected to the distal end of the elongated member 82. The end of the base 80 has a concave groove 88 disposed therein, and the concave groove 88 extends in a circular shape around the longitudinal axis of the base 80, and the circle is concentric with the outer cylindrical surface of the base 80. The elongated member 82 is 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 in the groove cross section. However, other examples may have grooves with non-circular cross-sectional profiles, such as elliptical or parabolic cross-sectional profiles. However, in the context of the present disclosure, a concave surface or groove need not be smooth, but may include a surface or groove having a piecewise linear profile, or a surface of a concave groove having a mixture of flat and curved portions. An example may be a groove having a V-shaped cross-sectional profile.

[0142] Fig.23 A cross section through the end of the base 80 is shown, and the annular member 83 is shown. The elongated member 82 is not shown. Torsional vibration of the base 80 about its longitudinal axis within the fluid causes shear waves to be generated from its ends, including from within the concave groove 88. The shear waves are emitted in a direction perpendicular to the surface. The shear waves generated from the surface within the concave groove 88 are focused to an area deviating from the base 80, as shown by ray 85, which represents the direction in which the shear waves propagate from the starting surface within the concave groove 88. The circular cross-section of the concave groove 88 results in a shallower focal area. At distances outside the focal area, the composite amplitude of the shear waves is not expected to be reversed as described above with respect to equation 12. This is because the shear waves focused together are all in phase.

[0143] Fig.23 The position of the annular member 83 is shown outside the focal region at a distance from the base 80. The shear wave shown by ray 85 is not expected to provide an amplitude reversal of motion relative to the base 80 outside the focal region 89.

[0144] Fig.24 An arrangement according to the technology of this disclosure is shown, which can be likened to a "pulley" radiator and a ring detector. Fig.24A side view of a fluid contacting element of a vibration transducer is shown on the left hand side, and an axial view of the same transducer is shown on the right hand side. The vibration transducer comprises a shaft 97 which is configured to vibrate in a torsional manner about a longitudinal axis. The shaft 97 comprises a pendulum 90 along its length, the pendulum 90 having a cylindrical shape aligned with the axis of the shaft 97. A concave groove 98 having a circular profile extends circumferentially around the cylindrical outer surface of the pendulum 90. The pendulum 90 including the concave groove 98 has the form of a pulley. A plurality of elongated members 92 extend radially outwardly from the concave groove 98, and the elongated members 92 are connected at their distal ends to an annular member 93 surrounding the pendulum 90 around the concave groove 98. The surface of the concave groove 98 serves as a radiator for the annular member 93, which serves as a detector.

[0145] Ray 95 represents a shear wave emanating from the surface of the concave groove 98. The radius of curvature of the concave groove 98 causes the shear wave emanating from the concave groove 98 to focus on an intermediate region between the concave groove 98 and the annular member 93.

[0146] Fig.25 An arrangement according to the disclosed technique is shown, which may be likened to a "half-pulley" radiator and annular detector. Fig.25 A side view of a fluid contact element of a vibration transducer is shown on the left hand side, and an axial view of the same transducer is shown on the right hand side. The vibration transducer includes a shaft 107, which is configured to vibrate in a torsional manner about a longitudinal axis. The shaft 107 includes a pendulum 100 along its length, and the pendulum 100 has a cylindrical shape aligned with the axis of the shaft 97. Although the pendulum 100 includes a concave groove 108, the concave groove 108 represents that the diameter of the pendulum 100 narrows from a maximum value to a minimum value. The concave groove 108 has a circular profile (constant radius of curvature). The pendulum 100 including the concave groove 108 has the form of a half pulley. A plurality of elongated members 102 extend radially outward from the concave groove 108, and the elongated members 92 are connected to an annular member 103 at their distal ends, and the annular member 103 surrounds the pendulum 100 around the concave groove 108. The surface of the concave groove 108 serves as a radiator for the annular member 103, and the annular member 103 serves as a detector.

[0147] Ray 105 represents a shear wave emanating from the surface of the concave groove 108. The radius of curvature of the concave groove 108 causes the shear wave emanating from the concave groove 108 to focus on an intermediate region between the concave groove 108 and the annular member 103.

[0148] Fig.26An arrangement according to the technology of the present disclosure is shown in which a base or pendulum 110 on a shaft 117 is provided with a concave groove 118 extending in an annular manner around the shaft 117. An annular member 113 extends circumferentially around the shaft 117 (connected to the shaft by an elongated member not shown) and is located axially offset from the pendulum 110. The shaft 117 and pendulum 110 vibrate in a torsional manner about the longitudinal axis of the shaft. The annular member 113 is closer to the pendulum 110 than the focal region 119, as shown by the rays 115 emanating from the concave groove 118. This means that the amplitude of the interfering shear waves from the radiator concave groove 118 experienced at the detector annular member 113 is enhanced, and the interference has a greater effect.

[0149] According to the technology disclosed in this disclosure, Fig. 27 Shown with Fig.26 Same arrangement, except that the annular member 123 is further away from the radiator than the focal area 129 .

[0150] According to the technology disclosed in this disclosure, Fig.28 An arrangement is shown in which two pendulums 130, 131 are respectively located on a torsional vibration shaft 137 at a certain distance from each other. On the first pendulum 130, on the axial side facing the second pendulum 131, a concave groove 138a extending around the axial side of the first pendulum 130 in an annular manner is provided around the shaft 137. On the second pendulum, on the axial side facing the first pendulum 130, a concave groove 138b extending around the axial side of the second pendulum 131 in an annular manner is provided around the shaft 137. The shear wave emitted from the concave groove 138a of the first pendulum 130 is focused to the area between the two pendulums 130, 131, and undergoes reversal outside the focused area. The shear wave emitted from the concave groove 138b of the second pendulum 131 is focused to the area between the two pendulums 130, 131.

[0151] According to the technology disclosed in this disclosure, Fig.29 An arrangement is shown in which two opposing disks 140, 141 are mounted on a shaft 147 and configured to vibrate in a torsional manner. A first face 144 of the first disk 140 faces a second face 146 of the second disk 141. Shear waves propagating through the gap distance between the first face 144 and the second face 146 may interfere with each other constructively or destructively.

[0152] According to the technology disclosed in this disclosure, Fig.30An arrangement is shown in which a pendulum 150 on a torsional vibration shaft 157 is provided with a disk 151 extending circumferentially around the pendulum 150. The outermost radial extent of the disk 151 is greater than the outermost radial extent of the pendulum 150. During torsional vibration of the shaft 157, shear waves are emitted radially from the outer cylindrical surface 154 of the pendulum 150. In addition, shear waves are emitted axially from the axial surface 156 of the disk. Such shear waves may interfere with each other constructively or destructively.

[0153] According to the technology disclosed in this disclosure, Fig.31 An arrangement of two pendulums 160 spaced apart from one another on a torsional vibration axis 167 is shown. Between the two pendulums 160 there is a disk 161 axially aligned with the pendulums 160 and the axis 167. The outermost radial extent of the disk 11 is greater than the outermost radial extent of either pendulum 160. During torsional vibration of the axis 167, shear waves are emitted radially from the outer cylindrical surface 164 of the pendulum 160. In addition, shear waves are emitted axially from the axial surface 166 of the disk. Such shear waves may interfere with one another constructively or destructively. Fig.30 Compared to the arrangement shown, Fig.31 The arrangement shown may provide improved destructive interference. This is because the diameter of the detector bob 160 adjacent the radiator disk 161 is greatly reduced, so the contribution of any constructive interference from this area is greatly reduced.

[0154] Fig.32 and Fig.33 shows an arrangement according to the technology of the present disclosure, which is similar to Fig.26 and Fig. 27 The arrangement shown differs in that the annular members 173, 183 are located on separate shafts 174, 184 from the shafts 177, 187 on which the pendulums are located. These shafts are configured to vibrate together in a torsional manner to provide the required shear wave interference.

[0155] According to the technology disclosed in this disclosure, Fig.34 An arrangement is shown in which two pendulums 190, 191 are respectively located on separate torsional vibration shafts 194, 197 at a distance from each other. The first pendulum 190 causes the shaft 137 to vibrate in a torsional manner at a distance from each other. On the first pendulum 190 attached to the shaft 197, on the axial side facing the second pendulum 191, a concave groove 198a extending around the axial side of the first pendulum 190 in an annular manner is provided. On the second pendulum 191 attached to the shaft 194, on the axial side facing the first pendulum 190, a concave groove 198b extending around the axial side of the second pendulum 191 in an annular manner is provided. The shear wave emitted from the concave groove 198a of the first pendulum 190 is focused to the area between the two pendulums 190, 191. The shear wave emitted from the concave groove 198b of the second pendulum 191 is focused to the area between the two pendulums 190, 191.

[0156] According to the technology disclosed in this disclosure, Fig.35 An arrangement according to the disclosed technique is shown in which two opposing disks 200, 201 are mounted on respective shafts 207, 208 and are configured to vibrate in a torsional manner. A first face 204 of the first disk 200 faces a second face 206 of the second disk 201. Shear waves propagating through the gap distance between the first face 204 and the second face 206 may interfere with each other constructively or destructively.

[0157] According to the technology disclosed in this disclosure, Fig.36 An arrangement is shown in which a first pendulum 210 is located on a first torsional vibration axis 217 and a second pendulum 211 is located on a second torsional vibration axis 218. The axes 217, 218 are axially aligned and vibrate about the same axis. There is a gap between the two pendulums 210, 211. The outermost radial extent of the first pendulum 210 is greater than the outermost radial extent of the second pendulum 211. During torsional vibration of the axis 218, a shear wave is radially emitted from the outer cylindrical surface 216 of the second pendulum 211. In addition, a shear wave is axially emitted from the axial surface 214 of the first pendulum 210 through the gap between the first pendulum 210 and the second pendulum 211. Such shear waves may interfere with each other constructively or destructively. Due to the gap between the first pendulum 210 and the second pendulum 211, the contribution of any constructive interference is reduced, advantageously allowing net destructive interference.

[0158] Fig.37 A vibration transducer is shown in which two elongated members 320a, 320b are connected to the second axial section of the pendulum 314. The two elongated members 320a, 320b are cylindrical and have the same radius, which is constant along their length. The first elongated member 320a is radially spaced from the other elongated member 320b around the pendulum 314. Each elongated member 320a, 320b extends outward from the pendulum 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 can provide a surface with which constructive or destructive interference can be generated with the waves emitted from the conical surface of the pendulum 314.

[0159] Fig.38A vibration transducer is shown in which two elongated members 320a, 320b are connected to the third axial section of the pendulum 314. Each elongated member 320a, 320b is aligned along a respective axis, which is parallel to the axis 312 of the shaft 310, but radially offset from the axis 312 of the shaft 310. The two elongated members 320a, 320b are cylindrical and have the same radius, which is constant along their length. The first elongated member 320a is radially spaced from the other elongated member 320b around the third axial section of the pendulum 314. Either or both of the first elongated member 320a and the second elongated member 320b can provide a surface with which waves emitted from the conical surface of the pendulum 314 or from each other can produce constructive or destructive interference.

[0160] Fig.39 A vibration transducer is shown in which two elongated members 340a, 340b are connected to the second axial section of the pendulum 314. The two elongated members 340a, 340b are conical. The first elongated member 340a is radially spaced from the other elongated member 340b around the pendulum 314. Each elongated member 340a, 340b extends outward from the pendulum 314 in a radial direction perpendicular to the axis 312 of the shaft 310. Each elongated member 340a, 340b has a maximum radius at the proximal end, where the elongated members 340a, 340b are connected to the second axial section of the pendulum 314. Either or both of the first elongated member 340a and the second elongated member 340b can provide a surface with which constructive or destructive interference can be generated with the waves emitted from the cylindrical surface of the pendulum 314.

[0161] Fig.40A vibration transducer is shown in which four elongated members 340a, 340b, 340c, 340d are connected to the second axial section of the pendulum 314. The four elongated members 340a, 340b, 340c, 340d are conical in shape. The first elongated member 340a is radially spaced from the second elongated member 340b around the pendulum 314, but the first elongated member 340a and the second elongated member 340b are located at the same axial position along the axis 312. The third elongated member 340c is radially spaced from the fourth elongated member 340d around the pendulum 314, but the third elongated member 340c and the fourth elongated member 340d are located at the same axial position 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 a proximal end where the elongated member 340a, 340b, 340c, 340d is connected to a second axial segment of the pendulum 314. Any or all of the first to fourth elongated members 340a, 340b, 340c, 340d may provide a surface with which constructive or destructive interference may be produced with waves emanating from the cylindrical surface of the pendulum 314 or with waves emanating from each other.

[0162] Fig.41 A vibration transducer is shown in which two elongated members 360a, 360b are connected to the second axial section of the pendulum 314. Both elongated members 360a, 360b have the form of a semicircular ring. The first elongated member 360a is curved and connected to the pendulum 314 at two axially spaced locations and has a circular cross-section along the bending axis passing through the elongated member 360a. The second elongated member 360b is curved and connected to the pendulum 314 at two axially spaced locations, which are radially spaced around the pendulum from the location where the first elongated member 360a is connected to the pendulum 314. The second elongated member also has a circular cross-section along the bending axis passing through the elongated member 360b. Either or both of the first elongated member 360a and the second elongated member 360b can provide a surface through which constructive or destructive interference can be produced with waves emanating from the cylindrical surface of the pendulum 314, either in an approximately radially aligned base portion close to the surface of the pendulum 314 or in an approximately axially aligned "ring" portion away from the surface of the pendulum 314.

[0163] Fig.42A vibration transducer is shown in which four elongated members 320a, 320b, 320c, 320d are connected to the second axial section of the pendulum 314. The four elongated members 320a, 320b, 320c, 320d are all cylindrical with the same constant radius and extend radially from the pendulum 314 from positions distributed around the circumference of the second axial section at 90° from the adjacent elongated members. Each distal end of the four elongated members 320a, 320b, 320c, 320d is connected to a fifth elongated member 324, which surrounds the pendulum 314 and is in the form of a ring or annulus. Any one or all of the first to fourth elongated members 320a, 320b, 320c, 320d, or the fifth elongated member 324 in the form of a ring or annulus, can provide a surface with which constructive or destructive interference can be generated with waves emitted from the cylindrical surface of the pendulum 314 or with waves emitted from each other.

[0164] Fig.43 A vibration transducer is shown in which four elongated members 320a, 320b, 320c, 320d are connected to the second axial section of the pendulum 314. The four elongated members 320a, 320b, 320c, 320d are cylindrical, but have different radii. The first elongated member 320a has the largest radius. The radius of the second elongated member 320b is smaller than the radius of the first elongated member 320a. The radius of the third elongated member 320c is smaller than the radius of the second elongated member 320b. The radius of the fourth elongated member 320d is 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 the second axial section of the pendulum 314 from respective positions that are axially offset relative to each other but circumferentially the same. The third elongated member 320c and the fourth elongated member 320d each extend radially outward from the second axial section of the pendulum 314 from respective positions that are axially offset relative to each other but circumferentially the same. The first and second elongated members 320a, 320b and the third and fourth elongated members 320c, 320d are spaced 90° apart around the circumference of the pendulum 314. Any or all of the first to fourth elongated members 320a, 320b, 320c, 320d may provide a surface with which constructive or destructive interference may be produced with waves emanating from the cylindrical surface of the pendulum 314 or with waves emanating from each other.

[0165] Fig.44 A vibration transducer is shown in which eight elongated members 370a, 370b, 370c, 370d, 370e, 370f, 370g, 370h are connected to a pendulum 314.

[0166] The first elongated member 370a is connected to the third axial section of the pendulum 314 and has a tapered shape extending in a direction inclined relative to the axis 312 of the shaft 310. The first elongated member 370a can provide a surface with which constructive or destructive interference can be generated with a wave emitted from the cylindrical surface of the pendulum 314.

[0167] The second elongated member 370b is connected to the second axial segment of the pendulum 314 and extends radially outward from the pendulum 314 from its proximal end. The second elongated member 370b is not straight, and it includes two straight segments that are connected at right angles to form an "L" shaped member. The distal segment of the second elongated member 370b extends in a direction parallel to the axis 312. Either or both of the proximal and distal segments of the second elongated member 370b can provide a surface with which constructive or destructive interference can be generated with waves emitted from the cylindrical surface of the pendulum 314 or with waves emitted from each other.

[0168] The third elongated member 370c is connected to the second axial section of the pendulum 314 and has a "T" shape. The proximal section of the third elongated member 370c is connected to the pendulum 314 and extends radially outward from the pendulum 314. The distal section of the third elongated member 370c is connected to the distal end of the proximal section of the third elongated member 370c and extends in a direction parallel to the axis 312, i.e., perpendicular to the direction of the proximal section. Either or both of the proximal and distal sections of the third elongated member 370c can provide a surface with which constructive or destructive interference can be generated with waves emitted from the cylindrical surface of the pendulum 314 or with waves emitted from each other or any other elongated member.

[0169] The fourth elongated member 370d is connected to the second axial section of the pendulum 314, and includes a proximal section connected to the pendulum 314 and extending in a direction inclined relative to the axis 312 of the shaft 310, and a distal section, one end of the distal section being connected to the distal end of the proximal section, and the distal section extending in a direction parallel to the axis 312. Either or both of the proximal section and the distal section of the fourth elongated member 370d may provide a surface with which constructive or destructive interference may be generated with waves emitted from the cylindrical surface of the pendulum 314 or with waves emitted from each other or any other elongated members.

[0170] The fifth elongated member 370e is connected to the second axial segment of the pendulum 314. The fifth elongated member 370e is not straight, but extends outwardly from the pendulum 314 in a generally radial direction, but has a generally circular cross-section along its length. The fifth elongated member 370e can provide a surface with which constructive or destructive interference can be generated with waves emanating from the cylindrical surface of the pendulum 314 or with waves emanating from any other elongated member.

[0171] The sixth elongated member 370f is connected to the second axial section of the pendulum 314 and extends radially outward from the pendulum 314. At the distal end of the sixth elongated member 370f, another elongated member is connected, which has the form of a closed loop, in particular a torus. Either or both of the proximal and distal sections of the fifth elongated member 370e can provide a surface with which constructive or destructive interference can be generated with waves emitted from the cylindrical surface of the pendulum 314 or with waves emitted from each other or any other elongated member.

[0172] The seventh elongated member 370g is connected to the second axial segment of the pendulum 314 and extends radially outward from the pendulum 314. At the distal end of the seventh elongated member 370g, another elongated member is connected, which is circumferentially bent around an arc concentric with the circumference of the second axial segment of the pendulum 314. Either or both of the proximal and distal segments of the seventh elongated member 370g can provide a surface with which constructive or destructive interference can be generated with waves emitted from the cylindrical surface of the pendulum 314 or with waves emitted from each other or any other elongated members.

[0173] The eighth elongated member 370h is connected to the third axial segment of the pendulum 314 and includes a proximal end and a distal end, the proximal end being connected to the pendulum 314 and extending outwardly from the surface of the third axial segment in an inclined direction relative to the axis 312 of the shaft 310, and one end of the distal end being connected to the distal end of the proximal end, and the distal end extending in a direction parallel to the axis 312. Either or both of the proximal segment and the distal segment of the eighth elongated member 370h may provide a surface with which constructive or destructive interference may be generated with waves emitted from the cylindrical surface or the conical surface of the pendulum 314 or with waves emitted from each other or any other elongated members.

[0174] Note that some embodiments may include only Figures 37 to 44 A subset of the elongated members shown, e.g. Fig.44 One or more of the many different elongated members shown. Those skilled in the art will particularly appreciate that

[0175] Fig.44 A variety of possible elongated members in a single device are shown, and actual implementations may not include Fig.44 All slender members shown.

[0176] Fig.45A configuration of a portion of a vibration transducer according to the technology of the present disclosure is shown, wherein elongated members 420a, 420b, 420c, 420d, 420e, 420f are connected to a shaft or pendulum 400, which is configured to vibrate in a torsional manner about an 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 the shaft or pendulum 400 from an axially offset position but circumferentially the same position from each other. The third elongated member 420c and the fourth elongated member 420d each extend radially outward from the shaft or pendulum 400 from an axially offset position but circumferentially the same position from each other. The fifth elongated member 420e and the sixth elongated member 420f each extend radially outward from the shaft or pendulum 400 from an axially offset position but circumferentially the same position from each other. The first and second elongated members 420a, 420b are spaced 45° from the third and fourth elongated members 420c, 420d about the circumference of the shaft or pendulum 400. The fifth and sixth elongated members 420a, 420b are spaced 45° from the third and fourth elongated members 420c, 420d about the circumference of the shaft or pendulum 400 and 90° from the first and second elongated members 420a, 420b. Any or all of the first to sixth elongated members 420a, 420b, 420c, 420d, 420e, 420f may provide a surface with which constructive or destructive interference may be produced with waves emitted from the cylindrical surface of the shaft or pendulum 400 or with waves emitted from other elongated members.

[0177] In addition, adjacent pairs of slender members (e.g., the first and second slender members 420a, 420b) are axially spaced apart from each other so that the shear waves emitted therefrom interfere destructively. Near the second slender member 420b, the shear waves emitted from the first slender member 420a are out of phase with the shear waves emitted from the second slender member 420b. Near the first slender member 420a, the shear waves emitted from the second slender member 420b are out of phase with the shear waves emitted from the first slender member 420a. The first and second slender members can act as radiators and detectors to each other. Similar destructive interference may occur between the shear waves emitted between the third and fourth slender members 420c, 420d and between the shear waves emitted between the fifth and sixth slender members 420e, 420f. According to the technology of the present disclosure, similar destructive interference (or constructive interference, if desired) may occur between any coupled pairs of slender members, depending on the geometry and shear wave propagation characteristics (propagation depth, wavelength, etc.).

[0178] In another configuration of the technology according to the present disclosure (when subjected to vibration, net constructive interference or destructive interference may optionally occur), the vibration transducer includes a shaft and a plurality of slender members. If the vibration transducer includes a pendulum, the slender member may be connected to the vibration transducer at the pendulum. Alternatively or additionally, the vibration transducer may include a slender member connected to the vibration transducer at the shaft. The plurality of slender members are spaced apart around the circumference of the shaft or pendulum, extending outwardly from the shaft or pendulum in an entire radial direction or in a direction having a radial component and an axial component or in an entire axial direction (not colinear with the longitudinal axis of the shaft / pendulum). The plurality of slender members may be evenly distributed around the circumference, which may mitigate or avoid any perturbation of the center of mass relative to the longitudinal axis, or may be unevenly distributed around the circumference. The plurality of slender members may be connected to the shaft or pendulum at the same axial position along the length of the shaft or pendulum, or may be connected at different axial positions, such as in a spiral pattern around the outer surface of the shaft or pendulum.

[0179] If the plurality of elongated members extend in an axial direction from the shaft or pendulum in whole or in part, the elongated members may include supports spaced from the outer surface of the shaft or pendulum to provide a radial offset to the elongated members. Alternatively, the plurality of elongated members may extend from one end of the shaft or pendulum, for example distributed in a circle around the longitudinal axis, and extend from one end of the shaft or pendulum. The end of the shaft or pendulum may be flat, curved, conical or have other contours.

[0180] The elongate member may have a width and a half-width such that during vibration of the vibration transducer geometric damping (monopole behavior) may occur around the elongate member.The vibration of the vibration transducer may be torsional about a longitudinal axis of the shaft.

[0181] The vibration transducer may include two or more elongated members, such as three, four, five, six, seven, eight, nine, ten or more elongated members. The elongated members may have a constant cross-section along their length (e.g., a cylindrical elongated member or an elongated member having a square / rectangular, rounded square / rectangular (e.g., superelliptical), triangular or elliptical cross-section), or may have a varying cross-sectional shape or size along their length, such as i) a cone with a linear decrease in cross-sectional area with increasing distance from the axis or pendulum, or ii) a step-wise change in size or shape with increasing distance from the axis or pendulum (e.g., a step-like decrease in size).

[0182] In a particular configuration, the vibration transducer includes a shaft configured for torsional vibration, the shaft having a proximal end and a distal end for driving vibration. At or near the distal end of the shaft (e.g., closer to the distal end than the proximal end, or within the last quarter of the fluid contact length of the shaft, or within the last tenth of the fluid contact length of the shaft, or within the last twentieth of the fluid contact length of the shaft), a plurality of elongated members extend radially outward from the axis at a common axial position along the length of the shaft. Eight elongated members are evenly distributed on the circumference of the shaft in 45° increments. In another particular configuration, there is a pendulum at the distal end of the shaft, and eight elongated members extend radially outward from the pendulum. Other configurations include more or fewer elongated members, evenly distributed or unevenly distributed around the shaft / pendulum. For example, a configuration includes six elongated members evenly distributed around the circumference of the shaft.

[0183] In another specific configuration, the vibration transducer includes a shaft and a plurality of elongated members that are axially aligned with the longitudinal axis of the shaft but not colinear with the longitudinal axis of the shaft. There is a pendulum at the distal end of the shaft. The pendulum has the form of a cylinder that is coaxial with the longitudinal axis of the shaft but has a larger radius than the shaft. A plurality of elongated members extend axially outward from one end of the pendulum, each of the elongated members being connected to one end of the pendulum at the same radial offset from the longitudinal axis and being evenly distributed around the longitudinal axis. The plurality of elongated members includes eight elongated members that are evenly distributed around the longitudinal axis in increments of 45°. The vibration transducer is configured to vibrate in a torsional manner around the longitudinal axis. Other configurations include more or fewer elongated members, evenly distributed or unevenly distributed around the longitudinal axis. For example, one configuration includes six elongated members evenly distributed around the longitudinal axis.

[0184] Fig.46 and 47 It is shown that the technology according to the present disclosure adopts an advantageous modular configuration.

[0185] Fig.46 A cross section of a segment 440 of a vibration transducer through an axis of torsional vibration is shown, wherein an axially symmetrical flange extends outwardly from the axis, on one axial side of the flange, the flange is provided with a convex surface 444, and a detector surface 442 (shown purely as an example as a rectangular cross section) is provided on a second side of the flange. The segment 440 can be axially aligned with other identical or similar segments so that the convex surface 444 can generate a focused shear wave at a detector of an adjacent segment, and the detector 442 can receive the focused shear wave from the convex surface of the adjacent segment.

[0186] Fig.47 shows a cross section of a vibration transducer, with Fig.46The four identical segments 440a, 440b, 440c, 440d shown in FIG. are axially adjacently aligned and configured to vibrate in a torsional manner 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. Fig.47 The modular configuration of the repeating segments shown can provide advantages in manufacturing and designing vibration transducers for specific operating requirements. In particular, the sensitivity of the transducer can be changed by increasing or decreasing the number of segments without having to change the geometry of the segments.

[0187] Both the radiator and detector surfaces may be surfaces of elongated members that employ geometric damping.

[0188] Some explanation of geometric damping and slender members employing geometric damping is given below, first considering a purely viscous fluid and then a viscoelastic fluid.

[0189] from Figure 1 and Equation 7For a purely viscous fluid, the propagation depth of the shear wave is given by:

[0190]

[0191] The reduction in wave amplitude caused by viscosity generates a shear stress τ on the oscillating surface Sμ , the shear stress is the rate of change of surface velocity (i.e., shear rate ) and the fluid viscosity μ′, is given by:

[0192]

[0193] Shear rate at the oscillating surface caused by wave decay This can be determined by differentiating the expression for wave speed with respect to distance from the surface and evaluating the expression at the surface, yielding the following expression:

[0194]

[0195] Among them, V 0 is the shear velocity of the oscillating surface.

[0196] 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 inverse of the viscosity.

[0197] Therefore, the shear stress at the surface (which is the product of the surface viscosity and the shear rate) is nonlinear:

[0198]

[0199] In addition to viscous effects, the fluid may also exhibit elastic behavior, depending on the storage modulus G'. The presence of G' reduces the loss tangent tanΔ.

[0200] As mentioned above, for a purely viscous fluid tanΔ = ∞. As elastic behavior increases, the losses in the fluid become smaller, allowing the wave to propagate further into the fluid. Taking elasticity into account, the propagation depth is given by Equation 7, where 1 / (sin(Δ / 2)√(2sinΔ)) is the amount by which the propagation depth is scaled due to the elastic behavior of the fluid. This amount is also equal to 1 / √(sinΔ(1-cosΔ)).

[0201] For a purely viscous fluid, Δ is equal to 90°, so (or equivalently 1 / √(sinΔ(1-cosΔ))) gives a scaling equal to 1, and a purely viscous propagation depth δ μ is recovered. Therefore, it is appropriate to use this expression to refer to the viscoelastic propagation depth even for fluids that exhibit little or no viscoelasticity. For values ​​of Δ less than 90°, the scaling amount is greater than 1, so the propagation depth increases relative to the purely viscous propagation depth.

[0202] Due to viscosity and elasticity, the shear rate at an oscillating surface is given by:

[0203]

[0204] Due to viscosity and elasticity, the shear stress on the oscillating surface is given by:

[0205]

[0206] Shear stress is a nonlinear function of fluid viscosity, fluid density, frequency, and storage modulus (via loss tangent). As G' elasticity increases, tanΔ decreases, Δ decreases from a maximum of π / 2, and both sinΔ and sinΔ / 2 decrease, so damping shear stress decreases as elasticity G' increases. This explains why viscoelastic fluids have reduced damping compared to Newtonian fluids of "similar" viscosity.

[0207] Fig.48 Figure 2 shows a shear wave propagating radially from a curved surface with radius R in a viscoelastic fluid. Although viscoelastic fluids are relatively lossless over short distances, Fig.48 The amplitude reduction is shown because the potential energy of each crest must be maintained as the radial distance increases, and the energy is spread over an increasing circumferential length (2πr). Fig.48A constant potential energy line 510 is shown in . The distribution of energy over increasing circumferential length results in less energy per unit volume and therefore a smaller peak height. The amplitude reduction due to geometric factors looks similar to damping, although it does not consume energy itself.

[0208] The change in height causes a decrease in velocity that is proportional to 1 / r, and this change in velocity causes a shear rate Shear rate combined with viscosity produces shear stress τ RAD , the shear stress has a component in phase with the surface velocity, resulting in energy dissipation. This effect is referred to herein as "geometric damping".

[0209] If not Figure 1 Instead of a plane surface oscillating in the center of the cylinder, the surface of the cylinder oscillates with radius R, then an expression for the velocity of the radial shear wave at position r from the central axis of the cylinder can be obtained and differentiated with respect to r to obtain the radial shear rate:

[0210]

[0211] Among them, V r is the shear velocity at the surface, and φ is given by tan -1 The phase adjustment angle is given by (β / α) and is equal to π / 2-Δ / 2, where β is the wave number of the propagating wave (i.e., 2π / λ, where λ is the wavelength of the propagating wave).

[0212] The shear stress on a cylindrical surface (where r = R) is given by:

[0213]

[0214] The term 1 / R is the in-phase shear gradient. For any degree of viscoelasticity, the shear rate of this component is in phase with the velocity. The term 1 / δ μG′ is the out-of-phase shear gradient. The shear rates of the components differ by φ, which depends on the degree of viscoelasticity. The phase adjustment angle represents the angle between shear stress and velocity. A shear stress that is in phase with the velocity consumes energy.

[0215] For much smaller than δ μG′ For values ​​of R, the in-phase part dominates and the shear rate becomes less or even uncorrelated with viscosity, density, frequency and storage modulus (via tanΔ / 2, which is a function of G″). If 1 / δ μG′ can be neglected compared to 1 / R, the shear stress on the cylindrical surface is given by the following expression:

[0216]

[0217] For much larger than δ μG′ For values ​​of R, the heterogeneous part dominates and the shear rate becomes increasingly a nonlinear function of viscosity, density, frequency, and storage modulus. If 1 / δ μG′ can be neglected compared to 1 / R, the shear stress on the cylindrical surface is given by the following expression:

[0218]

[0219] The critical value of R is R onset =δ μG′ , as this represents the crossover point for the R value where the shear stress due to the 1 / R term becomes greater than that due to 1 / δ μG′ According to the techniques described in this paper, this can be considered as the onset of geometric damping.

[0220] When R<δ μG′ The dependence of shear stress on the nonlinear functions of viscosity, density, frequency and storage modulus is further reduced when the cylinder radius is less than half of the viscoelastic propagation depth, that is, where R <R onset / 2. In other words, R geo =R onset / 2, where R geo can be understood as the radius of the cylinder that defines a state in which geometric damping can be assumed to dominate and define the damping behavior.

[0221] To measure the physical properties of the fluid, parameters can be selected to provide improved linearity of the fluid loading coefficients, such as the fluid damping coefficient C F , Stiffness load factor K F and inertia load factor J F If R = δ μG′ , then the expression for the fluid viscosity at which geometric damping begins to appear is given by:

[0222]

[0223] Among them, ω=2πf.

[0224] For example, suppose a cylindrical element with a radius R of 2 mm vibrates at a frequency of 5 kHz in a purely viscous fluid (sin(Δ / 2)√(2sinΔ)=1) with a density ρ of 1000 kg / m 3 , then choose the fluid viscosity appropriately, in Pa·s, R=R onset Given by:

[0225] μ′ onset =2 2π 5000 1000 = 62

[0226] For the geometric damping to begin to dominate (i.e., where R geo =R onset / 2), the required viscosity is four times higher, that is:

[0227] μ′ geo =(2·2) 2 ·π·5000·1000=250.

[0228] Similarly, the radius and / or vibration frequency of the vibrating element may be selected to exploit geometric damping for a given viscosity and density operating range depending on operational requirements.

[0229] Fig.50 The graph shows the damping coefficient of heavy mineral oil measured at a frequency of 5 kHz using a vibrating cylinder with a radius of 2 mm. The fluid has a mass of 1000 kg / m 3 The damping coefficient is measured within a certain range of viscosity values ​​(obtained by heating heavy mineral oil). The measured damping coefficient is given by Figure 4 If the damping is described by non-geometric damping, that is, 1 / R and 1 / δ μG′ The figure also shows the calculated damping coefficient. Figure 4 If the damping is described by geometric damping, that is, 1 / δ μG′ The figure also shows a graph of the calculated damping coefficient. This line is at Figure 4 It is indicated by "C".

[0230] Fig.50 It is shown that, despite relatively low viscosities, i.e. below about 60 Pa·s, the radius of the vibrating element is larger than the viscous penetration depth and the shear rate is a nonlinear function of the viscosity. When the viscosity is above about 60 Pa·s, the shear wave attenuation starts to be described by geometric damping and it can be seen that the damping coefficient becomes increasingly linear.

[0231] Figure 4 Three regions are identified. The first region, indicated by reference numeral 570, is a nonlinear region and covers μ onset The second region, indicated by reference numeral 580, is a linear transition region and covers the range between μ onset and μ geo The third region, indicated by reference numeral 590, is a completely linear region and covers μ geoOperating in the second region 580 provides improved linearity compared to operating in the first region 570. Operating in the third region 590 provides improved linearity compared to operating in the second region 580.

[0232] For a vibrating cylinder with a radius wide enough and negligible geometric damping, the fluid damping coefficient C F , Stiffness load factor K F and inertia load factor J F The expression for is given by the following expression:

[0233]

[0234]

[0235] In these expressions, each coefficient has a non-linear relationship with μ′, G′, or ρ due to the presence of these terms (or quantities that are functions of these terms, such as Δ and its relationship to G′) in brackets.

[0236] If the radius of the vibrating cylinder is small enough and the non-geometric damping can be neglected, then C F , K F and J F The expression of is given by:

[0237]

[0238] J F =(A·R G 2 ·R)ρ Equation 34

[0239] From these expressions, it can be seen that when the non-geometric damping can be neglected, the fluid damping coefficient C F , Stiffness load factor K F and inertia load factor J F There is no longer any nonlinear dependence on μ′, G′ or ρ. F , J F and K F They are proportional to μ′, G′ and ρ respectively, and the proportional constant is only related to the geometric parameters.

[0240] Improvements in the linearity of these fluid load coefficients may be advantageous. A mechanical system may have damping C, stiffness K, and inertia J. These determine the vibration frequency ω and Q factor of the system via the following equations:

[0241]

[0242] When the system vibrates in air or vacuum, these mechanical factors can be called C 0 , K0 and J 0 When the system vibrates the fluid, the physical properties of the fluid "load" these factors respectively. F , K F and J F .

[0243] Taking into account the fluid loads, the total value of the system's damping, stiffness, and inertia coefficients can be expressed as:

[0244] C=C 0 +C F Equation 37

[0245] K=K 0 +K F Equation 38

[0246] J=J 0 +J F Equation 39

[0247] The total value of C, K and J is related to the frequency and Q factor equations above and can be easily measured. The physical properties of the fluid can be calculated based on C F , K F and J F As described below, the technology of the present disclosure can provide C F , K F and J F Simple linear relationships between ρ and the physical properties of interest such as density ρ, viscosity μ′, and storage modulus G′.

[0248] In these expressions, A is the fluid contact surface area of ​​the cylindrical element, R G It is the "radius of gyration" of the element and is equal to the radius R of the cylindrical element when it vibrates in a torsional manner about its axis.

[0249] When considering the effect of moment of inertia on the rotational motion of an object, the radius of gyration refers to the radial distance from a point at which, if the total mass of the object is focused on this point, the moment of inertia of this point is the same as the actual mass distribution of the object. The term "radius of gyration" in this disclosure is a generalization of this concept to consider torsional factors in addition to the moment of inertia.

[0250] The damping coefficient C F In this case, the radius of gyration represents the radial distance to a point that, if damping were focused at that point, would have the same damping effect as the actual damping effect of the object.

[0251] The stiffness load factor K F In the case of , the radius of gyration represents the radial distance to a point where, if a stiffness load is focused on that point, the point will have the same stiffness load effect as the actual stiffness load effect of the body.

[0252] The inertia load factor K F In this case, the radius of gyration represents the radial distance to a point that, if the inertial load were focused at that point, would have the same inertial load effect as the actual inertial load effect of the object.

[0253] Therefore, the radius of gyration, as more generally defined in this disclosure, represents a convenient measure of the radial effect of these load factors. The radius of gyration will be defined by the specific geometry of the cylindrical element, but will generally be assumed to have upper and lower limits defined by the maximum and minimum radial extents of the cylindrical element from the axis of rotation, and to be equal to the radius R of the cylindrical element when the cylindrical element is vibrating in a torsional manner about its axis, since all surface loads occur at the cylindrical surface, at a distance R from the axis.

[0254] Fig.49 A first cylinder 520 is shown with a radius R twisted about an axis 25 running longitudinally through the center of the cylinder. The cylinder has a length l twisted about its axis, where the length is long enough so that the area of ​​the end (πR 2 ) is smaller than the area of ​​the two sides of the bend (2πRl), and R<<δ μG′ And R = R G , damping coefficient C F , Stiffness load factor K F and inertia load factor J F can be written as:

[0255] C F =A Rμ′=(2μR 2 l)μ′ Equation 40

[0256] K F =ARG′=(2μR 2 l) G′ Equation 41

[0257] J F =AR 3 ρ=(2πR 4 l)ρ Equation 42

[0258] Although geometric damping of radial wave propagation brings advantages by being related to geometric parameters rather than fluid properties, the conditions for geometric damping encourage the use of cylindrical elements with small radii, which results in a small effective surface area. 2 This means that even at high viscosities, the damping or elastic or inertial load factor for torsional vibrations is small.

[0259] Fig.49Also shown is a second cylinder 530 having the same dimensions as the first cylinder 520, wherein the second cylinder 530 is vertically displaced relative to the axis 525 of the first cylinder 520 by an offset radius R greater than R. O The second cylinder 530 also vibrates in a torsional manner about the axis 525 of the first cylinder 520. This has the effect of reducing the radius of gyration R G Change from R (the distance from the cylindrical surface to the axis 525) to R O (Radial offset of the cylinder as a whole).

[0260] If the damping coefficient C provided above is F , Stiffness load factor K F and inertia load factor J F The equation of holds true, then the equation can be expressed as:

[0261]

[0262] J F =(A·R O 2 ·R)ρ=(2 π R l R O 2 R)ρ Equation 45

[0263] =(2πl R O 4 )ρ

[0264] If Ro is greater than R, the load factor is magnified by R by offsetting the vibration of the cylindrical element relative to the axis. O The square of the ratio between R and O / R) 2 In J F In the case of O / R) 4 , that is, R O The fourth power of the ratio between R and R.

[0265] However, these equations only hold true if the cylindrical element is geometrically damped. By offsetting the cylindrical element, it is no longer subjected to pure torsional vibrations, but rather to transverse vibrations at the offset distance. These load factor equations do not automatically apply, because under transverse vibrations, the cylindrical element may form a dipole wave field, rather than a monopole wave field.

[0266] Fig.51A cylindrical element under transverse vibration is shown causing a dipole wave field. In a dipole wave field, there is a 180° phase difference between the wave fields on either side of the cylindrical element. The formation of a dipole wave field is problematic because the waves produced are pressure (P) waves rather than shear (S) waves. The fluid mechanics of pressure waves are different from shear waves, and the previously defined shear wave relationships no longer apply.

[0267] For example, the damping coefficients for shear waves and pressure waves are defined differently. For shear waves, the shear rate and the stress generated by the shear rate result in a relatively well-defined and controllable damped wave. In contrast, pressure waves follow what is known as "quadratic damping," where the damping force is proportional to the square of the velocity. This results in a damping coefficient of the following form:

[0268] C quadratic =b·v Equation 46

[0269] Here, b is a constant and v is the velocity. In other words, the damping coefficient varies unhelpfully with the velocity of the vibration.

[0270] However, if the Reynolds number is kept low, a monopolar wave field can be maintained. The Reynolds number represents the ratio between inertial and viscous forces. As the Reynolds number decreases, the viscous forces become larger relative to the inertial forces.

[0271] Fig.52 Laminar flow around a cylinder vibrating in a left-right direction perpendicular to the axis of the cylinder is shown. In the laminar flow case, the forces on either side of the cylinder become shear forces and so shear waves propagate as a result of the lateral vibrations. Without wishing to be bound by theory, it may be considered that the laminar flow results in sufficiently low inertial forces relative to the viscous forces that the wave field is largely or at least partially defined by shear waves arising from the upper and lower parts of the cross section of the cylinder, i.e. perpendicular to the axis and the direction of vibration. As a result, as the Reynolds number decreases, the extent to which the wave field has a dipole form decreases, while the extent to which the wave field has a monopole form increases. Low Reynolds numbers have recovered part of the shear wave field, which is in phase throughout its propagation space. The advantage of geometric damping is retained, but the load factor gain may be increased due to the element being off-axis.

[0272] Advantageously, off-axis cylindrical elements can achieve relatively large degrees of amplification with little increase in size and weight, since relatively low Reynolds numbers are readily achieved with smaller length scales. In some embodiments of the disclosed technology, equivalent fluid loading factors to much larger and heavier vibrating elements can be achieved.

[0273] It should also be recognized that relatively low Reynolds numbers can be readily achieved with micro- and nano-scale devices for nearly any fluid of interest, regardless of its physical properties. Submicron pin structures on a vibrating base can form the same radial displacement elements described above and achieve the same geometric damping benefits. Some embodiments can feature multiple cylindrical elements or quasi-cylindrical elements, such as pins and spikes formed by micro- or nano-fabrication processes, which can allow micro-surfaces to exhibit high fluid loading coefficients.

[0274] It should also be recognized that low Reynolds numbers may result in the wavefield being only partially defined by shear waves, so the load factor expressions for geometrically damped conditions may differ from those above, but may be proportional to them, with a proportionality constant related to the extent to which the shear waves define the wavefield. In the following expression, a proportionality constant h is introduced, where the value of the proportionality constant h is 1 if the wavefield is completely defined by shear waves and 0.5 if 50% of the wavefield is defined by shear waves, which may be a reasonable assumption in practice:

[0275] C F =h(2πl R O 2 )μ′ Equation 47

[0276] K F =h(2πl R O 2 )G′ Equation 48

[0277] J F =h(2πl R O 4 )ρ. Equation 49

[0278] If h is assumed to be 0.5, the above expression simplifies to:

[0279] C F =(πl R O 2 )μ′ Equation 50

[0280] K F =(πl R O 2 )G′ Equation 51

[0281] J F =(πl R O 4 )ρ. Equation 52

[0282] In the context of the present disclosure, a "low" Reynolds number means that the Reynolds number is low enough so that laminar flow is obtained, and the flow caused by vibration can be characterized to some extent by a shear wave field, and the advantages of geometric damping are provided at least to some extent. It is recognized that the transition from laminar to turbulent flow occurs over a certain range of Reynolds numbers, and the precise range in which this transition occurs is related to the geometry. Compared with higher Reynolds numbers, lower Reynolds numbers are more likely to result in flow behavior that leads to a partial shear wave field. Without wishing to be bound by theory, it can be considered that the degree of shear wave field development and some advantages of the disclosed technology obtained therefrom are related to the Reynolds number. For example, a Reynolds number of 1000 may exhibit a certain degree of laminar flow and lead to a certain degree of shear wave field. A Reynolds number of 100 may exhibit a greater degree of quasi-laminar flow and lead to a greater degree of shear wave field. A Reynolds number of 10 may exhibit a greater degree of quasi-laminar flow and lead to a greater degree of shear wave field. A Reynolds number of 1 may exhibit a greater degree of quasi-laminar flow and lead to a greater degree of shear wave field. Generally speaking, lower Reynolds numbers may be preferred, but one skilled in the art will recognize that achieving the lowest possible Reynolds number must be balanced with other technical considerations.

[0283] If the geometric damping conditions are met, the propagation depth of the wave is determined by the geometry of the cylindrical element (particularly its radius).

[0284] In view of the above discussion of geometric damping, the radiator or detector surface may be the surface of or include an elongated member. Such an elongated member is characterized by a width, a half-width equal to half the width, and a length greater than the width, wherein the half-width is less than the propagation depth of shear waves in the fluid at the vibration frequency, more preferably less than 50% of the propagation depth. Such an elongated member may not be colinear with or offset from an axis of vibration, such as an axis of torsional vibration. During vibration, the fluid flow around the elongated member may be laminar.

[0285] In some embodiments, the half-width of the slender 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.

[0286] In some embodiments, the elongated member has a substantially or completely circular cross-section along 50%, 70%, 90% or 100% of its length. Optionally, along 50%, 70%, 90% or 100% of its length, 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, wherein the circularity of the cross-sectional shape is given by 4πA / p 2 Calculate , where A is the convex area of ​​the cross-sectional shape and p is the convex perimeter of the cross-sectional shape.

[0287] In some embodiments, the half-width of the elongated member calculated at a point along its length is based on the convex perimeter or convex area of ​​the cross-section of the elongated member at that point along its length. Alternatively, the half-width is calculated based on the convex perimeter of the cross-sectional shape by the following expression p / 2π. Alternatively, the half-width can be calculated based on the convex area of ​​the cross-sectional shape by the following expression √(A / π). If the elongated member has a circular cross-section, both expressions produce the radius of the circle, so the half-width of the circular cross-section is the radius of the circle.

[0288] 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 more than 100% of its length.

[0289] In some embodiments, the elongated member has a constant cross-section along only less than 50%, less than 40%, less than 30%, less than 20%, less than 10% of its length, or the cross-section varies continuously along its length.

[0290] In some embodiments, the area of ​​the cross-section increases or decreases monotonically along the length of the elongated member.

[0291] In some embodiments, the elongated member is straight.

[0292] In some embodiments, the elongated member is axially symmetric along its length.

[0293] In some embodiments, the elongated member is non-straight. For example, the elongated member may comprise a closed loop.

[0294] In some embodiments, the elongated member comprises one of: a cylinder, a cone, a truncated cone, a torus, and an arcuate portion of a torus.

[0295] 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.

[0296] In some embodiments, the half width of the elongated member less than the propagation depth is the average half width along the length of the elongated member. Optionally, the average half width is calculated as the arithmetic mean of the half widths along the length of the elongated member, or is the average half width, which is calculated as twice the volume of the elongated member divided by the surface area of ​​the elongated member.

[0297] 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.

[0298] In some embodiments, the length of the elongated member is greater than a multiple of the half width of the elongated member (the half width is half of the width of the elongated member), and wherein 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 can be greater than a multiple of the width of the elongated member, and wherein 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.

[0299] In some embodiments, the width of the elongated member is between 1 nm and 500 nm. Such embodiments may be described as "nanoscale" or nanoscale 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 microscale embodiments. Appropriately sized devices, which may be nanoscale or microscale devices, may vibrate at low frequencies to advantageously measure fluid properties of fluids with low viscosities (e.g., less than 1 mPa·s), or may vibrate at high frequencies to advantageously measure fluid properties of fluids with low viscosities (e.g., less than 1 mPa·s), because at such small scales, the width of the elongated member is still small relative to the propagation depth at such high frequencies.

[0300] In some embodiments, the vibration transducer element comprises an axle with a longitudinal axis, wherein the elongated member is connected to the axle, and wherein the elongated member is not colinear with the longitudinal axis of the axle. Optionally, during the vibration of the vibration transducer element with a vibration frequency, the fluid flow around the elongated member is a laminar flow. Alternatively or additionally, the Reynolds number Re of the fluid flowing around the elongated member is less than 1, wherein the Reynolds number is equal to 2R vρ / μ, wherein μ is the viscosity of the fluid, p is the density of the fluid, R is the half width of the elongated member, and v is the maximum (vibration) speed of the elongated member relative to the fluid during the vibration transducer vibration, wherein optionally, the Reynolds number is less than 1000, or less than 300, or less than 100, or less than 30, or less than 10, or less than 3, or less than 1, or less than 0.9, or less than 0.7, or less than 0.7, or less than 0.6, or less than 0.5, or less than 0.4, or less than 0.3, or less than 0.25, or less than 0.2, or less than 0.1. Alternatively or additionally, the elongated member may have a first end and a second end, wherein one or both of the first end and the second end are spaced apart from the longitudinal axis of the shaft by an offset distance greater than half the width of the elongated member, wherein, optionally, the offset distance is greater than a multiple of the width, and the multiple is 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 30, or 50. Alternatively or additionally, the vibration transducer element may include a plurality of elongated members connected to the shaft, each elongated member not being co-linear with the axis of the shaft, each elongated member having a half-width less than a propagation depth of shear waves in the fluid at the vibration frequency, and wherein, optionally, the half-width of a first elongated member of the plurality of elongated members is different from the half-width of a second elongated member of the plurality of elongated members, and wherein, optionally, two, three, four, five, or more of the plurality of elongated members may have uniquely different half-widths. Alternatively or additionally, the elongated member may comprise a first end and a second end, wherein the elongated member is connected to the shaft at the first end and optionally also to the shaft at the second end.Alternatively or additionally, the shaft may comprise a pendulum and the elongated member may be connected to the shaft at the pendulum.

[0301] A vibration transducer according to the technology described herein can be used to determine a physical property of a fluid by vibrating the vibration transducer in the fluid at a vibration frequency and determining an amount indicative of damping based on the vibration. For example, to measure viscosity, the Q factor of the vibration can be determined. The Q factor is a dimensionless parameter that represents the level of damping of a resonator, where the damping level is a function of viscosity. In particular, it represents the degree of underdamping of the resonator. On a frequency response curve, a high Q factor provides a high and narrow peak at the resonant frequency, while a low Q factor provides a low and wide peak. Since the peak width varies with changes in damping, the Q factor can be defined as the ratio of the resonant frequency to the resonant bandwidth:

[0302]

[0303] Among them, ω R is the resonant frequency in radians per second, and Δω is the full width at half maximum (FWHM), the bandwidth over which the vibration power is greater than half of the maximum value (or equivalently, the vibration amplitude is greater than the maximum amplitude at resonance divided by √2), i.e. the bandwidth between the 3dB points. The fluid viscosity is a function of the Q factor.

[0304] It should be noted that the viscosity measurement at or corresponding to the vibration frequency may include making amplitude measurements at more than one frequency to estimate the Q factor, but a single viscosity measurement is obtained at the frequency corresponding to the resonant frequency. For example, the bandwidth may be determined based on the frequency required to drop the amplitude to 1 / √2 times the maximum amplitude at resonance. As a non-limiting example, the frequency required to drop the amplitude to 1 / √2 times the maximum amplitude at resonance may be determined by performing a frequency sweep around the resonant frequency, but those skilled in the art will recognize that the 3dB point frequency may be identified by various other techniques.

[0305] Another way to determine the Q factor is to measure the amplitude at a series of frequencies around the resonant frequency and fit a parabola to the frequency and amplitude values ​​(or their logarithms) by the least squares method. The 3dB point can then be obtained as the solution to a quadratic equation based on the parabola of the best fit measurements.

[0306] Another method to determine the Q factor is the logarithmic decay method. By stopping driving the transducer and measuring the decay of the vibration, the Q factor can be determined by monitoring the time series of the vibration and determining the natural logarithm of the ratio of two consecutive peaks A1 and A2, as shown below:

[0307]

[0308] As described above, the loss factor is the inverse of the Q factor and thus can be easily determined based on the above method.

[0309] Fig.53 A flow chart of a method according to the technology of the present disclosure is shown. 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 the first surface and the second surface are spaced and oriented relative to each other so that during vibration of the one or more vibration transducers, the first wave and the second wave combine with each other to provide net constructive interference or net destructive interference at one or both of the first surface and the second surface.

[0310] The method includes a second step 620 of determining a material property of the viscoelastic fluid based on vibrations of one or more vibration transducers in the viscoelastic fluid.

[0311] According to the technology of the present disclosure, the component 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 to cause the one or more vibration transducers to vibrate in the fluid in a manner according to the technology of the present disclosure.

[0312] According to the technology of the present disclosure, a component for determining material properties of a viscoelastic fluid based on vibrations of one or more vibration transducers in the viscoelastic fluid may include an electronic device configured to record measurements of vibrations of the one or more vibration transducers and process the measurements to determine the material properties.

[0313] The component for vibrating one or more vibration transducers and the component for determining the material properties of the viscoelastic fluid based on the one or more vibration transducers can be the same electronic device (i.e., a single electronic device causes vibrations and determines the material properties) or can be different electronic devices.

[0314] It will be further appreciated by those skilled in the art that the various illustrative logic blocks, configurations, modules, circuits, and algorithmic steps described in conjunction with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or a combination of the two. In order to clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, configurations, modules, circuits, and steps have been described above according to their functions. Whether such functions are implemented as hardware or software depends on specific applications and design constraints on the entire system. Those skilled in the art may implement the described functions in different ways for each specific application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.

[0315] The steps of the method or algorithm described in conjunction with the embodiments disclosed herein may be directly embodied in hardware, a software module executed by a processor, or a combination of the two. The software module may reside in a random access memory (RAM), a flash memory, a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a register, a hard disk, a removable disk, a compact disk read-only memory (CD-ROM), or any other form of storage medium known in the art. An exemplary storage medium is coupled to a processor so that the processor can read information from the storage medium and write information to the storage medium. Alternatively, the storage medium may be integrated into a 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 in a computing device or a user terminal as discrete components.

[0316] The content of the present disclosure can be described by the following numbered aspects:

[0317] Aspect 1. A method for measuring material properties of a viscoelastic fluid using one or more vibration transducers, the method comprising:

[0318] vibrating one or more vibration transducers in the 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 the first surface and the second surface are spaced and oriented relative to each other such that during vibration of the one or more vibration transducers, the first wave and the second wave combine with each other to provide net constructive interference or net destructive interference at one or both of the first surface and the second surface; and

[0319] Material properties of the viscoelastic fluid are determined based on vibrations of one or more vibration transducers in the viscoelastic fluid.

[0320] Aspect 2. The method of aspect 1, wherein the first wave and the second wave combine with each other to provide net destructive interference.

[0321] Aspect 3. The method of aspect 1, wherein the first wave and the second wave combine with each other to provide a net constructive interference.

[0322] Aspect 4. The method according to aspect 1 or aspect 2, wherein the first wave and the second wave are shear waves.

[0323] Aspect 5. The method according to any one of aspects 1 to 4, wherein determining the measurement of the material property of the viscoelastic fluid comprises determining a loss factor or Q factor of vibration of one or more vibration transducers in the viscoelastic fluid.

[0324] Aspect 6. The method according to aspect 5, wherein the determined loss factor or Q factor is a monotonic function of the viscosity or storage modulus of the viscoelastic fluid.

[0325] Aspect 7. The method according to any one of aspects 1 to 6, wherein the viscoelastic fluid has a tan Δ of less than 1, wherein tan Δ is the loss tangent of the viscoelastic fluid.

[0326] 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.

[0327] Aspect 9. The method of aspect 8, wherein one or both of the first surface and the second surface are convex.

[0328] 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 fully concave.

[0329] Aspect 11. A method according to Aspect 10, wherein the first surface is partially or fully concave, and the first wave generated from the first surface is configured to focus at a certain focal distance from the first surface, wherein: i) the distance between the second surface and the first surface is farther than the focal distance of the first surface, or ii) the distance between the second surface and the first surface is closer than the focal distance of the first surface, or iii) the second surface is located at the focal length of the first surface.

[0330] Aspect 12. A method according to any one of Aspects 1 to 11, wherein the first surface includes a concave portion configured to focus the first wave, wherein the concave portion includes a first area of ​​the concave portion and a second area of ​​the concave portion, and the second area of ​​the concave portion is configured to vibrate out of phase with the first area of ​​the concave portion to generate a wave that is out of phase with the wave generated from the first area of ​​the concave portion.

[0331] Aspect 13. A method according to Aspect 12, wherein vibrating one or more vibration transducers includes vibrating a concave portion of a first surface in a torsional manner about a vibration axis extending through the concave portion of the first surface, wherein: i) a first region of the concave portion and a second region of the concave portion are located on opposite sides of the vibration axis, and / or ii) the concave portion of the first surface is axially symmetrical about the vibration axis, and / or iii) the vibration axis extends through a focal region of the concave portion.

[0332] Aspect 14. The method according to aspect 12 or aspect 13, wherein a depth profile of the concave portion in a cross section passing through the vibration axis is smooth, and preferably has a circular arc shape, a parabolic arc shape, or an elliptical arc shape.

[0333] Aspect 15. The method of aspect 12, wherein vibrating the one or more vibration transducers comprises vibrating the first region and the second region of the concave portion along a path (eg, a linear path or a circular path).

[0334] Aspect 16. The method according to aspect 15, wherein the first area of ​​the concave portion and the second area of ​​the concave portion have a constant concave depth profile along the direction of the path.

[0335] Aspect 17. The method of aspect 16, wherein vibrating the one or more vibration transducers comprises vibrating the first region and the second region of the concave portion along the direction of the path.

[0336] Aspect 18. The method according to aspect 16 or aspect 17, wherein the depth profiles of the first region and the second region of the concave portion are smooth, and preferably in the shape of a circular arc, a parabolic arc, or an elliptical arc.

[0337] 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 comprises an elongated member.

[0338] Aspect 20. A method according to Aspect 19, wherein vibrating one or more vibration transducers in the viscoelastic fluid includes vibrating the one or more vibration transducers through or around corresponding vibration axes of the one or more vibration transducers, wherein the vibration axes are not co-linear with at least one slender member corresponding to the first surface or the second surface.

[0339] Aspect 21. The method according to aspect 19 or aspect 20, wherein vibrating one or more vibration transducers in the viscoelastic fluid comprises vibrating the one or more vibration transducers in a torsional manner about a common vibration axis.

[0340] Aspect 22. The method according to aspect 21, wherein one or both of the first surface and the second surface comprises an elongated member configured in the form of a ring.

[0341] Aspect 23. A method according to aspect 22, wherein an axis passing through the center of the ring is co-linear with the common vibration axis.

[0342] 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 the waves into the ring.

[0343] Aspect 25. The method according to any one of aspects 21 to 24, wherein the first surface comprises an elongated member configured in the form of a ring, the elongated member being connected to the second surface by one or more support members, the support members biasing the first surface away from the second surface.

[0344] Aspect 26. The method according to aspect 25, wherein the second surface includes a concave portion configured to generate shear waves under torsional vibration about the common vibration axis, and the generated shear waves are focused toward the first surface.

[0345] Aspect 27. The method of Aspect 19 or Aspect 20, wherein the one or more vibration transducers include a shaft and a plurality of slender members, the shaft having a longitudinal axis extending along the shaft, the plurality of slender members extending outward from the longitudinal axis and spaced apart from each other, wherein vibrating the one or more vibration transducers includes vibrating the shaft in a torsional manner about the longitudinal axis.

[0346] Aspect 28. The method of aspect 27, wherein a plurality of elongated members are connected to the shaft.

[0347] Aspect 28A. The method of Aspect 28, wherein the plurality of elongated members extend outwardly from the shaft in a radial direction from the longitudinal axis.

[0348] Aspect 29. The method of aspect 27, wherein the shaft includes a pendulum, and the plurality of elongated members are connected to the shaft at the pendulum.

[0349] Aspect 29A. The method of aspect 29, wherein the plurality of elongated members extend outwardly from the pendulum in a radial direction from the longitudinal axis.

[0350] Aspect 29B. A method according to Aspect 19 or Aspect 20, wherein the one or more vibration transducers include a shaft and a plurality of slender members, the shaft having a longitudinal axis extending along the shaft, the plurality of slender members extending in a direction aligned with the longitudinal axis and spaced apart from each other, wherein vibrating the one or more vibration transducers includes vibrating the shaft in a torsional manner about the longitudinal axis.

[0351] Aspect 29C. The method of Aspect 29B, wherein none of the plurality of elongated members is co-linear with the longitudinal axis of the shaft.

[0352] Aspect 29D. The method of Aspect 29B or Aspect 29C, wherein some or all of the plurality of elongated members extend axially outward from one end of the shaft.

[0353] Aspect 29E. The method of aspect 29B or aspect 29C, wherein the shaft comprises a pendulum, and the plurality of elongated members are connected to the shaft at the pendulum.

[0354] Aspect 29F. The method of aspect 29E, wherein the pendulum is cylindrical and coaxial with the longitudinal axis.

[0355] Aspect 29G. The method of aspect 29E or 29F, wherein the plurality of elongated members extend axially outward from one end of the pendulum.

[0356] Aspect 29H. The method of any of aspects 29B to 29G, wherein the plurality of elongated members are evenly distributed around the longitudinal axis of the shaft.

[0357] Aspect 29I. The method of any of aspects 29B to 29H, wherein the plurality of elongated members are all positioned at the same radial distance from the longitudinal axis of the shaft.

[0358] Aspect 30. A method according to any one of Aspects 25 to 29I, wherein the first wave and the second wave are shear waves, and wherein one or both of the first surface and the second surface comprises a slender member characterized by a width, a half-width equal to half the width, and a length greater than the width, wherein the half-width is less than the propagation depth of the shear wave in the fluid at the vibration frequency.

[0359] Aspect 31. A method according to aspect 30, wherein the propagation depth is the distance over which the amplitude of a shear wave propagating at the vibration frequency in the fluid decreases by 1 / e, where e is the base of the natural logarithm.

[0360] Aspect 32. A method according to aspect 30 or aspect 31, wherein the propagation depth of the shear wave propagating in the fluid at the vibration frequency is given by the following expression:

[0361]

[0362] where μ is the viscosity of the fluid, ρ is the density of the fluid, ω is the angular frequency of vibration, and Δ varies between 0 and π / 2 (in radians) and is defined by the loss tangent tanΔ, and where tanΔ is equal to the following expression where G' is the storage modulus of the fluid:

[0363]

[0364] 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.

[0365] Aspect 34. The method according to any one of aspects 30 to 33, wherein the one or more vibration transducers include a shaft having a longitudinal axis, wherein the elongated member is connected to the shaft, and wherein the elongated member is not co-linear with the longitudinal axis of the shaft.

[0366] Aspect 35. The method according to any one of aspects 30 to 34, wherein the shaft includes a pendulum, and the elongated member is connected to the shaft at the pendulum.

[0367] Aspect 36. A 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 being non-colinear with the longitudinal axis of the shaft, each elongated member having a half-width that is less than the propagation depth of the shear wave in the fluid at the vibration frequency.

[0368] Aspect 37. The method of aspect 36, wherein a half-width of a first elongated member of the plurality of elongated members is different than a half-width of a second elongated member of the plurality of elongated members.

[0369] Aspect 38. The method according to any one of aspects 30 to 37, wherein the elongated member has a cross-section having a circularity in the range of 0.75 to 1 along at least 50% of its length, wherein the circularity of the cross-section is calculated by the following formula:

[0370]

[0371] Where A is the convex area of ​​the cross section and p is the convex perimeter of the cross section.

[0372] 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 no more than 10% of its length.

[0373] Aspect 40. The method according to any one of aspects 30 to 39, wherein the elongated member is straight or non-straight, or comprises one of the following: a cylinder, a cone, a frustoconical body, a torus, and an arcuate portion of a torus.

[0374] Aspect 41. The method according to any one of aspects 30 to 40, wherein vibrating the vibration transducer comprises vibrating the vibration transducer in an oscillatory rotational motion and / or an oscillatory linear motion and / or an oscillatory curvilinear motion.

[0375] Aspect 42. The method of aspect 41, wherein the elongated member is straight, and wherein vibrating the vibration transducer comprises vibrating the elongated member in an oscillatory rotational motion about an axis along the length of the elongated member.

[0376] Aspect 43. The method of aspects 30 to 42, wherein the length of the elongated member is greater than twice the width of the elongated member.

[0377] Aspect 44. A method according to any one of aspects 30 to 43, wherein the half width of the elongated member is greater than 0.5 mm, wherein the viscosity of the fluid is greater than 100 Pa·s, wherein the density of the fluid is between 500 kg / m 3 and 1500kg / m 3 and wherein the vibration frequency is less than 10kHz.

[0378] Aspect 45. The method according to any one of aspects 35 to 44, wherein the fluid flow around the elongated member during the vibration of the elongated member at the vibration frequency is laminar.

[0379] Aspect 46. A method according to any one of Aspects 35 to 45, wherein the slender member has a first end and a second end, wherein one or both of the first end and the second end are spaced apart from the longitudinal axis of the shaft by an offset distance that is greater than the half-width of the slender member.

[0380] Aspect 47. A method according to any one of aspects 35 to 46, wherein during the vibration of the one or more vibration transducers in the fluid at the vibration frequency, the Reynolds number Re of the fluid flow around the slender member is less than 1000, preferably less than 100, more preferably less than 10, and even more preferably less than 1, wherein the Reynolds number is given by

[0381]

[0382] Where μ' is the viscosity of the fluid, ρ is the density of the fluid, R is the half width of the elongate member, and v is the maximum velocity of the elongate member relative to the fluid during vibration of the one or more vibration transducers.

[0383] Aspect 48. The method according to any one of aspects 30 to 34, wherein the elongated member is ring-shaped.

[0384] Aspect 49. A method according to any one of Aspects 1 to 48, wherein vibrating one or more vibration transducers includes vibrating one or more vibration transducers at a vibration frequency, wherein 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, and more preferably between 500 Hz and 2 kHz, even more preferably between 700 Hz and 1300 Hz, even more preferably at or approximately at 1 kHz, for example within 1 kHz ± 100 Hz, preferably within 1 kHz ± 50 Hz.

[0385] Aspect 50. The method according to any one of aspects 1 to 49, wherein the one or more vibration transducers vibrate in a torsional manner about a common axis.

[0386] Aspect 51. A method according to any one of Aspects 1 to 50, wherein determining the material properties of the viscoelastic fluid based on the measurement of vibration includes determining one or more of viscosity, viscoelasticity, density, fluid stiffness, loss tangent, storage modulus, loss modulus, and yield stress.

[0387] Aspect 52. The method according to any one of aspects 1 to 51, wherein determining a material property of the viscoelastic fluid based on vibration of one or more vibration transducers in the viscoelastic fluid comprises determining a quantity indicative of a degree of damping of the fluid at a vibration frequency.

[0388] Aspect 53. The method of aspect 52, wherein determining the quantity indicative of a degree of vibration damping of the fluid at a vibration frequency comprises determining a loss factor or a Q factor.

[0389] Aspect 54. A method according to Aspect 52 or Aspect 53, wherein determining an amount indicating the damping degree of the fluid at a vibration frequency includes determining a first amount indicating the damping degree at the vibration frequency, wherein the method also includes vibrating the vibration transducer at another vibration frequency and determining a second amount indicating the damping degree at the other vibration frequency, wherein determining the material properties of the fluid includes determining the viscoelasticity of the fluid based on the amount indicating the vibration frequency and the damping degree at the other vibration frequency.

[0390] Aspect 55. The method according to aspect 52 or aspect 53, wherein determining the material property of the fluid comprises determining the density of the fluid based on measuring the resonant frequency of a vibration transducer in the fluid.

[0391] Aspect 56. An apparatus for measuring material properties of a viscoelastic fluid using one or more vibration transducers, the apparatus comprising:

[0392] one or more vibration transducers, the one or more vibration transducers comprising a first surface and a second surface;

[0393] means for vibrating the one or more vibration transducers such that when vibrated in a viscoelastic fluid, a first wave is generated that propagates from a first surface of the one or more vibration transducers and a second wave is generated that propagates from a second surface of the one or more vibration transducers, wherein the first surface and the second surface are spaced and oriented relative to each other such that during vibration of the one or more vibration transducers, the first wave and the second wave combine with each other to provide net constructive interference or net destructive interference at one or both of the first surface and the second surface; and

[0394] A component for determining a material property of a viscoelastic fluid based on vibrations of one or more vibration transducers in the viscoelastic fluid, the vibrations of the one or more vibration transducers in the viscoelastic fluid comprising net constructive interference or net destructive interference.

[0395] Aspect 57. The device according to Aspect 56, wherein the first surface includes a concave portion.

[0396] Aspect 58. The device according to Aspect 56 or Aspect 57, wherein the first surface comprises an elongated member.

[0397] Aspect 59. The device according to any one of aspects 56 to 58, wherein the second surface comprises an elongated member.

[0398] Aspect 60. The device according to any one of aspects 56 to 58, wherein the second surface is planar, wherein optionally, the first surface comprises an elongated member extending outwardly from the second surface.

[0399] Aspect 61. The device according to Aspect 60, wherein the first surface includes a slender member extending in a direction perpendicular to the second surface.

[0400] Aspect 62. The device according to Aspect 61, wherein the first surface comprises an elongated member configured in the form of a ring.

[0401] Aspect 63. An apparatus according to Aspect 58, wherein the second surface faces radially outward from the axis of torsional vibration of the vibration transducer in which the second surface is located and is configured to generate a shear wave extending radially outward from the axis of torsional vibration, wherein optionally, the first surface includes a slender member extending outward from the second surface.

[0402] Aspect 64. The device according to Aspect 64, wherein the first surface includes a slender member extending in a direction perpendicular to the second surface.

[0403] Aspect 65. The device according to aspect 66, wherein the first surface includes a slender member that extends circumferentially around the second surface or extends in a direction aligned with the axis of torsional vibration.

[0404] Aspect 66. An apparatus according to any of Aspects 60 to 65, wherein the second surface includes a concave portion configured to generate a wave in the fluid that is focused at a focal distance from the second surface, wherein: i) the distance between the first surface and the second surface is farther than the focal distance of the second surface, or ii) the distance between the first surface and the second surface is closer than the focal distance of the second surface, or iii) the first surface is located at the focal distance of the second surface.

[0405] Aspect 67. The device according to any one of aspects 56 to 71, wherein the first surface includes a slender member configured in the form of a ring, the slender member is connected to the second surface by one or more support members, and the support members bias the first surface away from the second surface.

[0406] Aspect 68. The device according to Aspect 67, wherein the second surface includes a concave portion, the concave portion is configured to generate shear waves under torsional vibration about the common vibration axis, and the generated shear waves are focused toward the first surface.

[0407] Aspect 69. An apparatus according to any of Aspects 56 to 66, wherein the one or more vibration transducers include a shaft and a plurality of slender members, the shaft having a longitudinal axis extending along the shaft, the plurality of slender members extending outward from the longitudinal axis and spaced apart from each other, wherein vibrating the one or more vibration transducers includes vibrating the shaft in a torsional manner about the longitudinal axis.

[0408] Aspect 70. The device of aspect 69, wherein the plurality of elongated members are connected to the shaft and extend radially outward from the shaft.

[0409] Aspect 70A. The device of Aspect 70, wherein the plurality of elongated members extend outwardly from the shaft in a radial direction throughout the longitudinal axis.

[0410] Aspect 71. The device according to aspect 69, wherein the shaft includes a pendulum, and the plurality of elongated members are connected to the shaft at the pendulum.

[0411] Aspect 71A. The device of Aspect 71, wherein the plurality of elongated members extend outwardly from the pendulum along an entire radial direction from the longitudinal axis.

[0412] Aspect 71B. An apparatus according to any of Aspects 56 to 66, wherein the one or more vibration transducers include a shaft and a plurality of slender members, the shaft having a longitudinal axis extending along the shaft, the plurality of slender members extending in a direction aligned with the longitudinal axis and spaced apart from each other, wherein vibrating the one or more vibration transducers includes vibrating the shaft in a torsional manner about the longitudinal axis.

[0413] Aspect 71C. The device of Aspect 71B, wherein none of the plurality of elongated members is co-linear with the longitudinal axis of the shaft.

[0414] Aspect 71D. The device of Aspect 71B or 71C, wherein some or all of the plurality of elongated members extend axially outward from one end of the shaft.

[0415] Aspect 71E. The device of aspect 71B or 71C, wherein the shaft comprises a pendulum, and the plurality of elongated members are connected to the shaft at the pendulum.

[0416] Aspect 71F. The device according to Aspect 71E, wherein the pendulum is cylindrical and coaxial with the longitudinal axis.

[0417] Aspect 71G. The device of aspect 71E or 71F, wherein the plurality of elongated members extend axially outward from one end of the pendulum.

[0418] Aspect 71H. The device of any of aspects 71B to 71G, wherein the plurality of elongated members are evenly distributed around the longitudinal axis of the shaft.

[0419] Aspect 71I. The device of any of aspects 71B to 71H, wherein the plurality of elongated members are all positioned at the same radial distance from the longitudinal axis of the shaft.

[0420] Aspect 72. An apparatus according to any of Aspects 56 to 71I, 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 of the width, and a length greater than the width, wherein the half-width is less than the propagation depth of the shear wave in the fluid at the vibration frequency.

[0421] Aspect 73. The device according to aspect 72, wherein the half width is less than 50% of the propagation depth.

[0422] Aspect 74. An apparatus according to Aspect 72 or Aspect 73, wherein the one or more vibration transducers include a shaft having a longitudinal axis, wherein the elongated member is connected to the shaft, and wherein the elongated member is not co-linear with the longitudinal axis of the shaft.

[0423] Aspect 75. The device according to aspect 74, wherein during the vibration of the one or more vibration transducers in the fluid at the vibration frequency, the Reynolds number Re of the fluid flow around the slender member is less than 1000, preferably less than 100, more preferably less than 10, and even more preferably less than 1, wherein the Reynolds number is given by the following formula

[0424]

[0425] Where μ' is the viscosity of the fluid, ρ is the density of the fluid, R is the half width of the elongated member, and v is the maximum velocity of the elongated member relative to the fluid during vibration of the vibration transducer.

[0426] Aspect 76. The device according to any one of aspects 56 to 75, wherein the first surface is flat and / or includes a concave portion configured to generate a wave in the fluid that is focused at a focal distance from the first surface.

[0427] Aspect 77. The device according to Aspect 76, wherein the first surface includes a concave portion configured to generate a wave in the fluid that is focused at a focal distance from the first surface.

[0428] Aspect 78. The device according to aspect 77, wherein the distance between the second surface and the first surface is farther than the focal length of the first surface.

[0429] Aspect 79. The device according to Aspect 77, wherein the distance between the second surface and the first surface is closer than the focal length of the first surface.

[0430] Aspect 80. An apparatus according to any one of Aspects 76 to 79, wherein the second surface is flat and / or the first surface and the second surface both include a concave portion, the concave portion being configured to generate a wave in the fluid focused on a focal area between the first surface and the second surface.

[0431] Aspect 81. The device according to Aspect 80, wherein the first surface and the second surface each include a concave portion configured to generate a wave in the fluid focused at a focal region between the first surface and the second surface.

[0432] Aspect 82. The apparatus according to aspect 81, wherein the focal region is equidistant between the first surface and the second surface.

[0433] Aspect 83. The device according to Aspect 81, wherein the first surface and the second surface are configured to vibrate in a torsional manner about a common axis, and the concave portion of each of the first surface and the second surface is axisymmetric about the common axis of vibration.

[0434] Aspect 84. The device according to Aspect 83, wherein one or both of the concave portion of the first surface and the concave portion of the second surface are circular grooves in the first surface and the second surface surrounding a common axis.

[0435] Aspect 85. An apparatus according to any of Aspects 76 to 84, wherein the first surface is configured to vibrate in a torsional manner about an axis perpendicular to the first surface, and wherein the second surface surrounds the axis and faces radially outward from the vibration axis, wherein the radius of the second surface is less than the maximum outermost extent of the first surface about the axis, and wherein the second surface is axially displaced from the first surface.

[0436] Aspect 86. An apparatus according to any of Aspects 56 to 85, wherein vibrating one or more vibration transducers comprises vibrating one or more vibration transducers at a vibration frequency, wherein 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, and even more preferably at or about 1 kHz.

[0437] Aspect 87. The device according to any one of aspects 56 to 86, wherein the first surface and the second surface are located on the same vibration transducer.

[0438] Aspect 88. The device according to Aspect 87, wherein the first surface and the second surface are located on different vibration transducers configured to vibrate at the same frequency.

[0439] Aspect 89. The device according to any one of aspects 56 to 88, wherein the first surface and the second surface are configured to vibrate in phase with each other.

[0440] Aspect 90. The apparatus according to any one of aspects 56 to 89, wherein the first surface is configured to vibrate with a phase offset relative to the second surface.

[0441] Aspect 91. The device according to any one of aspects 56 to 90, wherein the first wave and the second wave are shear waves.

[0442] Aspect 92. The apparatus according to any of Aspects 56 to 91, wherein determining the measurement of the material property of the viscoelastic fluid comprises determining a loss factor or Q factor of vibration of one or more vibration transducers in the viscoelastic fluid.

[0443] Aspect 93. The apparatus of aspect 92, wherein the determined loss factor or Q factor is a monotonic function of the viscosity or storage modulus of the viscoelastic fluid.

[0444] Aspect 94. A non-transitory computer-readable medium having instructions stored thereon, which, when executed by one or more processors of a system including one or more vibration transducers, cause the one or more processors to perform a method according to any one of aspects 1 to 55.

[0445] Aspect 95. An apparatus as described herein or substantially as described herein with reference to the specification, claims, and drawings, wherein, during vibration of one or more vibration transducers, the first wave and the second wave do not combine with each other to provide net constructive interference or net destructive interference at one or both of the first surface and the second surface.

[0446] Aspect 96. A method as described herein or substantially as described herein with reference to the specification, claims and drawings, wherein, during vibration of one or more vibration transducers, the first wave and the second wave do not combine with each other to provide net constructive interference or net destructive interference at one or both of the first surface and the second surface.

[0447] The foregoing description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the disclosed embodiments. Various modifications to these embodiments will be 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 present disclosure. Therefore, the present disclosure is not intended to be limited to the embodiments shown herein, but to be consistent with the widest scope consistent with the principles and novel features defined by the appended claims.

Claims

1. A method for measuring material properties of a viscoelastic fluid using one or more vibration transducers, the method comprising: vibrating one or more vibration transducers in the 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 the first surface and the second surface are spaced and oriented relative to each other such that during vibration of the one or more vibration transducers, the first wave and the second wave combine with each other to provide net constructive interference or net destructive interference at one or both of the first surface and the second surface; and A material property of the viscoelastic fluid is determined based on vibrations of the one or more vibration transducers in the viscoelastic fluid.

2. The method according to claim 1, wherein: The first wave and the second wave combine with each other to provide net destructive interference at one or both of the first surface and the second surface.

3. The method according to claim 1 or 2, wherein: The first wave and the second wave are shear waves.

4. The method according to any one of claims 1 to 3, wherein: Determining a measurement of a material property of the viscoelastic fluid includes determining a loss factor or Q factor of vibration of the one or more vibration transducers in the viscoelastic fluid.

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

6. The method according to any one of claims 1 to 5, wherein: The viscoelastic fluid has a tanΔ smaller than 1, wherein tanΔ is the loss tangent of the viscoelastic fluid.

7. The method according to any one of claims 1 to 7, wherein: One or both of the first surface and the second surface is curved or includes 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 include a concave portion, wherein 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 that is greater than a focal length of the first surface.

10. The method according to claim 8 or 9, wherein: The concave portion of the first surface includes a first region of the concave portion and a second region of the concave portion, the second region of the concave portion being configured to vibrate out of phase with the first region of the concave portion to generate a wave out of phase with a wave generated from the first region of the concave portion.

11. The method according to any one of claims 1 to 10, wherein: One or both of the first surface and the second surface include a slender member, wherein causing the one or more vibration transducers to vibrate in the viscoelastic fluid includes: causing the one or more vibration transducers to vibrate through or around a vibration axis of the one or more vibration transducers, wherein the vibration axis is not co-linear with the slender member.

12. The method according to claim 11, wherein: Causing the one or more vibration transducers to vibrate in the viscoelastic fluid includes: vibrating the one or more vibration transducers in a torsional manner about a common vibration axis, wherein one or both of the first surface and the second surface includes a slender member configured in the form of a ring, wherein an axis passing through the center of the ring is colinear with the common vibration axis.

13. The method according to claim 12, wherein: The first surface includes an elongated member configured in the form of a loop connected to the second surface by one or more support members that bias the first surface away from the second surface.

14. The method according to claim 12 or 13, wherein: The second surface includes a concave portion configured to generate shear waves under torsional vibration about the common vibration axis, the generated shear waves being focused toward the first surface.

15. The method according to claim 11, wherein: The one or more vibration transducers include a shaft and a plurality of elongated members, wherein the shaft has a longitudinal axis extending along the shaft, and the plurality of elongated members extend outward from the longitudinal axis and are spaced apart from each other, wherein vibrating the one or more vibration transducers includes vibrating the shaft in a torsional manner about the longitudinal axis.

16. The method according to any one of claims 1 to 15, wherein: The first wave and the second wave are shear waves, and 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 greater than the width, wherein the half-width is less than a propagation depth of the shear wave in the fluid at the vibration frequency.

17. The method according to any one of claims 1 to 16, wherein: Vibrating the one or more vibration transducers includes vibrating the one or more vibration transducers at a vibration frequency, wherein the vibration frequency is between 500 Hz and 2 kHz.

18. An apparatus for measuring material properties of a viscoelastic fluid using one or more vibration transducers, the apparatus comprising: one or more vibration transducers, the one or more vibration transducers comprising a first surface and a second surface; means for vibrating the one or more vibration transducers so as to generate, when vibrated in a viscoelastic fluid, 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 the first surface and the second surface are spaced and oriented relative to each other such that during vibration of the one or more vibration transducers, the first wave and the second wave combine with each other to provide net constructive interference or net destructive interference at one or both of the first surface and the second surface; as well as Means for determining a material property of the viscoelastic fluid based on vibrations of the one or more vibration transducers in the viscoelastic fluid, the vibrations of the one or more vibration transducers in the viscoelastic fluid comprising net constructive interference or net destructive interference.

19. The device according to claim 18, wherein: The first surface comprises an elongated member, a flat surface and / or a concave portion, the first surface being configured to generate waves focused toward the second surface under vibration, and wherein the second surface comprises an elongated member, a flat surface and / or a concave portion, the second surface being configured to generate waves focused toward the first surface under vibration.

20. The device according to claim 18 or 19, wherein: One or both of the first surface and the second surface include a slender member, wherein causing the one or more vibration transducers to vibrate in the viscoelastic fluid includes causing the one or more vibration transducers to vibrate through or around a vibration axis of the one or more vibration transducers, wherein the vibration axis is not co-linear with the slender member.

21. The device according to claim 20, wherein: Causing the one or more vibration transducers to vibrate in the viscoelastic fluid includes vibrating the one or more vibration transducers in a torsional manner about a common vibration axis, wherein one or both of the first surface and the second surface includes a slender member configured in the form of a ring, wherein an axis passing through the center of the ring is colinear with the common vibration axis.

22. The method according to claim 21, wherein: The first surface includes an elongated member configured in the form of a loop connected to the second surface by one or more support members that bias the first surface away from the second surface.

23. The device according to claim 21 or 22, wherein: The second surface includes a concave portion configured to generate shear waves under torsional vibration about the common vibration axis, the generated shear waves being focused toward the first surface.

24. The device according to claim 20, wherein: The one or more vibration transducers include a shaft and a plurality of elongated members, wherein the shaft has a longitudinal axis extending along the shaft, and the plurality of elongated members extend outward from the longitudinal axis and are spaced apart from each other, wherein vibrating the one or more vibration transducers includes vibrating the shaft in a torsional manner about the longitudinal axis.

25. The device according to any one of claims 18 to 24, wherein: One or both of the first surface and the second surface include a slender member characterized by a width, a half-width equal to half of the width, and a length greater than the width, wherein the half-width is less than the propagation depth of the shear wave in the fluid at the vibration frequency.

26. The device according to any one of claims 18 to 25, wherein: The first surface and the second surface are located on the same vibration transducer, or the first surface and the second surface are located on different vibration transducers configured to vibrate at the same frequency.

27. The device according to any one of claims 18 to 26, wherein: The first surface and the second surface are configured to vibrate in phase with respect to each other or to vibrate in a manner shifted by a phase with respect to each other.

28. A non-transitory computer readable medium having stored thereon instructions which, when executed by one or more processors of a system including one or more vibration transducers, cause the one or more processors to perform the method according to any one of claims 1 to 17.

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