Devices and methods employing attenuation of fluid vibrations

Abstract

Vibrating a vibration transducer element within a fluid at a vibration frequency, the vibration transducer element comprising an elongated member in contact with the fluid characterized by a width, a half-width equal to half of the width, and a length longer than the width, the half-width being smaller than the propagation depth of the shear wave of the fluid at the vibration frequency; measuring the vibration of the vibration transducer element within the fluid at the vibration frequency; and determining a physical property of the fluid, such as viscosity, viscoelasticity, density, fluid stiffness, loss tangent, storage modulus, loss modulus, or yield stress, based on the measurement of the vibration, to determine the physical property of the fluid.

Description

Technical Field

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

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

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

[0004] According to the techniques of the present disclosure, geometric attenuation is employed to attenuate the vibrations of an object vibrating in a fluid and / or to determine properties of the fluid such as viscosity, viscoelasticity, density, fluid stiffness, loss tangent, storage modulus, loss modulus, and yield stress. As will be explained in more detail below, geometric attenuation may be achieved using an elongated member vibrating in the fluid, where the elongated member has a relatively small half-width compared to the viscoelastic propagation depth of the shear wave of the fluid at the vibration frequency. The elongated member may be cylindrical (in which case the half-width is equal to the radius of the cylinder), but it does not have to be cylindrical.

[0005] By adopting geometric attenuation, linearity may be improved. In any measurement scenario, if the measurement does not require correction of non-linearity, such as an algorithm that needs to modify the measurement output to correct the non-linear deviation of the output with respect to the measurement variable, the quality and integrity of the measurement will be improved. In addition to simplicity, linearity may improve accuracy because non-linear correction, which may cause errors due to an incomplete correction algorithm, becomes unnecessary. Furthermore, by adopting geometric attenuation, higher independence from secondary variables may be obtained. For example, attenuation-related measurements may depend on viscosity and not on density, elasticity, or frequency. Therefore, any change in density, elasticity, or frequency that may occur in the actual measurement situation will not affect the measurement of viscosity. For example, when determining viscosity, it may not be necessary to measure all these elements individually and correct for their changes.

[0006] According to a first aspect, a method for determining a physical property of a fluid is provided, the method comprising vibrating a vibrating transducer element within a fluid at a vibration frequency, the vibrating transducer element comprising an elongated member in contact with the fluid characterized by a width, a half-width equal to half of the width, and a length longer than the width, the half-width being smaller than the propagation depth of a shear wave of the fluid at the vibration frequency; measuring the vibration of the vibrating transducer element within the fluid at the vibration frequency; and determining the physical property of the fluid based on the measurement of the vibration.

[0007] In some embodiments, determining the physical property of the fluid based on the measurement of the vibration comprises determining one or more of viscosity, viscoelasticity, density, fluid rigidity, loss tangent, storage modulus, loss modulus, and yield stress.

[0008] In some embodiments, the step of measuring the vibration includes determining a first quantity indicative of the degree of attenuation of the vibration transducer element in the fluid at the vibration frequency, the method further includes vibrating the vibration transducer element in the fluid at a further vibration frequency and determining a second quantity indicative of the degree of attenuation of the vibration transducer element in the fluid at the further vibration frequency, and the step of determining the physical properties of the fluid based on the measurement of the vibration includes determining the viscoelasticity of the fluid based on the vibration frequency and the quantity indicative of the degree of attenuation at the further vibration frequency.

[0009] In some embodiments, the step of measuring the vibration includes determining the resonance frequency of the vibration transducer element in the fluid, and the step of determining the physical properties of the fluid based on the measurement of the vibration includes determining the density of the fluid based on the resonance frequency.

[0010] In some embodiments, the propagation depth is the distance at which the amplitude of the shear wave propagating in the fluid at the vibration frequency decreases by a factor of 1 / e, where e is the base of the natural logarithm.

[0011] In some embodiments, the propagation depth of the shear wave propagating in the fluid at the vibration frequency is represented by the following equation.

Equation

Equation

[0012] In some embodiments, the half-width of the elongated member is less than 75% of the propagation depth, optionally less than 60%, optionally less than 50%, optionally less than 40%, optionally less than 25%, optionally less than 10%, optionally less than 5%, optionally less than 2%, optionally less than 1%, or optionally less than 0.5% of the propagation depth.

[0013] In some embodiments, the elongated member has a substantially or completely circular cross-section along 50%, 70%, 90%, or 100% of the length of the elongated member. Optionally, the elongated member has a circularity in the range of 0.75 to 1, optionally in the range of 0.8 to 1, optionally in the range of 0.85 to 1, optionally in the range of 0.9 to 1, optionally in the range of 0.95 to 1, more preferably in the range of 0.9 to 1, optionally in the range of 0.95 to 1 along 50%, 70%, 90%, or 100% of the length of the elongated member, and the circularity of the cross-sectional shape is 4πA / p 2 which is calculated by this formula, where A is the convex area of the cross-sectional shape and p is the convex perimeter of the cross-sectional shape.

[0014] In some embodiments, the half-width of the elongated member calculated at a point along the length of the elongated member is based on the convex perimeter or convex area of the cross-section of the elongated member at a point along the length of the elongated member. Optionally, the half-width is calculated by the formula p / 2π based on the convex perimeter of the cross-sectional shape. Alternatively, the half-width may be calculated based on the convex area of the cross-sectional shape by the formula √(A / π). When the elongated member has a circular cross-section, both of these formulas generate the radius of the circle, so the half-width of the circular cross-section becomes the radius of the circle.

[0015] In some embodiments, the elongated member has a constant cross-section along more than 50%, more than 60%, more than 70%, more than 80%, more than 90%, or 100% of the length of the elongated member.

[0016] In some embodiments, the elongated member has a constant cross-section only along less than 50%, less than 40%, less than 30%, less than 20%, less than 10% of the length of the elongated member, or the cross-section varies continuously along the length of the elongated member.

[0017] In some embodiments, the cross-section monotonically increases or decreases along the length of the elongated member.

[0018] In some embodiments, the elongated member is linear.

[0019] In some embodiments, the elongated member is axially symmetric along the length of the elongated member.

[0020] In some embodiments, the elongated member is not linear. For example, the elongated member may comprise a closed loop.

[0021] In some embodiments, the elongated member comprises one of a cylinder, a cone, a frustum of a cone, a torus, and an arc portion of a torus.

[0022] 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.

[0023] In some embodiments, the half-width of the elongated member that is less than the propagation depth is the average half-width along the length of the elongated member. Optionally, the average half-width is calculated as the arithmetic mean of the half-widths along the length of the elongated member, or is the average half-width calculated by dividing twice the volume of the elongated member by the surface area of the elongated member.

[0024] 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.

[0025] 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 being half of the width of the elongated member), and the multiple is one of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 45, or 50. In other words, the length of the elongated member is greater than a multiple of the width of the elongated member, and the multiple is one of 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10, 12.5, 15, 17.5, 20, 22.5, and 25.

[0026] In some embodiments, the viscosity of the fluid is greater than 100 Pa·s, and / or greater than 200 Pa·s, and / or greater than 500 Pa·s.

[0027] In some embodiments, the density of the fluid is 500 kg / m 3 ~1500 kg / m 3 and / or 700 kg / m 3 ~1300 kg / m 3 and / or 900 kg / m 3 ~1100 kg / m 3 is.

[0028] In some embodiments, the vibration frequency is less than 10 kHz, and / or less than 7 kHz, and / or less than 5 kHz, and / or less than 3 kHz, and / or less than 2 kHz, and / or less than 1 kHz, and / or less than 500 Hz.

[0029] In some embodiments, the width of the elongated member is between 1 nm and 500 nm. Such embodiments may be described as "nanoscale" or nanoscopic-scale embodiments. In some other embodiments, the width of the elongated member is between 500 nm and 500 μm. Such embodiments may be described as "microscale" or microscopic-scale embodiments. A device of appropriate dimensions, which may be a nanoscale or microscale device, may vibrate at a low frequency to advantageously measure the fluid properties of a low-viscosity fluid, such as less than 1 mPa·S, or may vibrate at a high frequency to advantageously measure the fluid properties of a low-viscosity fluid, such as less than 1 mPa·S, because at such small scales, the width of the elongated member may still be small compared to the propagation depth at such high frequencies.

[0030] In some embodiments, the viscosity of the fluid may be less than 100 Pa·s, less than 10 Pa·s, less than 1 Pa·s, less than 100 mPa·s, less than 10 mPa·s, or less than 1 mPa·s. At any such viscosity, the vibration frequency may be greater than 500 Hz, greater than 1 kHz, greater than 2 kHz, greater than 3 kHz, greater than 4 kHz, greater than 5 kHz, greater than 7 kHz, and / or greater than 10 kHz.

[0031] In some embodiments, the fluid is a Newtonian fluid. In other embodiments, the fluid is a non-Newtonian fluid, such as a viscoelastic fluid or a yield stress fluid.

[0032] In some embodiments, the oscillating transducer element comprises a shaft having a longitudinal axis, the elongate member is connected to the shaft, and the elongate member is not collinear with the longitudinal axis of the shaft. Optionally, while the oscillating transducer element is oscillating at the oscillation frequency, the fluid flow around the elongate member is laminar. Alternatively or additionally, the Reynolds number Re of the fluid flow around the elongate member is less than 1, the Reynolds number is equal to 2Rνρ / μ, where μ is the viscosity of the fluid, ρ is the density of the fluid, R is the half-width of the elongate member, ν is the maximum (oscillation) velocity of the elongate member with respect to the fluid during oscillation of the oscillating transducer, and optionally, the Reynolds number is less than 1000, or less than 300, or less than 100, or less than 30, or less than 10, or less than 3, or less than 1, or less than 0.9, or less than 0.8, or less than 0.75, or less than 0.7, or less than 0.6, or less than 0.5, or less than 0.4, or less than 0.3, or less than 0.25, or less than 0.2, or less than 0.1. Alternatively or additionally, the elongate member may have a first end and a second end, and one or both of the first end and the second end are separated from the longitudinal axis of the shaft by an offset distance greater than the half-width of the elongate member, and optionally, the offset distance is greater than a multiple of the width, and the multiple is 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 30, or 50. Alternatively or additionally, the oscillating transducer element comprises a plurality of elongate members connected to the shaft, each elongate member is not collinear with the axis of the shaft, each elongate member has a half-width less than the propagation depth of the shear wave of the fluid at the oscillation frequency, and optionally, the half-width of the first elongate member among the plurality of elongate members is different from the half-width of the second elongate member among the plurality of elongate members, and optionally, two, three, four, five, or more of the plurality of elongate members may have uniquely different half-widths. Alternatively or additionally, the elongate member may comprise a first end and a second end, the elongate member is connected to the shaft at the first end, and optionally, is also connected to the shaft at the second end. Alternatively or additionally, the shaft may comprise a bobbin, and the elongate member may be connected to the shaft at the bobbin.

[0033] In some embodiments, the step of vibrating the vibration transducer element includes vibrating the vibration transducer element using a vibratory rotational motion. Optionally, the elongated member may be linear, and the step of vibrating the transducer element may include vibrating the elongated member using a vibratory rotational motion about an axis along the length of the elongated member.

[0034] In some embodiments, the step of vibrating the vibration transducer may include vibrating the vibration transducer using a vibratory linear motion or a curvilinear motion. Optionally, if the vibration transducer comprises a shaft having a longitudinal axis and the elongated member is connected to the shaft but not in the same straight line as the longitudinal axis of the shaft, the step of vibrating the vibration transducer using a vibratory linear motion or a curvilinear motion may include vibrating the shaft using a vibratory rotational motion, a linear motion, or a curvilinear motion and vibrating the elongated member using a vibratory linear motion or a curvilinear motion.

[0035] According to a further aspect, a method of determining a property of a fluid is provided, the method comprising vibrating a vibration transducer element within a fluid at a vibration frequency, first at a first amplitude of vibration and then at a second amplitude of vibration, the vibration transducer element comprising an elongated member in contact with the fluid characterized by a width, a half-width equal to half of the width, and a length longer than the width, determining a first quantity indicative of a degree of attenuation based on the vibration of the vibration transducer element within the fluid at the first amplitude, determining a second quantity indicative of a degree of attenuation based on the vibration of the vibration transducer element within the fluid at the second amplitude, and determining a property of the fluid based on a difference between the first quantity and the second quantity.

[0036] In some embodiments, the step of determining the properties of the fluid includes determining the bipolarity of the wave field around the vibration transducer at the vibration frequency based on the difference between the first quantity and the second quantity. Optionally, the method may include determining, based on the determined bipolarity, the extent to which the half-width of the elongated member is smaller than the propagation depth of the shear wave of the fluid at the vibration frequency, and / or determining whether the half-width of the elongated member is smaller than the propagation depth of the shear wave of the fluid at the vibration frequency or smaller than some predetermined fraction of the propagation depth, such as less than 50% of the propagation depth.

[0037] In some embodiments, the quantity indicating the bipolarity of the wave field around the vibration transducer at the vibration frequency is not explicitly determined, and the difference between the first quantity and the second quantity indicating the degree of attenuation may be used to determine whether the half-width of the elongated member is smaller than the propagation depth of the shear wave of the fluid at the vibration frequency (or some predetermined fraction of the propagation depth, such as less than 50% of the propagation depth) and / or the extent to which the half-width of the elongated member is smaller than the propagation depth of the shear wave of the fluid at the vibration frequency.

[0038] In some embodiments, the step of determining the properties of the fluid includes determining the Reynolds number of the fluid based on the difference between the first quantity and the second quantity.

[0039] In some embodiments, the step of determining the properties of the fluid includes determining the velocity of the vibration with respect to the fluid, the viscosity of the fluid, or the density of the fluid based on the difference between the first quantity and the second quantity.

[0040] In some embodiments, the step of determining the first quantity and the second quantity indicating the degree of attenuation includes determining the first Q factor and the second Q factor. In other embodiments, the step of determining the first quantity and the second quantity indicating the degree of attenuation includes determining the first loss factor and the second loss factor, where the loss factor is the reciprocal of the Q factor.

[0041] In some embodiments, the determined property of the fluid is a property of the fluid flow due to the vibration of a vibration transducer element within the fluid at the vibration frequency of one or both of the first and second amplitudes.

[0042] In some embodiments, the change in the Reynolds number may be considered to be proportional to the ratio of the change in the Q factor and the change in the amplitude of the vibration. If the ratio is zero or negligibly small, the Reynolds number is low and the oscillatory flow may be presumed to be laminar. If the ratio is non - zero or greater than a threshold value, the fluid flow may not be fully laminar and the Reynolds number may be increasing. The degree of increase in the Reynolds number may depend on the value of the ratio.

[0043] In some embodiments, the method further includes performing any of the methods described above to determine a physical property of the fluid. For example, performing a plurality of vibration tests at different amplitudes may indicate whether quadratic or geometric damping is present and thus whether geometric damping is considered in determining the physical properties of the fluid. In quadratic damping, the damping force varies quadratically in proportion to the square of the velocity. As will be explained in more detail later, in geometric damping, the damping force varies linearly in proportion to the velocity.

[0044] According to a further aspect, there is provided a device comprising a shaft configured to vibrate at a vibration frequency, the shaft having a longitudinal axis, and an elongate member connected to the shaft but not on the same straight line as the longitudinal axis of the shaft, the elongate member being characterized by a width, a half - width equal to half of the width, and a length longer than the width. The device may be configured to vibrate the shaft within a fluid such as a liquid. This fluid may be a Newtonian fluid or a non - Newtonian fluid.

[0045] In some embodiments, at least a portion of the elongated member is offset from the longitudinal axis by an offset distance greater than the half-width of the elongated member. Optionally, the offset distance is greater than a multiple of the half-width of the elongated member, and the multiple is 2, 3, 4, 5, 10, 15, 20, 30, or 50. At least a portion of the elongated member offset by such an offset distance from the longitudinal axis may be a portion along the longitudinal axis along the length of the elongated member extending through the center of the elongated member.

[0046] In some embodiments, the elongated member has a first end and a second end, and one or both of the first end and the second end are separated from the longitudinal axis of the shaft by an offset distance greater than the half-width. Optionally, the offset distance is greater than a multiple of the half-width of the elongated member, and the multiple is 2, 3, 4, 5, 10, 15, 20, 30, or 50.

[0047] In some embodiments, the elongated member has a substantially or completely circular cross-section along 50%, 70%, 90%, or 100% of the length of the elongated member. Optionally, the elongated member has a circularity in the range of 0.75 to 1, optionally in the range of 0.8 to 1, optionally in the range of 0.85 to 1, optionally in the range of 0.9 to 1, optionally in the range of 0.95 to 1, optionally in the range of 0.98 to 1, optionally in the range of 0.99 to 1 along 50%, 70%, 90%, or 100% of the length of the elongated member, and the circularity of the cross-sectional shape is 4πA / p 2 is calculated by this formula, where A in this formula is the convex area of the cross-sectional shape and p is the convex perimeter length of the cross-sectional shape.

[0048] In some embodiments, the half-width of the elongated member is calculated at a point along the length of the elongated member based on the convex perimeter or convex area of the cross-section of the elongated member at that point along the length of the elongated member. Optionally, the half-width is calculated by the formula p / 2π based on the convex perimeter of the cross-sectional shape. Alternatively, the half-width may be calculated based on the convex area of the cross-sectional shape by the formula √(A / π). When the elongated member has a circular cross-section, both of these formulas yield the radius of the circle, so the half-width of the circular cross-section is the radius of the circle.

[0049] In some embodiments, the elongated member has a constant cross-section along more than 50%, more than 60%, more than 70%, more than 80%, more than 90%, or 100% of the length of the elongated member.

[0050] In some embodiments, the elongated member has a constant cross-section only along less than 50%, less than 40%, less than 30%, less than 20%, less than 10% of the length of the elongated member, or the cross-section varies continuously along the length of the elongated member.

[0051] In some embodiments, the cross-section increases or decreases monotonically along the length of the elongated member.

[0052] In some embodiments, the elongated member is straight.

[0053] In some embodiments, the elongated member is axisymmetric along the length of the elongated member.

[0054] In some embodiments, the elongated member is not straight. For example, the elongated member may comprise a closed loop.

[0055] In some embodiments, the elongated member comprises one of a cylinder, a cone, a frustum of a cone, an anchor ring, and an arc portion of an anchor ring.

[0056] 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.

[0057] In some embodiments, the half-width of the elongated member that is less than the propagation depth is the average half-width along the length of the elongated member. Optionally, the average half-width is calculated as the arithmetic mean of the half-widths along the length of the elongated member, or is the average half-width calculated by dividing twice the volume of the elongated member by the surface area of the elongated member.

[0058] 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.

[0059] In some embodiments, the length of the elongated member is greater than a multiple of the half-width of the elongated member, and the multiple is one of 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.

[0060] In some embodiments, the device comprises a plurality of elongated members connected to a shaft, and each elongated member has its respective width, half-width, and length. Optionally, the half-width of the first elongated member among the plurality of elongated members is different from the half-width of the second elongated member among the plurality of elongated members, and optionally, two, three, four, five, or more of the elongated members among the plurality of elongated members may have uniquely different half-widths.

[0061] In some embodiments, the device is configured to torsionally vibrate the shaft about its longitudinal axis and / or vibrate longitudinally along the longitudinal axis of the shaft and / or transversely with respect to the longitudinal axis of the shaft.

[0062] In some embodiments, the device comprises a bob. Optionally, at least one elongated member is connected to the shaft at the bob.

[0063] In some embodiments, the device is a device for determining the physical properties of a fluid. The device is configured to vibrate a shaft within the fluid while an elongated member is in contact with the fluid. The device measures the vibration of the shaft within the fluid and is configured to determine the physical properties of the fluid based on the measurement of the vibration. The determined physical property may be the viscosity of the fluid, or the density of the fluid, or the storage modulus of the fluid, or the loss modulus of the fluid, or the loss tangent of the fluid. Such a device may be used to implement any of the methods described above.

[0064] According to a further aspect, a system is provided that includes a fluid and any one of the devices described above. At least a portion of the elongated member and the shaft are in contact with the fluid. The shaft is configured to vibrate at a vibration frequency. The half-width of the elongated member is less than the propagation depth of the shear wave of the fluid at the vibration frequency. In some embodiments, the system may include a fluid confined within a container. In some embodiments, the fluid may flow through a system such as an open-loop or closed-loop conduit system, and the fluid flows through the elongated member and the shaft. In some embodiments, the device may be a damper, and the elongated member is configured to damp vibrations such as torsional vibrations of the shaft at the vibration frequency. In this way, the shaft may be coupled or integrated with a vibration source in a machine or device, and such vibrations can be damped.

[0065] According to a further aspect, a method for controlling the damping behavior of a shaft configured to vibrate in a fluid, the method comprising the steps of: providing a shaft configured to vibrate at a vibration frequency, the shaft having a longitudinal axis; providing an elongate member connected to the shaft but not on the same straight line as the longitudinal axis of the shaft, the elongate member being characterized by a width, a half-width equal to half of the width, and a length longer than the width, at least a portion of the elongate member and the shaft being configured to vibrate in the fluid at the vibration frequency, the half-width of the elongate member being less than the propagation depth of a shear wave in the fluid at the vibration frequency. The propagation depth may be the distance at which the amplitude of a shear wave propagating in the fluid at the vibration frequency decreases by a factor of 1 / e, where e is the base of the natural logarithm, and may be the viscoelastic propagation depth described herein.

[0066] In some embodiments, the elongate member has a first end and a second end, and one or both of the first end and the second end are spaced from the longitudinal axis of the shaft by an offset distance greater than the half-width of the elongate member.

[0067] In some embodiments, the elongate member is provided such that the flow of fluid around the elongate member is laminar while the shaft is vibrating at the vibration frequency.

[0068] In some embodiments, the Reynolds number Re of the fluid flow around the elongate member is less than 1000, or less than 300, or less than 100, or less than 30, or less than 10, more preferably less than 3, or less than 1, or less than 0.9, or less than 0.8, or less than 0.75, or less than 0.7, or less than 0.6, or less than 0.5, or less than 0.4, or less than 0.3, or less than 0.25, or less than 0.2, or less than 0.1 while the shaft is vibrating in the fluid at the vibration frequency, and the Reynolds number is expressed as follows:

Equation

[0069] In some embodiments, the shaft is provided with a plurality of elongated members connected to the shaft. Each elongated member is not on the same straight line as the longitudinal axis of the shaft, and each elongated member has a half-width smaller than the propagation depth of the shear wave of the fluid at the vibration frequency. Optionally, the half-width of the first elongated member among the plurality of elongated members may be different from the half-width of the second elongated member among the plurality of elongated members.

[0070] In some embodiments, one or more of the elongated members provided on the shaft are all linear, all non-linear, or a mixture of linear and non-linear elongated members.

[0071] According to a further aspect, a device is provided that includes means for performing any of the above-described methods. The device may include means for performing each step of the method for each step of the method. The means for performing any step of the method may be the means for performing a plurality of steps of the method.

[0072] According to a further aspect, a computer-readable medium is provided that stores instructions that, when executed by a processor of a vibration transducer including an elongated member such as the elongated member according to the techniques described herein, cause the device to perform any of the above-described methods.

Brief Description of the Drawings

[0073] The present invention will be described in more detail by way of example only with reference to the accompanying drawings.

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[0074] FIG. 1 is a diagram showing the propagation of shear waves in a viscous fluid from a flat plane vibrating at a surface velocity V 0 The depth at which the amplitude or velocity (shear velocity) of the wave decreases to 1 / e of the value at the surface due to viscous attenuation is the propagation depth δ μ and is represented by the following equation.

Equation

[0075] Due to the decrease in the amplitude of the wave caused by viscosity, a shear stress τ sμ is generated on the vibration surface, which is the product of the rate of change of the surface velocity (i.e., the shear velocity

Equation

Equation

[0076] The shear velocity

Equation

Equation

[0077] The shear rate due to viscous damping is proportional to the square root of the frequency, proportional to the square root of the density, and proportional to the square root of the reciprocal of the viscosity.

[0078] Therefore, the shear stress on the surface (the product of the surface viscosity and the shear rate) is non-linear.

Number

[0079] In addition to the viscous effect, the fluid may exhibit elastic behavior, which depends on the storage modulus G'. The presence of G' reduces the loss tangent tanΔ, which is defined by the following equation.

Number

[0080] For a purely viscous fluid, tanΔ = ∞. As the elastic behavior increases, the loss of the fluid decreases, allowing the wave to propagate further into the fluid. Considering elasticity, the propagation depth is represented by the following equation.

Number

[0081] For a purely viscous fluid, Δ is equal to 90°, so

Number

[0082] The shear rate on the vibration plane due to both viscosity and elasticity is represented by the following equation.

Equation

[0083] The shear stress on the vibration plane due to both viscosity and elasticity is represented by the following equation.

Equation

[0084] The shear stress is a non - linear function of the fluid viscosity, fluid density, frequency, and storage modulus (due to the loss tangent). As the elastic modulus G’ increases, tanΔ decreases, Δ decreases from its maximum value of π / 2, and both sinΔ and sinΔ / 2 decrease. Therefore, the attenuated shear stress decreases as the elastic modulus G’ increases. This explains why viscoelastic fluids exhibit reduced attenuation compared to Newtonian fluids with a “similar” viscosity.

[0085] Figure 2 shows a shear wave propagating radially within a viscoelastic fluid from a curved surface with radius R. The viscoelastic fluid has relatively little loss over short distances, but Figure 2 shows that as the radial distance increases, the peak position energy of each wave needs to be maintained, and since the energy spreads over the increasing circumference (2πr), the amplitude decreases. A line 10 of constant position energy is shown in Figure 2. As the energy is dispersed over the increasing circumference, the energy per unit volume decreases, and thus the peak height also becomes smaller. This attenuation of the amplitude due to geometric considerations appears to be similar to attenuation, although it does not itself dissipate energy.

[0086] The change in height causes a decrease in velocity proportional to 1 / r, and this change in velocity causes a shear rate

Number

[0087] Instead of the plane vibrating as in Figure 1, when a cylindrical surface of radius R vibrates, an equation for the velocity of the radial shear wave at a position r from the central axis of the cylinder may be obtained, and it may be differentiated with respect to r to obtain the radial shear rate.

Number

[0088] Next, the shear stress r = R on the cylindrical surface is expressed by the following equation.

Equation

[0089] The 1 / R term is the in-phase shear gradient. The shear rate of this component is in phase with the velocity, regardless of the degree of viscoelasticity. 1 / δ μG’ The term is an out-of-phase shear gradient. The shear rate of this component is phase-shifted by φ, which depends on the degree of viscoelasticity. The phase adjustment angle represents the angle between the shear stress and the velocity. The shear stress in phase with the velocity dissipates energy.

[0090] When the value of R is much smaller than δ μG’ the in-phase part becomes dominant, and the shear rate decreases its dependence on viscosity, density, frequency, and the storage modulus (through tanΔ / 2 which is a function of G’’), or becomes even more independent. 1 / δ μG’ When 1 / δ is negligible compared to 1 / R, the shear stress on the cylindrical surface is expressed by the following equation.

Equation

[0091] When the value of R is much larger than δ μG’ the out-of-phase part becomes dominant, and the shear rate increasingly depends on the non-linear function of viscosity, density, frequency, and the storage modulus. When 1 / R is negligible compared to 1 / δ μG’ the shear stress on the cylindrical surface is expressed by the following equation.

Equation

[0092] The critical value of R is at R onset = δ μG’ where the shear stress due to the 1 / R term is equal to that due to 1 / δ μG’This is to represent the intersection of the value of R that is greater than the shear stress according to the item. According to the techniques described in this specification, this may be considered the beginning of geometric attenuation.

[0093] R < δ μG’ In the case of, the dependence of the shear stress on the non-linear function of viscosity, density, frequency, and storage modulus further decreases. When the radius of the cylinder is less than half of the viscoelastic propagation depth, it may be considered that geometric attenuation begins to dominate, that is, R < R onset / 2. In other words, R geo = R onset / 2, and in this formula, R geo is understood to be the radius of the cylinder that defines the region where geometric attenuation is assumed to be dominant and can define the attenuation behavior.

[0094] In the measurement of the physical properties of the fluid, parameters such as the fluid attenuation coefficient C F , the stiffness load coefficient K F , and the inertia load coefficient J F can be selected to improve the linearity of the fluid load coefficient. When R = δ μG’ , the formula for the viscosity of the fluid at the beginning of geometric attenuation is expressed as follows.

Equation

[0095] For example, a cylindrical element with a radius R of 2 mm is vibrating in a purely viscous fluid (sin(Δ / 2)√(2sinΔ) = 1) at a frequency of 5 kHz, and when the fluid has a density ρ of 1000 kg / m 3 , with an appropriate selection of the viscosity of the fluid in Pa·S units, R = R onset is expressed as follows. μ’ onset = 2 2 ·π·5000·1000 = 62

[0096] For geometric attenuation to begin to dominate (i.e., R geo =R onset / 2), the required viscosity becomes four times higher, i.e., as follows. μ’ geo =(2·2) 2 ·π·5000·1000 = 250

[0097] Similarly, the radius of the vibrating element and / or the vibration frequency can be selected to utilize geometric attenuation for a given operating range of viscosity and density, depending on the operating requirements.

[0098] Figure 4 shows a graph of the attenuation coefficient of a heavy mineral oil measured at a frequency of 5 kHz using a vibrating cylinder with a radius of 2 mm, where the density ρ of the fluid is 1000 kg / m 3 and the attenuation coefficient has been measured over a range of viscosity values (obtained by heating the heavy mineral oil). The measured attenuation coefficient is shown by the solid line indicated by "A" in Figure 4. The graph also shows a plot of the calculated attenuation coefficient when the attenuation is described by non - geometric attenuation, i.e., when 1 / R is negligible compared to 1 / δ μG’ This line is indicated by "B" in Figure 4. The graph also shows a plot of the calculated attenuation coefficient when the attenuation is described by geometric attenuation, i.e., when 1 / δ μG’ is negligible compared to 1 / R. This line is indicated by "C" in Figure 4.

[0099] Figure 4 shows that while the viscosity is relatively low, i.e., less than about 60 Pa·S, the radius of the vibrating element is larger than the viscous penetration depth and the shear rate is a non - linear function of the viscosity. When the viscosity exceeds about 60 Pa·S, it can be seen that the attenuation of the shear wave begins to be explained by geometric attenuation and the attenuation coefficient becomes increasingly linear.

[0100] Figure 4 shows three regions. The first region, indicated by reference numeral 70, is the non - linear region, where μ onsetcovers viscosity values less than (62 Pa·S determined above). The second region indicated by reference numeral 80 is a linear transition region, μ onset and μ geo covers viscosity values between (250 Pa·S determined above). The third region indicated by reference numeral 90 is a complete linear region, covering viscosity values exceeding μ geo . When operating in the second region 80, the linearity is improved compared to when operating in the first region 70. When operating in the third region 90, the linearity is improved compared to when operating in the second region 80.

[0101] For a vibrating cylindrical tube with a radius wide enough that geometric attenuation can be neglected, the fluid damping coefficient C F , the stiffness load coefficient K F , and the inertia load coefficient J F are expressed by the following equations.

Equation

[0102] In these equations, since these terms (or quantities that are functions of these terms, such as Δ and the dependence of Δ on G’) are present within the parentheses, each of the coefficients has a non - linear dependence on μ’, G’, or ρ.

[0103] When the radius of the vibrating cylindrical tube is small enough and non - geometric attenuation can be neglected, the equations for C F , K F , and J F are expressed as follows.

Equation

[0104] From these equations, when non - geometric attenuation can be neglected, the fluid damping coefficient C F , the stiffness load coefficient K F , and the inertia load coefficient J FIt can be seen that it no longer has a non - linear dependence on μ’, G’, or ρ. C F , K F , and J F Each of the quantities is directly proportional to μ’, G’, and ρ respectively, and the proportionality constants depend only on the geometric parameters.

[0105] It may be advantageous to improve the linearity of these fluid loading coefficients. The mechanical system may have damping C, stiffness K, and inertia J. These determine the vibration frequency ω and Q - factor of the system through the following equations.

Equation

[0106] When the system is vibrating in air or in a vacuum, these mechanical coefficients can be denoted as C 0 , K 0 , and J 0 When the system is vibrating in a fluid, due to the physical properties of the fluid, these coefficients are “loaded” by the amounts C F , K F , and J F respectively.

[0107] The overall values of the damping, stiffness, and inertia coefficients of the system considering fluid loading may be expressed as follows. C = C 0 + C F (Equation 24) K = K 0 + K F (Equation 25) J = J 0 + J F (Equation 26)

[0108] The overall values of C, K, and J are related to the above - mentioned equations of the frequency and Q - factor that can be easily measured. The physical properties of the fluid may be determined based on the contributions of C F , K F , and J F to the vibration behavior. As will be described below, the techniques of the present disclosure are for CF , K F , and J F may provide a simple linear relationship with physical properties of interest such as density ρ, viscosity μ', and storage modulus G'.

[0109] In these equations, A is the fluid contact surface area of the cylindrical element, and R G is the "radius of gyration" of the element and is equal to the radius R of the cylindrical element when the cylindrical element twists and vibrates about its axis.

[0110] When considering the influence of the moment of inertia on the rotational motion of an object, the radius of gyration is the radial distance to a point that has the same moment of inertia as the actual mass distribution of the object if all of the object's mass were concentrated there. The term "radius of gyration" in the present disclosure generalizes this concept to account for torsional coefficients other than the moment of inertia.

[0111] For the damping coefficient C F , the radius of gyration represents the radial distance to a point that has the same damping effect as the actual damping effect of the object if the damping were concentrated at that point.

[0112] For the stiffness load coefficient K F , the radius of gyration represents the radial distance to a point that has the same stiffness load effect as the actual stiffness load effect of the object if the stiffness load were concentrated at that point.

[0113] For the inertia load coefficient K F , the radius of gyration represents the radial distance to a point that has the same inertia load effect as the actual inertia load effect of the object if the inertia load were concentrated at that point.

[0114] Therefore, the radius of rotation, more generally defined in the present disclosure, represents a convenient measure of the radial influence of these load factors. The radius of rotation is defined by the specific shape of the cylindrical element, but generally has upper and lower limits defined by the maximum and minimum radius ranges of the cylindrical element from the axis of rotation. When the cylindrical element torsional oscillates about its axis, all surface loads occur on the cylindrical surface and are all at a distance R from the axis, and thus is assumed to be equal to the radius R of the cylindrical element.

[0115] Figure 3 shows a first cylinder 20 of radius R torsional rotating about a longitudinal axis 25 passing through the center of the cylinder. The cylinder has a length l that rotates about the axis, and since the length of the cylinder is long enough, the area of the end (πR 2 ) is small compared to the area of the curved side (2πRl), R << δ μG’ , and when R = R G , the damping coefficient C F , the stiffness load coefficient K F , and the inertia load coefficient J F may be expressed as follows. C F =A R μ’=(2πR 2 l)μ’ (Equation 27) K F =A R G’=(2πR 2 l)G’ (Equation 28) J F =A R 3 ρ=(2πR 4 l)ρ (Equation 29)

[0116] Geometric attenuation due to the propagation of radiated waves provides an advantage because it depends on geometric parameters rather than fluid properties, but the conditions for geometric attenuation recommend the use of cylindrical elements with small radii, resulting in a small active surface area. The smaller R 2· terms in the damping, stiffness, and inertia load coefficients means that the damping, elastic, or inertia load coefficients due to torsional vibration are small even when the viscosity is high.

[0117] FIG. 3 also shows a second cylinder 30 having the same size as the first cylinder 20, and the second cylinder 30 is offset vertically by an offset radius R greater than R from the axis of the axis 25 of the first cylinder 20. 0 The second cylinder 30 also torsional vibrates about the axis 25 of the first cylinder 20. As a result, the radius of rotation R G is changed from R (the distance from the cylindrical surface to the axis 25) to R 0 (the radius offset of the entire cylinder).

[0118] Damping coefficient C F and stiffness load coefficient K F and inertia load coefficient J F For the above - shown equations, when geometric damping holds (that is, when non - geometric damping can be ignored), the equations may be expressed as follows.

Equation

[0119] R 0 When R is greater than R, by offsetting the vibration of the cylindrical element from the axis, the load coefficient is squared by the ratio of R 0 to R, that is, (R 0 / R) 2 and amplified. In the case of J F , the load coefficient is (R 0 / R) 4 , that is, amplified by the fourth power of the ratio of R 0 to R.

[0120] However, these equations hold only under the geometric damping of the cylindrical element. By offsetting the cylindrical element, pure torsional vibration no longer occurs, but instead vibrates horizontally at the offset distance. These equations for the load coefficients are not automatically applicable because the cylindrical element may form a bipolar wave field rather than a monopole wave field under horizontal vibration.

[0121] Figure 5 shows a cylindrical element in which a bipolar wave field occurs under lateral vibration. In the case of a bipolar wave field, there is a 180° phase difference between the wave fields on both sides of the cylindrical element. There is a problem in the formation of a bipolar wave field because the resulting wave is a pressure wave (P) rather than a shear wave (S). The hydrodynamics of a pressure wave is different from that of a shear wave, and the relationships previously defined for shear waves are no longer applicable.

[0122] For example, the attenuation coefficient is defined differently for shear waves and pressure waves. In the case of shear waves, it is relatively clearly defined by the shear velocity and the stress generated by the shear velocity, resulting in a controllable attenuated wave. In contrast, pressure waves follow a phenomenon known as "quadratic attenuation", and the attenuation force is proportional to the square of the velocity. As a result, the attenuation coefficient is as follows. C quadratic =b·ν (Equation 33) In the above equation, b is a constant and ν is the velocity. In other words, the attenuation coefficient changes unhelpfully according to the vibration velocity.

[0123] However, if the Reynolds number is kept low, a monopole wave field may be maintained. The Reynolds number represents the ratio between the inertial force and the viscous force. As the Reynolds number decreases, the viscous force becomes larger relative to the inertial force.

[0124] Figure 6 shows the laminar flow around a cylinder vibrating in the left - right direction perpendicular to the axis of the cylinder. In laminar flow, the forces on both sides of the cylinder become shear, and thus shear waves propagate as a result of the lateral vibration. Without intending to be bound by theory, it is considered that due to laminar flow, the inertial forces become sufficiently lower than the viscous forces, and the wave field is mainly or at least partially defined by the shear waves generated from the upper and lower parts of the cylinder cross - section, that is, perpendicular to the axis and the direction of vibration. As a result, as the Reynolds number decreases, the degree to which the wave field has a dipole shape decreases, and the degree to which the wave field has a monopole shape increases. At low Reynolds numbers, a partial shear wave field in - phase across the propagation space is restored. The advantage of geometric attenuation is retained, but there is also the advantage that the load coefficient gain increases by offsetting the elements from the axis.

[0125] Cylindrical elements offset from the axis are advantageous because a relatively low Reynolds number can be easily achieved at a short length scale, enabling a relatively high amplification factor to be achieved with little increase in size and weight. In some implementations of the techniques of the present disclosure, a fluid load coefficient equivalent to that of a much larger and heavier vibrating element may be achieved.

[0126] Regardless of the physical properties, it is further recognized that relatively low Reynolds numbers can be easily achieved in micro - scale and nano - scale devices for almost all fluids of interest. The sub - micron needle structure of the vibrating substrate may form elements offset in the same radial direction as described above and achieve the same advantages of geometric attenuation. In some implementations, it may be characterized by a plurality of cylindrical elements or elements shaped like cylinders, such as pins and spikes formed by a micro - manufacturing process or a nano - manufacturing process, which may also make it possible to achieve a high fluid load coefficient on a small surface.

[0127] It has been further recognized that when the Reynolds number is low, the wave field may be only partially defined by shear waves, and therefore the equations for the load coefficients under geometric attenuation conditions may not be the same as the above equations, but may be proportional to those equations, and the proportionality constant may vary depending on the degree to which the wave field is defined by shear waves. In the following equations, a proportionality constant h is introduced. When the wave field is completely defined by shear waves, the value of h has a value of 1. When the wave field is 50% defined by shear waves, the value of h has a value of 0.5, which is a reasonable assumption in practice. C F =h(2πlR 0 2 )μ’ (Equation 34) K F =h(2πlR 0 2 )G’ (Equation 35) J F =h(2πlR 0 4 )ρ (Equation 36)

[0128] Assuming h is 0.5, the above equations are simplified as follows. C F =h(πlR 0 2 )μ’ (Equation 37) K F =h(πlR 0 2 )G’ (Equation 38) J F =h(πlR 0 4 )ρ (Equation 39)

[0129] Furthermore, it is recognized that the techniques of the present disclosure may be particularly applicable in the measurement of the properties of yield stress fluids in accordance with the techniques described in WO 2018 / 197902 A1 of Hydramotion Ltd ("The Measurement Of Properties Of Flowing yield stress fluids") and WO 2018 / 197900 A1 of Hydramotion Ltd ("The Measurement Of Properties Of Vibrated Yield Stress Fluids"), the entire contents of both documents being incorporated herein by reference.

[0130] In the context of the present disclosure, the meaning of a "low" Reynolds number is that the Reynolds number is low enough that laminar flow is obtained, the flow due to vibration may be characterized to some extent by a shear wave field, and the advantage of geometric attenuation is provided at least to some extent. The transition from laminar flow to turbulent flow occurs over a range of Reynolds numbers, and it is recognized that the exact range at which the transition from laminar flow to turbulent flow occurs depends on the shape. When the Reynolds number is low, there is a higher likelihood of flow behavior that results in a partial shear wave field than when the Reynolds number is high. Without intending to be bound by theory, it is believed that the extent to which the shear wave field develops, and thus the extent to which some of the advantages of the techniques of the present disclosure are obtained, depends on the Reynolds number. For example, when the Reynolds number is 1000, a flow such as some laminar flow may occur and a shear wave field of some extent may occur. When the Reynolds number is 100, the flow such as laminar flow becomes larger and the shear wave field also becomes larger. When the Reynolds number is 10, the flow such as laminar flow becomes larger and the shear wave field also becomes larger. When the Reynolds number is 1, the flow such as laminar flow becomes larger and the shear wave field also becomes larger. Generally, a lower Reynolds number may be desirable, but the reader will recognize that in order to achieve the lowest possible Reynolds number, it is necessary to balance other technical considerations.

[0131] In these disclosures, an explanation of the viscoplastic boundary region of a yield stress fluid is presented together with a technique for determining the physical properties of a fluid by transmitting shear waves with different propagation depths, such as those extending only into the viscoplastic boundary region and those extending through the liquid boundary region. According to the technique of the present disclosure, if the geometric attenuation condition is satisfied, the propagation depth of the wave is determined by the shape of the cylindrical element, specifically the radius of the cylindrical element. By using a plurality of cylindrical elements including at least two cylindrical elements with different radii, the cylindrical elements generate waves that propagate a known distance into the yield stress fluid, enabling a simple design and specification of a measurement system for probing the liquid boundary layer and beyond of a yield stress fluid such as a flowing yield stress fluid.

[0132] Such a technique may comprise a method for estimating the yield stress of a flowing yield stress fluid using one or more vibration transducers having a vibration surface in contact with the yield stress fluid, the method comprising vibrating the vibration surface of the vibration transducer to transmit a wave to the viscoplastic boundary layer of the flowing yield stress fluid from the vibration surface, using the vibration of the vibration transducer to make one or more measurements of the degree of attenuation of the vibration, and estimating the yield stress of the flowing yield stress fluid based on one or more measured values of the degree of attenuation of the vibration, wherein the one or more vibration transducers include the plurality of cylindrical elements described herein and are optionally offset from the axis of the vibration transducer, whether on a single vibration transducer or distributed among a plurality of vibration transducers, and the criteria for geometric attenuation are satisfied.

[0133] For example, a first measurement of the degree of vibration attenuation may be performed by transmitting a wave that propagates a first distance to the viscoplastic boundary layer of the flowing yield stress fluid using the vibration surface of a vibration transducer that vibrates at a first vibration frequency. A second measurement of the degree of vibration attenuation may be performed by transmitting a wave that propagates a second distance lower than the first distance to the viscoplastic boundary layer of the flowing yield stress fluid using the vibration surface of a vibration transducer that vibrates at a second vibration frequency different from the first frequency. Based on a linear combination of the first measurement value and the second measurement value of the degree of vibration attenuation, the yield stress of the flowing yield stress fluid may be estimated. The method may further include a step of performing a correction on one or both of the first measurement value and the second measurement value of the degree of vibration attenuation based on the first vibration frequency, the second vibration frequency, and the power law index of the yield stress fluid. The estimated value of the yield stress of the flowing yield stress fluid is [Number] proportional to, where in the above formula, V1 is the first measurement value of the degree of vibration attenuation, V2 is the second measurement value of the degree of vibration attenuation, ω1 is the angular frequency of the first vibration frequency of the vibration, ω2 is the angular frequency of the second vibration frequency of the vibration, and n is the power law index. The method may further include: i) transmitting a wave that propagates a third distance shorter than the first distance to the viscoplastic boundary layer of the flowing yield stress fluid using the vibration surface of a vibration transducer that vibrates at a third vibration frequency different from the first and second vibration frequencies of the vibration, and performing a third measurement of the degree of vibration attenuation; and ii) estimating the power law index of the flowing yield stress fluid based on the third measurement value of the degree of vibration attenuation and the third vibration frequency, and further based on one of the first measurement value and the first vibration frequency of the degree of vibration attenuation, and the second measurement value and the second vibration frequency of the degree of vibration attenuation. Therefore, the generation of shear waves with a known propagation depth according to the techniques of the present disclosure is easily and advantageously applicable.

[0134] The techniques of the present disclosure also enable determination of whether a cylindrical element radiates waves in a pattern like a monopole or in a pattern like a dipole, and making inferences based on such determination.

[0135] The attenuation of a dipole does not follow shear wave theory. Since a dipole generates P waves, the magnitude of the attenuation force is aν 2 represented by, where a is a constant and ν is the velocity of the fluid. In other words, the attenuation force is proportional to the square of the velocity. As a result, the attenuation coefficient is represented by (Equation 33). In other words, the attenuation coefficient varies with velocity.

[0136] However, the geometric attenuation described herein does not depend on the vibration velocity, as described above in connection with, for example, (Equation 30), (Equation 31), and (Equation 32).

[0137] The vibration velocity is a function of the vibration amplitude, and the vibration velocity changes as the vibration amplitude changes. By changing the vibration amplitude and measuring the vibration of the fluid at different vibration amplitudes (i.e., without changing the frequency), the degree of dipole behavior, i.e., the "bipolarity," of the wave field around the cylindrical element can be detected. Bipolarity can be considered as a quantity indicating the extent to which the wave field takes the shape of a dipole rather than a monopole. In particular, since the Q factor is inversely proportional to the attenuation coefficient, a change in the Q factor indicates a change in the attenuation coefficient.

[0138] Therefore, the change in the Q factor is proportional to the degree of bipolarity, i.e.,

Number

[0139] Furthermore, bipolarity is a function of the Reynolds number and is represented by Re = 2Rνρ / μ'. Therefore,

Number

[0140] Therefore, the change in Q by modulating the speed (and as a result, by modulating the amplitude of the vibration) can be used to indicate a change in the Reynolds number, which is useful in determining whether there is a behavior like that of a monopole of geometric attenuation, and also serves as an alternative means for determining parameters of the Reynolds number such as speed, viscosity, or density.

[0141] For the oscillating element in the fluid to change from a state where the generated wave causes a wave field of a high dipole where the generated wave is an acoustic wave (i.e., a pressure wave) to a state where the generated wave causes a wave field of a monopole or near-monopole where the generated wave is only a shear wave or mostly a shear wave, it is necessary that the disturbed fluid around the oscillating element is laminar when the oscillating element vibrates and moves within the fluid. Therefore, the condition of laminar flow is that the Reynolds number is low in small-amplitude vibration conditions such as less than 1000, less than 100, less than 10, or less than 1, indicating that the lower the Reynolds number, the greater the degree of laminar flow.

[0142] In particular, determining parameters of the Reynolds number such as viscosity can be advantageous because it may be assumed that the length scale and density are fixed within the system. The change in the Reynolds number may be entirely or mostly determined by the ratio between speed and viscosity. When the viscosity is very high, the Reynolds number remains small even with a wide range of vibration speeds. When the viscosity is low, the change in speed modulates the Reynolds number to a higher value, the laminar state is lost, and sound waves may be generated. Since sound waves follow quadratic attenuation that changes according to the square of the speed, the change in the amplitude of the vibration changes the local speed, leading to a detectable change in attenuation. Therefore, an estimated value of the Reynolds number may be obtained from the difference in the Q factor.

[0143] In some examples according to the techniques of the present disclosure, the change in the Reynolds number may be considered to be proportional to the ratio of the change in the Q factor and the change in the amplitude of the vibration.

Number

[0144] When determining the Reynolds number or determining whether (or to what extent) there is a behavior such as that of a monopole of geometric attenuation, this technique represents determining the properties of the fluid, and the determined properties of the fluid are the properties of the fluid flow due to the oscillation of the oscillating transducer element in the fluid at one or both of the oscillation frequencies of the first amplitude and the second amplitude. Determining the velocity, viscosity, or density based on the determined Reynolds number also means determining the properties of the fluid that are the properties of the fluid flow due to the oscillation of the oscillating transducer element in the fluid at one or both of the oscillation frequencies of the first amplitude and the second amplitude.

[0145] These techniques for determining the properties of the fluid flow around the oscillating element or the properties of the fluid itself, such as viscosity, by using the change in the Q factor between oscillations of different amplitudes, may be applied to fluids with a yield stress. Since these techniques do not depend on fluids having a yield stress, they may also be applied to fluids with a zero yield stress.

[0146] Figures 7 to 31 show a vibration transducer according to the technique of the present disclosure or a part thereof, or a vibration transducer or a part thereof for use in a process according to the technique of the present disclosure. These figures show vibrations with respect to an axis in a specific direction such as torsional, lateral, or longitudinal directions, but it will be recognized that the technique of the present disclosure is not limited to a specific vibration direction. A vibration transducer having a vibration element according to the technique of the present disclosure may be configured to vibrate in a plurality of vibration directions including a combination of torsional vibration and lateral vibration, or torsional vibration and longitudinal vibration. Further, in the foregoing description, the vibration element has been treated as a cylinder. However, while this simplifies the analysis, the vibration element need not be cylindrical and need not have a perfectly circular cross-section in order to realize at least some of the advantages identified herein. Accordingly, at least a part of the vibration transducer or a part thereof is described using the more general expression "elongated member".

[0147] Figures 7 to 9 each show a vibration transducer for use in the technique of the present disclosure. In each of Figures 7 to 9, the vibration transducer has a cylindrical vibration element 110 in contact with a fluid 100. The cylindrical vibration element has a radius R about an axis 112 along the length of the cylindrical vibration element. According to the technique of the present disclosure, geometric attenuation is obtained when the radius R is smaller than the viscoelastic propagation depth of the shear wave of the fluid 100, which is a function of the angular frequency ω of the vibration and the physical properties of the fluid 100.

[0148] In Figure 7, the cylindrical vibration element 110 is configured to torsional vibrate about the axis 112 at an angular frequency ω.

[0149] In Figure 8, the cylindrical vibration element 110 is configured to vibrate longitudinally along the axis 112 at an angular frequency ω.

[0150] In Figure 9, the cylindrical vibration element 110 is configured to vibrate laterally in a direction perpendicular to the axis 112 at an angular frequency ω.

[0151] Figures 10 and 11 show a vibration transducer for use with the techniques of the present disclosure. In each of Figures 10 and 11, the vibration transducer has an elongated member that contacts a fluid, the elongated member has a circular cross-section along the length of a major axis passing through the elongated member, and the elongated member is configured to torsionally vibrate about the major axis at an angular frequency ω.

[0152] In Figure 10, at the end of the elongated member 120, the radius of the circular cross-section linearly decreases with the position along the axis 122, and one end of the elongated member 120 forms a conical shape.

[0153] In Figure 11, the radius of the circular cross-section along the elongated member 130 discontinuously decreases at a constant rate with the position along the axis 132, and the radius varies stepwise from a maximum radius R max to a minimum radius R min and the elongated member 130 has an average radius R along the length of the axis 132. ave

[0154] When a portion of the elongated member has a radius smaller than the viscoelastic propagation depth of the fluid 100, geometric attenuation occurs along at least a portion of the elongated member. According to the techniques of the present disclosure, when the average radius R of the elongated member along the length of the axis is smaller than the viscoelastic propagation depth of the shear wave of the fluid 100, a beneficial level of geometric attenuation is obtained. When the maximum radius R ave is smaller than the viscoelastic propagation depth, a higher level of geometric attenuation may be obtained. max

[0155] ​​FIG. 12 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer has an elongated member 140 that contacts a fluid 100. The elongated member 140 is not straight but instead describes a curve. An axis 142 extends longitudinally through the center of the elongated member. The axis 142 itself also describes a curve. The elongated member is configured to vibrate in a linear direction that substantially coincides with the axis 142. The elongated member 140 has a circular cross-section along the length of the elongated member 140 and has a radius R around the axis 142, despite the curvature. According to the techniques of the present disclosure, geometric attenuation is obtained when the radius R is less than the viscoelastic propagation depth of the shear wave of the fluid 100, which is a function of the angular frequency ω of the vibration and the physical properties of the fluid 100.

[0156] FIGS. 13-20 show additional vibration transducers for use with the techniques of the present disclosure, in which the elongated member is connected to a shaft having a longitudinal axis and the elongated member is offset from the longitudinal axis of the shaft.

[0157] FIG. 13 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210 and an elongated member 220 attached to the shaft. The shaft 210 is cylindrical and is configured to torsional vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at an angular frequency ω of vibration. The elongated member 220 is also cylindrical and is connected to the shaft 210 at one end of the shaft 210. The elongated member 220 has a longitudinal axis 222 that is parallel to the axis 212 of the shaft 210, and the shaft 210 vibrates about the longitudinal axis 222 but is offset by a distance R from the axis 212 of the shaft 210 0It is only offset radially. The elongated member 220 has a radius R. The shaft 210 and the elongated member 220 are in contact with the fluid 200. According to the techniques of the present disclosure, when the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is greater than the radius R of the elongated member 220 and the Reynolds number of the flow of the fluid 200 around the elongated member 220 is low, a beneficial level of geometric attenuation can be obtained. By offsetting the elongated member 220 from the axis 212 of the shaft 210, the attenuation is increased compared to the case where the axis 222 of the elongated member 220 is in line with the axis 212 of the shaft 210.

[0158] FIG. 14 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210 and an elongated member 220 attached to the shaft. The shaft 210 is cylindrical and is configured to torsional vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at an angular frequency ω of vibration. The elongated member 220 is also cylindrical and is connected to the shaft 210. In contrast to the arrangement shown in FIG. 13, the elongated member 220 of FIG. 14 is connected to the curved sidewall of the shaft 210, has a longitudinal axis 222 perpendicular to the axis 212 of the shaft 210, and the shaft 210 vibrates about the longitudinal axis 222. The elongated member 220 has a radius R. The proximal end of the elongated member 220 is offset from the axis 212 of the shaft 210 by a first offset distance R equal to the radius of the shaft 210 0,1 only. The distal end of the elongated member 220 is offset from the axis 212 of the shaft 210 by a second offset distance R equal to the sum of the radius of the shaft 210 and the length of the elongated member 220 0,2It is only offset. The elongated member 220 is offset from the axis 212 of the shaft 210 over its entire length. The shaft 210 and the elongated member 220 are in contact with the fluid 200. According to the techniques of the present disclosure, when the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is greater than the radius R of the elongated member 220 and the Reynolds number of the flow of the fluid 200 around the elongated member 220 is low, a beneficial level of geometric attenuation can be obtained. By offsetting the elongated member 220 from the axis 212 of the shaft 210, the attenuation is increased compared to the case where the axis 222 of the elongated member 220 is collinear with the axis 212 of the shaft 210.

[0159] FIG. 15 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210 and an elongated member 220 attached to the shaft. The shaft 210 is cylindrical and is configured to torsional vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at the angular frequency ω of vibration. The elongated member 220 is also cylindrical and is connected to the shaft 210. In contrast to the arrangement shown in FIG. 13, the elongated member 220 of FIG. 15 is connected to the curved sidewall of the shaft 210. In contrast to the arrangements shown in FIGS. 13 and 14, the elongated member 220 of FIG. 15 extends in an oblique direction that is neither completely radial nor completely axial. The elongated member 220 has a longitudinal axis 222 that is oblique to the axis 212 of the shaft 210, and the shaft 210 vibrates about the longitudinal axis 222. The elongated member 220 has a radius R. The proximal end of the elongated member 220 is offset from the axis 212 of the shaft 210 by a first offset distance R equal to the radius of the shaft 210 0,1 only. The distal end of the elongated member 220 is offset from the axis 212 of the shaft 210 by a second offset distance R equal to the sum of the radius of the shaft 210 and the radial component of the length of the elongated member 220 0,2It is only offset. The elongated member 220 is offset from the axis 212 of the shaft 210 over its entire length. The shaft 210 and the elongated member 220 are in contact with the fluid 200. According to the technique of the present disclosure, when the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is greater than the radius R of the elongated member 220 and the Reynolds number of the flow of the fluid 200 around the elongated member 220 is low, a beneficial level of geometric attenuation can be obtained. By offsetting the elongated member 220 from the axis 212 of the shaft 210, the attenuation increases compared to the case where the axis 222 of the elongated member 220 is collinear with the axis 212 of the shaft 210.

[0160] FIG. 16 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210 and an elongated member 230 attached to the shaft. The shaft 210 is cylindrical and is configured to torsional vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at the angular frequency ω of vibration. The elongated member 230 is connected to the shaft 210 at one end of the shaft 210 and extends in a direction parallel to the axis 212 of the shaft 210, but is offset by an offset distance R 0 from the axis 212 of the shaft and has a longitudinal axis 232. In contrast to the arrangement shown in FIG. 13, the elongated member 230 has a circular cross-section along its length, but the elongated member 230 does not have a constant radius along its length. Instead, the elongated member 230 includes a first cylindrical portion having a first radius and a second cylindrical portion having a second radius different from the first radius. The first cylindrical portion of the elongated member 230 is connected to the shaft 210, and the second cylindrical portion is connected to the first cylindrical portion. The first cylindrical portion and the second cylindrical portion of the elongated member 230 share the same common axis 232. The first radius is the maximum radius R max of the elongated member 230, and the second radius is the minimum radius R min of the elongated member 230. The average radius along the length of the elongated member 230 is R aveIt is. The shaft 210 and the elongated member 230 are in contact with the fluid 200. According to the technique of the present disclosure, the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is the radius R min is greater than (more preferably R ave is greater than, more preferably R max is greater than), and when the Reynolds number of the flow of the fluid 200 around the elongated member 230 is low, a beneficial level of geometric attenuation can be obtained. By offsetting the elongated member 230 from the axis 212 of the shaft 210, the attenuation is increased compared to the case where the axis 232 of the elongated member 230 is in line with the axis 212 of the shaft 210.

[0161] FIG. 17 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210 and an elongated member 240 attached to the shaft. The shaft 210 is cylindrical and is configured to torsional vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at an angular frequency ω of vibration. The elongated member 240 is connected to the shaft 210 at one end of the shaft 210 and extends in a direction parallel to the axis 212 of the shaft 210, but is offset by an offset distance R 0 from the axis 212 of the shaft and has a longitudinal axis 242. In contrast to the arrangement shown in FIG. 13, the elongated member 240 has a circular cross-section along its length, but the elongated member 240 does not have a constant radius along its length. Instead, the elongated member 240 is conical and has a maximum radius R max at the portion where the elongated member 240 is connected to the shaft 210. The average radius along the length of the elongated member 240 is R ave The shaft 210 and the elongated member 240 are in contact with the fluid 200. According to the technique of the present disclosure, the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is the radius R ave is greater than (more preferably R maxWhen the Reynolds number of the flow of fluid 200 around the elongated member 240 is low (greater than), a beneficial level of geometric attenuation is obtained. By offsetting the elongated member 240 from the axis 212 of the shaft 210, the attenuation is increased compared to the case where the axis 242 of the elongated member 240 is in line with the axis 212 of the shaft 210.

[0162] FIG. 18 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210 and an elongated member 240 attached to the shaft. The shaft 210 is cylindrical and is configured to torsionally vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at an angular frequency ω of vibration. The elongated member 240 is connected to the shaft 210. The elongated member 240 is conical and has a maximum radius R at the portion where the elongated member 240 is connected to the shaft 210. max The average radius along the length of the elongated member 240 is R. ave As opposed to the arrangement shown in FIG. 17, the elongated member 240 of FIG. 18 is connected to the curved sidewall of the shaft 210, has a longitudinal axis 242 perpendicular to the axis 212 of the shaft 210, and the shaft 210 vibrates about the longitudinal axis 242. The proximal end of the elongated member 240 is offset from the axis 212 by a first offset distance R equal to the radius of the shaft 210. 0,1 The distal end of the elongated member 240 is offset from the axis 212 by a second offset distance R equal to the sum of the radius of the shaft 210 and the length of the elongated member 240. 0,2 The entire elongated member 240 (including both ends) is offset from the axis 212 of the shaft 210. The shaft 210 and the elongated member 240 are in contact with the fluid 200. According to the techniques of the present disclosure, the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is greater than the radius R (more preferably R). ave and even more preferably R. maxWhen the Reynolds number of the flow of fluid 200 around the elongated member 240 is low (greater than), a beneficial level of geometric attenuation is obtained. By offsetting the elongated member 240 from the axis 212 of the shaft 210, the attenuation is increased compared to the case where the axis 242 of the elongated member 240 is in line with the axis 212 of the shaft 210.

[0163] FIG. 19 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210 and an elongated member 250 attached to the shaft. The shaft 210 is cylindrical and configured to torsionally vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at an angular frequency ω of vibration. The elongated member 250 is connected to the shaft 210. The elongated member 250 does not form a straight line but instead describes a curve. An axis 252 extends longitudinally through the center of the elongated member 250. The axis 252 itself also describes a curve. The elongated member 250 has a circular cross-section along the length of the elongated member 250 and has a radius R around the axis 242, despite the curvature. The elongated member 250 is connected to the shaft 210 at the end of the shaft and extends in a direction generally in line with the axis of the shaft 210, but the elongated member 250 is offset from the axis 212 of the shaft 210. The proximal end of the elongated member 250 is offset from the axis 212 of the shaft 210 by a first offset distance R 0,1 only, and the distal end of the elongated member 250 is at a second distance R from the axis 212 of the shaft 210 0,2It is only offset. An axis 252 extending longitudinally through the center of the elongated member 250 is offset from the axis 212 of the shaft 210 along the entire length of the elongated member 250. The shaft 210 and the elongated member 250 are in contact with the fluid 200. According to the techniques of the present disclosure, when the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is greater than the radius R and the Reynolds number of the flow of the fluid 200 around the elongated member 250 is low, a beneficial level of geometric attenuation can be obtained. By offsetting the elongated member 250 from the axis 212 of the shaft 210, the attenuation is increased compared to the case where the axis 252 of the elongated member 250 is aligned with the axis 212 of the shaft 210.

[0164] FIG. 20 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210 and an elongated member 260 attached to the shaft. The shaft 210 is cylindrical and is configured to torsional vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at an angular frequency ω of vibration. The elongated member 260 is not straight but instead describes a curve. The elongated member 260 has a first end and a second end. Both the first end and the second end of the elongated member 260 are connected to the shaft 210 at positions longitudinally separated from each other (in a direction coinciding with the axis 212 of the shaft) along the curved sidewall of the shaft 210, and the elongated member 260 forms a closed loop with the shaft 210. An axis 262 extends longitudinally through the center of the elongated member 260 along a curved path. The elongated member 260 has a circular cross-section along the length of the elongated member 260 and has a radius R around the axis 262, despite the curvature. In FIG. 20, the elongated member 260 has the shape of a semi-annular body. Both the first end and the second end of the elongated member 260 are at a first offset distance R from the axis 212 of the shaft 210 0,1 and a second offset distance R 0,2It is only offset, and both of these offset distances are equal to the radius of the shaft 210. The axis 262 of the elongated member 260 is offset from the axis 210 of the shaft 210 along the entire length of the elongated member 260. The average offset distance R of the elongated member 262 along the length of the elongated member 260 0,ave is the offset distance R at either end of the elongated member 260 0,1 and R 0,2 is longer. The shaft 210 and the elongated member 250 are in contact with the fluid 200. According to the technique of the present disclosure, when the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is greater than the radius R and the Reynolds number of the flow of the fluid 200 around the elongated member 260 is low, a beneficial level of geometric attenuation can be obtained. By offsetting the elongated member 260 from the axis 212 of the shaft 210, the attenuation increases more than when the axis 262 of the elongated member 260 is in line with the axis 212 of the shaft 210.

[0165] Figures 21 to 23 show a vibration transducer for use with the techniques of the present disclosure, which is different from the vibration transducers shown in Figures 13 to 20. The vibration transducers shown in Figures 21 to 23 include an elongated member connected to a shaft, but differ in that each shaft includes a bob at the end of the shaft and the elongated member is connected to the shaft at the bob.

[0166] FIG. 21 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210, a bob 214 at an end of the shaft 210, and an elongated member 220 connected to the shaft 210 at the bob 214. The shaft 210 is cylindrical and configured to torsionally vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at an angular frequency ω of vibration. The bob 214 represents an end of the shaft 210 that is larger in diameter than the remainder of the shaft 210. The bob 214 has three axial portions that are axially aligned with the axis 212 of the shaft 210, including: i) a frustoconical first axial portion whose radius linearly increases from an initial radius equal to the shaft radius to a final radius over an axial portion; ii) a second axial portion that is cylindrical and has a radius equal to the final radius of the first axial portion; and iii) a conical third axial portion whose radius linearly decreases from the radius of the second axial portion to zero. The elongated member 220 is cylindrical, has a radius R, and is connected to the third axial portion of the bob 214. The elongated member 220 has a longitudinal axis 222 that is parallel to the axis 212 of the shaft 210, and the shaft 210 vibrates about the longitudinal axis 222, but is radially offset from the axis 212 of the shaft 210 by an offset distance R 0 only. The shaft 210 (including the bob 214) and the elongated member 220 are in contact with a fluid 200. According to the techniques of the present disclosure, when the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is greater than the radius R of the elongated member 220 and the Reynolds number of the flow of the fluid 200 around the elongated member 220 is low, a beneficial level of geometric attenuation is obtained. By offsetting the elongated member 220 from the axis 212 of the shaft 210, the attenuation is increased compared to the case where the axis 222 of the elongated member 220 is collinear with the axis 212 of the shaft 210.

[0167] Figure 22 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210, a bob 214 at an end of the shaft 210, and an elongated member 220 connected to the shaft 210 at the bob 214. The shaft 210 is cylindrical and configured to torsionally vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at an angular frequency ω of vibration. Similar to the vibration transducer of FIG. 21, the bob 214 has three axial portions axially aligned with the axis 212 of the shaft 210, including: i) a first frustoconical axial portion whose radius linearly increases from an initial radius equal to the shaft radius to a final radius over the axial portion; ii) a second axial portion that is cylindrical and has a radius equal to the final radius of the first axial portion; and iii) a third frustoconical axial portion whose radius linearly decreases from the radius of the second axial portion to zero. The elongated member 220 is cylindrical, has a radius R, and is connected to the second axial portion of the bob 214. The elongated member 220 has a longitudinal axis 222 perpendicular to the axis 212 of the shaft 210, and the shaft 210 vibrates about the longitudinal axis 222. The proximal end of the elongated member 220 is offset from the axis 212 of the shaft 210 by a first offset distance R 0,1 equal to the radius of the axial portion of the bob 214. The distal end of the elongated member 220 is offset from the axis 212 of the shaft 210 by a second offset distance R 0,2 equal to the sum of the radius of the second axial portion of the bob 214 and the length of the elongated member 220. The elongated member 220 is offset from the axis 212 of the shaft 210 over its entire length. The shaft 210 (including the bob 214) and the elongated member 220 are in contact with a fluid 200. According to the techniques of the present disclosure, when the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is greater than the radius R of the elongated member 220 and the Reynolds number of the flow of the fluid 200 around the elongated member 220 is low, a beneficial level of geometric attenuation is obtained. By offsetting the elongated member 220 from the axis 212 of the shaft 210, the attenuation is increased compared to the case where the axis 222 of the elongated member 220 is collinear with the axis 212 of the shaft 210.

[0168] FIG. 23 shows a vibration transducer for use with the techniques of the present disclosure. The vibration transducer includes a shaft 210, a bob 214 at an end of the shaft 210, and two elongated members 240a, 240b connected to the shaft 210 at the bob 214. The shaft 210 is cylindrical and configured to torsionally vibrate about a longitudinal axis 212 passing through the center of the shaft 210 at an angular frequency ω of vibration. Similar to the vibration transducer of FIG. 21, the bob 214 has three axial portions that are axially aligned with the axis 212 of the shaft 210, including: i) a first axial portion in the shape of a frustum of a cone whose radius increases linearly from an initial radius equal to the shaft radius to a final radius over an axial portion, ii) a second axial portion that is cylindrical and has a radius equal to the final radius of the first axial portion, and iii) a third axial portion in the shape of a cone whose radius decreases linearly from the radius of the second axial portion to zero. Each elongated member 240a, 240b is connected to the second axial portion of the bob 214 on opposite sides of the second axial portion of the bob 214. Each elongated member 240a, 240b is conical about an axis 242 perpendicular to the axis of the shaft 210, and the shaft 210 vibrates about the longitudinal axis 242. Each elongated member 240a, 240b has a maximum radius R max at the proximal end where it is connected to the bob 214. The average radius along the length of the elongated members 240a, 240b is R ave , which is smaller than R max . For each of the elongated members 240a, 240b, the proximal end is offset from the axis 212 by a first offset distance R 0,1 equal to the radius of the second axial portion of the bob 214, and the distal end is offset from the axis 212 by a second offset distance R 0,2 equal to the sum of the radius of the second axial portion of the bob 214 and the length of the elongated members 240a, 240b. The entirety (including both ends) of each elongated member 240a, 240b is offset from the axis 212 of the shaft 210. Both the shaft 210 (including the bob 214) and the elongated members 240a, 240b are in contact with a fluid 200. According to the techniques of the present disclosure, the viscoelastic propagation distance of the shear wave of the fluid 200 at the angular frequency of vibration is greater than the radius R ave (more preferably Rmax When the Reynolds number of the flow of the fluid 200 around the longer (greater than) and elongated members 240a, 240b is low, a beneficial level of geometric attenuation can be obtained. By offsetting the elongated members 240a, 240b from the axis 212 of the shaft 210, the attenuation increases compared to the case where the axis 242 of each elongated member 240a, 240b is in line with the axis 212 of the shaft 210.

[0169] In another configuration according to the techniques of the present disclosure, the vibration transducer includes a shaft and a plurality of elongated members. If the vibration transducer includes a bobbin, the elongated members may be connected to the vibration transducer at the bobbin. Alternatively or additionally, the vibration transducer may comprise elongated members connected to the vibration transducer at the shaft. The plurality of elongated members are spaced along the circumference of the shaft or bobbin and extend completely radially outward from the shaft or bobbin, or in a direction having a radial component and an axial component, or completely axially (not on the same straight line as the longitudinal axis of the shaft / bobbin). The plurality of elongated members may be evenly distributed along the circumference, thereby reducing or avoiding the disturbance of the center of mass with respect to the longitudinal axis, but may also be unevenly distributed along the circumference. The plurality of elongated members may be connected to the shaft or bobbin at the same axial position along the length of the shaft or bobbin, for example in a helical pattern around the outer surface of the shaft or bobbin, or at different axial positions.

[0170] When the plurality of elongated members extend completely or partially axially from the shaft or bobbin, the elongated members may include a spacer support from the outer surface of the shaft or bobbin to provide a radial offset to the elongated members. Alternatively, the plurality of elongated members may be circularly distributed around the longitudinal axis and extend from the end of the shaft or bobbin, such as extending from the end of the shaft or bobbin. The end of the shaft or bobbin may be flat, curved, conical, or have any other profile.

[0171] The elongated member may have a width and a half-width such that geometric attenuation (monopole behavior) may occur around the elongated member during the vibration of the vibration transducer. The vibration of the vibration transducer may be torsional about the longitudinal axis of the shaft.

[0172] The vibration transducer may comprise two or more elongated members, such as 3, 4, 5, 6, 7, 8, 9, 10 or more elongated members. The elongated member may have a constant cross-section along the length of the elongated member (such as a cylindrical elongated member, or a square / rectangular, rounded square / rectangular (e.g., super-elliptical shape), triangular, or elliptical cross-section elongated member, etc.), or may have a cross-sectional shape or size that varies along its length, such as i) a cone whose cross-sectional area decreases linearly as the distance from the shaft or bob increases, or ii) one whose size or shape changes stepwise (e.g., the size decreases stepwise) as the distance from the shaft or bob increases.

[0173] In a particular configuration, the vibration transducer comprises a shaft configured for torsional vibration, the shaft having a proximal end where the vibration is driven and a distal end. At the distal end of the shaft, or near the distal end of the shaft (e.g., closer to the distal end than the proximal end, or within the last quarter, or within the last tenth, or within the last twentieth of the fluid contact length of the shaft), a plurality of elongated members extend radially outward from the shaft at a common axial position along the length of the shaft. Eight elongated members are evenly distributed at 45° intervals along the circumference of the shaft. In another particular configuration, the bob is at the distal end of the shaft and eight elongated members extend radially outward from the bob. Other configurations comprise more or fewer elongated members evenly or unevenly distributed around the shaft / bob. For example, one configuration comprises six elongated members evenly distributed along the circumference of the shaft.

[0174] In another specific configuration, the vibration transducer includes a shaft and a plurality of elongated members that are aligned axially with the longitudinal axis of the shaft but not on the same straight line as the longitudinal axis of the shaft. There is a bob at the distal end of the shaft. The bob has the shape of a cylinder coaxial with the longitudinal axis of the shaft, but with a larger radius than the shaft. The plurality of elongated members extend axially outward from the end of the bob, each being connected to the end of the bob with the same radial offset from the longitudinal axis and evenly distributed around the longitudinal axis. The plurality of elongated members includes eight elongated members evenly distributed at 45° intervals around the longitudinal axis. The vibration transducer is configured to torsionally vibrate about the longitudinal axis. Other configurations include more or fewer elongated members and are either evenly or unevenly distributed around the longitudinal axis. For example, one configuration includes six elongated members evenly distributed around the longitudinal axis.

[0175] Figures 24 - 31 show further vibration transducers for use in the techniques of the present disclosure. The shaft 310 is configured to torsionally vibrate about the longitudinal axis 312. The shaft has three axial portions axially aligned with the axis 312 of the shaft 310. i) A frustoconical first axial portion with a radius that linearly increases from an initial radius equal to the shaft radius to a final radius over the axial portion. ii) A second axial portion that is cylindrical and has a radius equal to the final radius of the first axial portion. And iii) A conical third axial portion with a radius that linearly decreases from the radius of the second axial portion to zero. It has a bob 314 with three axial portions axially aligned with the axis 312 of the shaft 310. In each of Figures 24 - 31, a plurality of elongated members are connected to the shaft 310 at the bob 314.

[0176] FIG. 24 shows a vibration transducer in which two elongated members 320a, 320b are connected to the second axial portion of the bob 314. The two elongated members 320a, 320b are cylindrical and have a constant same radius along the lengths of the two elongated members 320a, 320b. The first elongated member 320a is disposed diametrically opposite the other elongated member 320b around the bob 314. Each of the elongated members 320a, 320b extends outward from the bob 314 in a radial direction perpendicular to the axis 312 of the shaft 310.

[0177] FIG. 25 shows a vibration transducer in which two elongated members 320a, 320b are connected to the third axial portion of the bob 314. Each of the elongated members 320a, 320b is parallel to the axis 312 of the shaft 310 but is aligned along respective axes that are radially offset from the axis 312 of the shaft 310. The two elongated members 320a, 320b are cylindrical and have a constant same radius along the lengths of the two elongated members 320a, 320b. The first elongated member 320a is disposed diametrically opposite the other elongated member 320b around the third axial portion of the bob 314.

[0178] FIG. 26 shows a vibration transducer in which two elongated members 340a, 340b are connected to the second axial portion of the bob 314. The two elongated members 340a, 340b are conical. The first elongated member 340a is disposed diametrically opposite the other elongated member 340b around the bob 314. Each of the elongated members 340a, 340b extends outward from the bob 314 in a radial direction perpendicular to the axis 312 of the shaft 310. Each of the elongated members 340a, 340b has a maximum radius at the proximal end and is connected to the second axial portion of the bob 314 at the proximal end.

[0179] Figure 27 shows a vibration transducer in which four elongated members 340a, 340b, 340c, and 340d are connected to the second axial portion of the bob 314. The four elongated members 340a, 340b, 340c, and 340d are conical. The first elongated member 340a is disposed around the bob 314, diametrically opposite to the second elongated member 340b, but at the same axial position as the second elongated member 340b along the axis 312. The third elongated member 340c is disposed around the bob 314, diametrically opposite to the fourth elongated member 340d, but at the same axial position as the fourth elongated member 340d along the axis 312. The first elongated member 320a and the second elongated member 320b are axially spaced from the third elongated member 340c and the fourth elongated member 340d, respectively, along the axis 312. Each of the elongated members 340a, 340b, 340c, and 340d has a maximum radius at its proximal end and is connected to the second axial portion of the bob 314 at the proximal end.

[0180] Figure 28 shows a vibration transducer in which two elongated members 360a, 360b are connected to the second axial portion of the bob 314. The two elongated members 360a, 360b each have a semi-annular shape. The first elongated member 360a is curved and is connected to the bob 314 at two axially spaced positions, and has a circular cross-section along a curved axis passing through the elongated member 360a. The second elongated member 360b is curved and is connected to the bob 314 at two axially spaced positions that are diametrically opposite around the bob from the positions where the first elongated member 360a is connected to the bob 314. The second elongated member also has a circular cross-section along a curved axis passing through the elongated member 360b.

[0181] Figure 29 shows a vibration transducer in which four elongated members 320a, 320b, 320c, and 320d are connected to a second axial portion of the bobbin 314. Each of the four elongated members 320a, 320b, 320c, and 320d is cylindrical with the same constant radius, and extends radially from the bobbin 314 from positions distributed along the circumference of the second axial portion at 90° from adjacent elongated members. The distal end of each of the four elongated members 320a, 320b, 320c, and 320d is connected to a fifth elongated member 324 that surrounds the bobbin 314 and has an annular shape.

[0182] Figure 30 shows a vibration transducer in which four elongated members 320a, 320b, 320c, and 320d are connected to a second axial portion of the bobbin 314. The four elongated members 320a, 320b, 320c, and 320d are cylindrical but have different radii. The first elongated member 320a has the largest radius. The second elongated member 320b has a radius smaller than that of the first elongated member 320a. The third elongated member 320c has a radius smaller than that of the second elongated member 320b. The fourth elongated member 320d has a radius smaller than that of the third elongated member 320c. The first elongated member 320a and the second elongated member 320b each extend radially outward from respective positions that are axially offset from each other from the second axial portion of the bobbin 314 but have the same circumferential position at other points. The third elongated member 320c and the fourth elongated member 320d each extend radially outward from respective positions that are axially offset from each other from the second axial portion of the bobbin 314 but have the same circumferential position at other points. The first elongated member 320a and the second elongated member 320b are arranged at an interval of 90° from the third elongated member 320c and the fourth elongated member 320d along the circumference of the bobbin 314.

[0183] Figure 31 shows a vibration transducer in which eight elongated members 370a, 370b, 370c, 370d, 370e, 370f, 370g, and 370h are connected to a bobbin 314. The first elongated member 370a is connected to the third axial portion of the bobbin 314 and has a conical shape extending in a direction oblique to the axis 312 of the shaft 310. The second elongated member 370b is connected to the second axial portion of the bobbin 314 and extends radially outward from the bobbin 314 from the proximal end of the second elongated member 370b. The second elongated member 370b is not linear, and two linear portions are connected at a right angle to form an "L"-shaped member. The distal portion of the second elongated member 370b extends in a direction parallel to the axis 312. The third elongated member 370c is connected to the second axial portion of the bobbin 314 and has a "T"-shaped configuration. The proximal portion of the third elongated member 370c is connected to the bobbin 314 and extends radially outward from the bobbin 314. The distal portion of the third elongated member 370c is connected to the distal end of the proximal portion of the third elongated member 370c and extends in a direction parallel to the axis 312, that is, in a direction perpendicular to the direction of the proximal portion. The fourth elongated member 370d is connected to the second axial portion of the bobbin 314 and includes a proximal portion and a distal portion. The proximal portion is connected to the bobbin 314 and extends in a direction oblique to the axis 312 of the shaft 310. The end of the distal portion is connected to the distal end of the proximal portion, and the distal portion extends in a direction parallel to the axis 312. The fifth elongated member 370e is connected to the second axial portion of the bobbin 314. The fifth elongated member 370e is not linear and extends radially outward from the bobbin 314 in a wide radius direction, but has a wide circular cross-section along the length of the fifth elongated member 370e. The sixth elongated member 370f is connected to the second axial portion of the bobbin 314 and extends radially outward from the bobbin 314. A further elongated member is connected to the distal end of the sixth elongated member 370f, and this further elongated member has a closed loop, specifically, an annular shape. The seventh elongated member 370g is connected to the second axial portion of the bobbin 314 and extends radially outward from the bobbin 314.At the distal end of the seventh elongated member 370g, a further elongated member is connected, and this further elongated member is curved circumferentially about an arc concentric with the circumference of the second axial portion of the bob 314. The eighth elongated member 370h is connected to the third axial portion of the bob 314 and has a proximal portion and a distal portion. The proximal portion is connected to the bob 314 and extends outward from the surface of the third axial portion in an oblique direction with respect to the axis 312 of the shaft 310. The end of the distal portion is connected to the distal end of the proximal portion, and the distal portion extends in a direction parallel to the axis 312.

[0184] In the embodiments described above, the elongated members used for geometric attenuation have a circular cross-section, and the radius can be easily determined from the circular cross-section. In the analysis presented above, the radius of the elongated member is utilized when determining whether the conditions for geometric attenuation are met. However, a skilled reader will recognize that the techniques of the present disclosure do not completely rely on elongated members having exactly circular cross-sections. A circular cross-section may be a preferred embodiment, especially for torsional vibrations about the axis of the elongated member, because such vibrations generate only shear waves. However, as described above, by offsetting the elongated member from the axis of vibration, in some conditions, i.e., when the Reynolds number is sufficiently low and the flow is laminar, monopole-like behavior may still be generated in the wave field. Therefore, the requirements regarding the circularity of the elongated member are only loose. Elongated members having cross-sections that are not exactly circular may still provide geometric attenuation by the techniques of the present disclosure.

[0185] One measure of the circularity of the shape is represented by the following equation.

Equation

[0186] Therefore, when characterizing the techniques of the present disclosure and considering the requirements for obtaining geometric attenuation, it may be more appropriate to consider the half-width of the elongated member rather than the radius. The elongated member has an axis extending along the length of the elongated member and a cross-section that is constant or varies along the axis. The cross-section has a half-width that represents the radius in the analysis presented above. The characteristic half-width used to characterize the geometric attenuation behavior of the elongated member at its position along the axis may be the minimum distance from the centroid of the cross-sectional area, the maximum distance from the centroid, or a value between the minimum and maximum distances from the centroid. This may be the average of the minimum and maximum distances, or the average of the distances from the centroid obtained by averaging the perimeter length of the cross-section. Alternatively, the half-width may be determined from the perimeter length of the equivalent circle itself, or in the case of a concave shape, it may be determined from the convex perimeter length. For example, if the convex perimeter length is p, the half-width characterizing the shape may be calculated as p / 2π. In the case of a circle, this formula returns the radius of the circle. However, if the shape is not a perfect circle, this formula returns an equivalent "radius" (i.e., half-width) that characterizes the geometric attenuation behavior of the elongated member. Alternatively, the half-width characterizing the shape may be based on the convex area of the equivalent circle shape, i.e., √(A / π).

[0187] In some embodiments, the elongated member has a constant cross-section along its length. Thus, the calculation of the half-width characterizing the geometric attenuation behavior of the elongated member can be performed at any point along the length. In some other embodiments, the elongated member has a non-constant cross-section along its length. The radius or half-width may vary along the length of the elongated member. Thus, it may be more appropriate to calculate the radius characterizing the elongated member. Conservatively, if the maximum half-width along the length of the elongated member is smaller than the viscoelastic propagation depth, geometric attenuation can be assumed to exist. However, as shown in FIG. 4, even when the radius slightly exceeds the viscoelastic propagation depth, the deviation from linearity of the linear relationship between the attenuation coefficient and the viscosity may remain somewhat gradual. Thus, adopting a less conservative approach, geometric attenuation may be achieved even when the average measured value of the non-constant half-width is smaller than the viscoelastic propagation depth. Such an average may be calculated from the average of the half-widths along the length of the elongated member, such as the arithmetic mean of the half-widths along the length of the elongated member, or may be calculated by calculating the average from the volume and surface area of the elongated member according to the following formula.

Number

[0188] FIG. 32 schematically shows an exemplary apparatus for analyzing a fluid using one or more techniques of the present disclosure. The apparatus includes a vibrating transducer 415 within a fluid sample 400. The fluid sample 400 in this example is a substantially stationary fluid of a fixed volume within a chamber 406, the fluid having a free surface 407, and a portion of the viscosity transducer penetrates the free surface 407 from above.

[0189] FIG. 32 depicts the chamber 406 with its upper wall closed as would be required if the contents were pressurized, but the chamber may equally well be open at the top. Thus, the fluid sample may be at atmospheric pressure. In such a configuration, at least a portion of the oscillating transducer may extend up to the upper opening of the chamber 407, or alternatively the oscillating transducer may be disposed over the chamber 407 so as to contact the fluid sample 405 instead.

[0190] The oscillating transducer 415 includes an oscillating element configured to oscillate in a torsional mode. The oscillating element is immersed in the fluid, and the viscosity is determined by the correlation of the damping received by the element, i.e., the Q factor. In particular, the oscillating transducer includes a sensor mount 413, a semi-rigid connecting member 411, a shaft 410, and a bob or "sense element" 414. The shaft 410 and the bob 414 are driven to torsionally oscillate about the longitudinal axis of the shaft 410 at an angular frequency ω. The bob 414 has a relatively large mass, and the shaft 410 and the bob 414 are at least mostly, and in some cases entirely, formed of a metallic material such as stainless steel. Both the bob 414 and the shaft 410 have a circular cross-section, and differ in that there is an elongate member 420 according to the technique of the present disclosure that extends radially outward from the circumference of the bob 414. The entire elongate member 420 is offset from the longitudinal axis of the shaft 410.

[0191] The bob 414 and the elongate member 420 are exposed to the viscous effects of the fluid within the sample 400. As the viscosity of the fluid increases, the damping of the oscillations within the sensor increases, and as a result the oscillation efficiency of the system decreases measurably. A measured value of a quantity indicating the degree of damping within the system, such as the Q factor or the loss factor, is provided from the oscillating transducer to a processor 418 configured to process the measured value to determine a physical property of the fluid sample 400 such as viscosity. The processor 418 may be integrated with the oscillating transducer 415 or may be connected to the oscillating transducer via a data interface.

[0192] FIG. 33 schematically shows a further exemplary apparatus for analyzing a fluid using one or more techniques of the present disclosure. This apparatus includes the same vibrating transducer 415 as in FIG. 32, but in this example, the fluid sample 400 is flowing through conduit 418 at an upstream average velocity of, for example, 1 m / s. The vibrating transducer 415 extends through the wall of conduit 408 from above, and the portion extending through the wall of conduit 408 is in contact with the fluid sample 400 as it passes through the vibrating transducer 415. As shown in FIG. 32, the vibrating transducer 415 includes an elongated member 420 that extends radially outward from the circumference of the bob 414 in accordance with the techniques of the present disclosure. The entire elongated member 420 is offset from the longitudinal axis of the shaft 410.

[0193] FIGS. 32 and 33 each show a vibrating transducer with a bob 414, but it is emphasized that the techniques of the present disclosure are not limited to vibrating transducers with a bob.

[0194] FIG. 34 shows a flowchart of a method according to the techniques of the present disclosure. The method includes a first step 510 of vibrating a vibrating transducer element within a fluid at a vibration frequency, the step including a vibrating transducer element including an elongated member in contact with a fluid having a half-width smaller than the propagation depth of a shear wave of the fluid at the vibration frequency. The method includes a second step 520 of measuring the vibration of the vibrating transducer element within the fluid at the vibration frequency. The method includes a third step 530 of determining a physical property of the fluid based on the measurement of the vibration. According to the techniques of the present disclosure, the step of determining a physical property of the fluid based on the measurement of the vibration may include determining one or more of viscosity, viscoelasticity, density, fluid rigidity, loss tangent, storage modulus, loss modulus, and yield stress.

[0195] FIG. 35 shows a flowchart of a further method according to the techniques of the present disclosure. The method includes a first step 610 of vibrating a vibrating transducer element in a fluid at a vibration frequency, first at an amplitude of a first vibration and then at an amplitude of a second vibration, the step including a slender member in which the vibrating transducer element is in fluid contact. The method includes a second step 620 of determining a respective first quantity and second quantity indicative of a degree of attenuation based on the vibration of the vibrating transducer element in the fluid at the first amplitude and the second amplitude, respectively, the first quantity and the second quantity being, in some embodiments, the Q factor. The method includes a third step 630 of determining a property of the fluid based on a difference between the first quantity and the second quantity, the step including i) determining the bipolarity of the wave field surrounding the vibrating transducer at the vibration frequency based on the difference between the first quantity and the second quantity, ii) determining the Reynolds number of the fluid based on the difference between the first quantity and the second quantity, or iii) determining the velocity of the vibration with respect to the fluid, the viscosity of the fluid, or the density of the fluid based on the difference between the first quantity and the second quantity.

[0196] In some embodiments, the method described in FIG. 35 is combined with the method described in FIG. 34, and the method of FIG. 35 is used to check or determine the Reynolds number of the fluid or to determine the bipolarity of the wave field surrounding the vibrating transducer to determine or check whether geometric attenuation is present.

[0197] The vibration transducer according to the techniques described in this specification may be used to determine the physical properties of a fluid by vibrating the vibration transducer at the vibration frequency within the fluid and determining a quantity indicative of the degree of attenuation based on the vibration. For example, to measure viscosity, the Q factor of the vibration can be determined. The Q factor is a dimensionless parameter indicating the attenuation level of the resonator, and the attenuation level is a function of viscosity. In particular, it indicates the extent to which the resonator has insufficient attenuation. In a plot of the frequency response, a high Q factor results in a high and narrow peak at the resonance frequency, while a low Q factor results in a low and wide peak. Due to the change in the width of the peak due to attenuation, the Q factor can be defined as the ratio of the resonance frequency to the resonance bandwidth.

Number

[0198] Measurement of viscosity at an oscillation frequency, or measurement of viscosity corresponding to an oscillation frequency, may include performing amplitude measurements at multiple frequencies to estimate the Q factor, but it should be noted that a single viscosity measurement is obtained at its resonance frequency or a frequency corresponding to a certain resonance frequency. For example, the bandwidth can be determined based on the frequency required to reduce the amplitude to a factor of 1 / √2 of the maximum amplitude at resonance. As a non-limiting example, the frequency required to reduce the amplitude to a factor of 1 / √2 of the maximum amplitude at resonance may be determined by performing a frequency sweep near the resonance frequency, but the skilled reader will recognize that the 3dB point frequency can be identified by various other techniques.

[0199] Another method for determining the Q factor is to measure the amplitude of the oscillation at a series of frequencies near the resonance frequency and fit a parabola to the frequency and amplitude values (or their logarithms) by the least squares method. Then, the 3dB point can be obtained as the solution of the quadratic equation based on the parabola that best fits the measured values.

[0200] Another method for determining the Q factor is to use logarithmic decrement. By stopping the driving of the transducer and measuring the decay of the oscillation, the Q factor can be determined by monitoring the time series of the oscillation and determining the natural logarithm of the ratio of two consecutive peaks A 1 and A 2 by the following formula.

Equation

[0201] Instead of determining the Q factor, the techniques of the present disclosure include determining a "loss factor", which is the reciprocal of the Q factor and may be determined by techniques corresponding to the techniques described above with respect to the Q factor.

[0202] In the techniques described in this specification, when it is necessary to determine the position of the "end" of an elongated member, the position of the end of the elongated member should be considered to be the position of the centroid of the cross-sectional area of the elongated member at that end.

[0203] Some of the embodiments described in this disclosure relate to determining the properties of fluids, but those skilled in the art will recognize that the geometric attenuation techniques described herein may have broader applications.

[0204] For example, geometric attenuation may be employed to intentionally modify or control the attenuation characteristics of any item that is vibrating or potentially vibrating within a fluid. As an example, a shaft vibrating within a fluid, which is commonly seen in the industry, may be mentioned. By providing one or more elongated members to the shaft according to the techniques of this disclosure, the attenuation characteristics may be controlled. If one or more elongated members are set to appropriate sizes relative to the propagation depth of the shear wave of the fluid at the vibration frequency of the shaft, geometric attenuation may occur. Further, if one or more elongated members are away from the longitudinal axis of the shaft, an amplification of the attenuation effect may be obtained, and if the state of the fluid flow enables at least a partial recovery of the monopole wave field, geometric attenuation may be maintained. By providing an appropriate number of elongated members having an appropriate shape to the shaft according to the techniques of this disclosure, if the geometric attenuation criteria are met, desired attenuation characteristics independent of the fluid properties can be realized. In some cases, vibration may be undesirable, and thus the purpose of controlling the attenuation behavior is to provide a relatively high degree of attenuation such that the vibration is attenuated.

[0205] A method for controlling the damping behavior of a shaft configured to vibrate in a fluid includes providing a shaft configured to vibrate at a vibration frequency, the shaft having a longitudinal axis, and providing an elongated member connected to the shaft and not on the same straight line as the longitudinal axis of the shaft, the elongated member being characterized by a width, a half-width equal to half of the width, and a length longer than the width, at least a portion of the elongated member and the shaft being configured to vibrate in the fluid at the vibration frequency, and the half-width of the elongated member being less than the propagation depth of the shear wave of the fluid at the vibration frequency.

[0206] As described above, the propagation depth may be the distance at which the amplitude of the shear wave propagating in the fluid at the vibration frequency decreases by a factor of 1 / e, or may be the viscoelastic propagation depth according to (Equation 1).

[0207] Such an elongated member may be any of the elongated members described herein, including any of the elongated members shown in FIGS. 7-31. In some embodiments, the elongated member has a first end and a second end, and one or both of the first end and the second end are separated from the longitudinal axis of the shaft by an offset distance greater than the half-width of the elongated member.

[0208] The elongated member may be provided such that the flow of the fluid around the elongated member is laminar while the shaft is vibrating at the vibration frequency. This may affect the selection of the dimensions of the elongated member in order to obtain a laminar flow around the elongated member during the vibration of the shaft.

[0209] In some embodiments, for the elongated member, the Reynolds number Re of the fluid flow around the elongated member is less than 1 while the shaft is vibrating in the fluid at the vibration frequency, and the Reynolds number is expressed as follows: Re = 2Rνρ / μ In the above formula, μ is the viscosity of the fluid, ρ is the density of the fluid, R is the half-width of the elongated member, and ν is the maximum velocity of the elongated member with respect to the fluid during the vibration of the shaft. The selection of the length and half-width of the elongated member affects the Reynolds number, and thus the Reynolds number represents a constraint on the dimensions of the elongated member.

[0210] For example, if the dimensions of the elongated member according to the Reynolds number criterion do not provide the desired attenuation level, the shaft may be provided with a plurality of elongated members connected to the shaft, each elongated member not being on the same straight line as the longitudinal axis of the shaft, and each elongated member having a half-width smaller than the propagation depth of the shear wave of the fluid at the vibration frequency. Thus, the attenuation characteristics of the shaft are affected by the combined effect of the plurality of elongated members.

[0211] Skilled readers will further recognize that these techniques are not limited to providing elongated members to a vibrating shaft, and may also include providing one or more elongated members on any vibrating object, such as a plate configured to vibrate in-plane at the vibration frequency to generate shear waves. Geometric attenuation as described herein may occur by providing one or more elongated members (e.g., extending perpendicular or obliquely outward from the plate) connected to the plate and having a half-width lower than the propagation depth of the shear wave of the fluid at the vibration frequency.

[0212] Skilled readers will further understand that the various illustrative logical blocks, configurations, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or a combination of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, configurations, modules, circuits, and steps have been described generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementations should not be construed as departing from the scope of the present disclosure.

[0213] The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in Random Access Memory (RAM), flash memory, Read Only Memory (ROM), Programmable Read Only Memory (PROM), Erasable Programmable Read Only Memory (EPROM), Electrically Erasable Programmable Read Only Memory (EEPROM), registers, hard disk, a removable disk, a Compact Disc Read Only Memory (CD-ROM), or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an Application Specific Integrated Circuit (ASIC). The ASIC may reside in a computing device or a user terminal. Alternatively, the processor and the storage medium may reside as discrete components of a computing device or a user terminal.

[0214] The foregoing description of the disclosed embodiments is provided to enable a person skilled in the art to make or use the disclosed embodiments. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the principles defined herein may be applied to other embodiments without departing from the scope of the disclosure. Accordingly, the disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features defined by the appended claims.

Claims

Claim 1 A method for determining a physical property of a fluid, comprising: vibrating a vibrating transducer element within the fluid at a vibration frequency, the vibrating transducer element comprising an elongated member in contact with the fluid characterized by a width, a half-width equal to half of the width, and a length longer than the width, the half-width being smaller than the propagation depth of a shear wave of the fluid at the vibration frequency; measuring the vibration of the vibrating transducer element within the fluid at the vibration frequency; determining the physical property of the fluid based on the measurement of the vibration; and a method comprising the steps of: Claim 2 The step of determining the physical property of the fluid based on the measurement of the vibration includes determining one or more of viscosity, viscoelasticity, density, fluid rigidity, loss tangent, storage modulus, loss modulus, and yield stress. The method according to claim 1. Claim 3 The step of measuring the vibration includes determining a quantity indicating the degree of attenuation of the vibrating transducer element within the fluid at the vibration frequency, The step of determining the physical property of the fluid based on the measurement of the vibration includes determining the viscosity of the fluid based on the quantity indicating the degree of attenuation. The method according to claim 2. Claim 4 The step of measuring the vibration includes determining a first quantity indicating the degree of attenuation of the vibrating transducer element within the fluid at the vibration frequency, The method further includes vibrating the vibrating transducer element within the fluid at a further vibration frequency and determining a second quantity indicating the degree of attenuation of the vibrating transducer element within the fluid at the further vibration frequency, The step of determining the physical property of the fluid based on the measurement of the vibration includes determining the viscoelasticity of the fluid based on the quantities indicating the degree of attenuation at the vibration frequency and the further vibration frequency. The method according to claim 2. Claim 5 The step of measuring the vibration includes determining the resonance frequency of the vibrating transducer element within the fluid, and the step of determining the physical property of the fluid based on the measurement of the vibration includes determining the density of the fluid based on the resonance frequency. The method according to claim 2. Claim 6 The method according to any one of claims 1 to 5, wherein the propagation depth is the distance at which the amplitude of the shear wave propagating in the fluid at the vibration frequency decreases by a factor of 1 / e, and e is the base of the natural logarithm.

7. The propagation depth of the shear wave propagating in the fluid at the vibration frequency is represented by the following formula: 【Number 1】 In the above formula, μ is the viscosity of the fluid, ρ is the density of the fluid, ω is the angular frequency of vibration, Δ varies between 0 and π / 2, is defined by the loss tangent tanΔ, and tanΔ is equal to the following formula: μω / G' The method according to any one of claims 1 to 6, wherein G' in the above formula is the storage modulus of the fluid.

8. The method according to any one of claims 1 to 7, wherein the half-width of the elongated member is less than 50% of the propagation depth.

9. The vibration transducer element includes a shaft having a longitudinal axis, the elongated member is connected to the shaft, and the elongated member is not on the same straight line as the longitudinal axis of the shaft. The method according to any one of claims 1 to 8.

10. The method according to claim 9, wherein the flow of the fluid around the elongated member becomes laminar while the vibration transducer element is vibrating at the vibration frequency.

11. The elongated member has a first end and a second end, and one or both of the first end and the second end are separated from the longitudinal axis of the shaft by an offset distance greater than the half-width of the elongated member. The method according to claim 9 or 10.

12. While the vibration transducer element is vibrating in the fluid at the vibration frequency, the Reynolds number Re of the fluid flow around the elongated member is less than 1000, preferably less than 100, more preferably less than 10, and even more preferably less than 1. The Reynolds number is represented as follows: Re = 2Rνρ / μ In the above formula, μ is the viscosity of the fluid, ρ is the density of the fluid, R is the half-width of the elongated member, and ν is the maximum velocity of the elongated member with respect to the fluid during the vibration of the vibration transducer. The method according to any one of claims 9 to 11.

13. The method according to any one of claims 9 to 12, wherein the shaft includes a bob, and the elongated member is connected to the shaft at the bob.

14. The method according to any one of claims 9 to 13, wherein the vibration transducer element comprises a plurality of elongated members connected to the shaft, each elongated member is not on the same straight line as the longitudinal axis of the shaft, and each elongated member has a half-width smaller than the propagation depth of the shear wave of the fluid at the vibration frequency.

15. The method according to claim 14, wherein the half-width of the first elongated member among the plurality of elongated members is different from the half-width of the second elongated member among the plurality of elongated members.

16. The elongated member has a cross-section having a roundness in the range of 0.75 to 1 along at least 50% of its length, and the roundness of the cross-section is 4πA / p ２ calculated by, where in the above formula, A is the convex area of the cross-section and p is the convex perimeter of the cross-section. The method according to any one of claims 1 to 15.

17. The method according to any one of claims 1 to 16, wherein the elongated member has a constant cross-section along at least 90% of its length or has a constant cross-section along 10% or less of its length.

18. The method according to any one of claims 1 to 17, wherein the elongated member is linear or non-linear, or comprises one of a cylinder, a cone, a frustum of a cone, an annular body, and an arc portion of an annular body.

19. The method according to any one of claims 1 to 18, wherein the step of vibrating the vibration transducer element includes vibrating the vibration transducer element using a vibrating rotational motion and / or a vibrating linear motion and / or a vibrating curvilinear motion.

20. The method according to claim 19, wherein the elongated member is linear, and the step of vibrating the transducer element includes vibrating the elongated member using a vibrating rotational motion about an axis along the length of the elongated member.

21. The method according to any one of claims 1 to 20, wherein the length of the elongated member is greater than twice the width of the elongated member.

22. The half-width of the elongated member is greater than 0.5 mm, the viscosity of the fluid is greater than 100 Pa·s, and the density of the fluid is 500 kg / m ３ ~1500 kg / m ３ The method according to any one of claims 1 to 21, wherein the frequency of the vibration is less than 10 kHz.

23. A device for determining the physical properties of a fluid, comprising An oscillating transducer comprising a shaft configured to oscillate at an oscillation frequency, the shaft having a longitudinal axis, the oscillating transducer further comprising an elongate member connected to the shaft but not on the same straight line as the longitudinal axis of the shaft, the elongate member being characterized by a width, a half-width equal to half of the width, and a length greater than the width. The device is configured to determine a physical property of a fluid by oscillating the shaft at the oscillation frequency within the fluid while the elongate member is in contact with the fluid, and at the oscillation frequency, the half-width of the elongate member is less than the propagation depth of a shear wave of the fluid. The device is configured to measure the oscillation of the oscillating transducer within the fluid at the oscillation frequency and determine a physical property of the fluid based on the measurement of the oscillation at the oscillation frequency.

24. The device according to claim 23, wherein at least a portion of the elongate member is offset from the longitudinal axis by an offset distance greater than the half-width of the elongate member.

25. The device according to claim 24, wherein the elongate member has a first end and a second end, and one or both of the first end and the second end are separated from the longitudinal axis of the shaft by an offset distance greater than the half-width.

26. The elongate member has a cross-section having a roundness in the range of 0.75 to 1 along at least 50% of its length, and the roundness of the cross-section is 4πA / p ２ calculated by the above formula, where A is the convex area of the cross-section and p is the convex perimeter length of the cross-section. The device according to any one of claims 23 to 25.

27. The device according to any one of claims 23 to 26, wherein the elongate member has a constant cross-section along at least 90% of its length or along 10% or less of its length.

28. The device according to any one of claims 23 to 27, wherein the elongate member is straight or non-straight, or comprises one of a cylinder, a cone, a frustum of a cone, a torus, and an arc portion of a torus.

29. The device according to any one of claims 23 to 28, wherein the length of the elongate member is greater than twice the width of the elongate member.

30. The device according to any one of claims 23 to 29, wherein the half-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.

31. The device according to any one of claims 23 to 30, comprising a plurality of elongated members connected to the shaft, each elongated member having its respective width, half-width, and length.

32. The device according to claim 31, wherein the half-width of the first elongated member among the plurality of elongated members is different from the half-width of the second elongated member among the plurality of elongated members.

33. The device according to any one of claims 23 to 32, wherein the shaft is configured to vibrate torsionally around its longitudinal axis, and / or longitudinally along the longitudinal axis of the shaft, and / or transversely with respect to the longitudinal axis of the shaft.

34. The device according to any one of claims 23 to 33, wherein the shaft comprises a bob, and the elongated member is connected to the shaft at the bob.

35. A method for determining the properties of a fluid, comprising: vibrating a vibration transducer element in a fluid at a vibration frequency, first at a first amplitude of vibration and then at a second amplitude of vibration, the vibration transducer element comprising an elongated member in contact with the fluid characterized by a width, a half-width equal to half of the width, and a length longer than the width; determining a first quantity indicative of the degree of attenuation based on the vibration of the vibration transducer element in the fluid at the first amplitude; determining a second quantity indicative of the degree of attenuation based on the vibration of the vibration transducer element in the fluid at the second amplitude; determining the properties of the fluid based on the difference between the first quantity and the second quantity; and including the method.

36. The step of determining the characteristics of the fluid includes determining whether the half-width of the elongated member is less than the propagation depth of the shear wave of the fluid at the frequency of vibration, and / or the degree to which the half-width of the elongated member is less than the propagation depth of the shear wave of the fluid at the frequency of vibration, based on the difference between the first quantity and the second quantity, according to the method of claim 35.

37. The step of determining the characteristics of the fluid includes determining the Reynolds number of the fluid based on the difference between the first quantity and the second quantity, according to the method of claim 35 or claim 36.

38. The step of determining the characteristics of the fluid includes determining the velocity of vibration with respect to the fluid, the viscosity of the fluid, or the density of the fluid, based on the difference between the first quantity and the second quantity, according to the method of any one of claims 35 to 37.

39. The step of determining the first quantity and the second quantity includes determining a first Q factor and a second Q factor, according to the method of any one of claims 35 to 38.

40. The determined characteristics of the fluid are the characteristics of the flow of the fluid due to the vibration of the vibration transducer element in the fluid at the frequency of vibration of one or both of the first amplitude and the second amplitude, according to the method of any one of claims 35 to 39.

41. The method further includes the step of performing the method according to any one of claims 1 to 22, according to the method of any one of claims 35 to 40.

42. The method is performed using the device according to any one of claims 23 to 34, according to the method of any one of claims 35 to 41.

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