Hollow cylindrical viscometer employing trapped torsional modes

Abstract

A viscometer includes a hollow cylinder with an axially varying vibrational property configured to axially localize a resonant torsional acoustic mode; a torsional vibration exciter configured to excite higher-order torsional modes in the cylinder; and a detection unit configured to determine a viscosity of fluid in the cylinder based on measured fluid-induced changes in one or more of acoustic loss or frequency of a trapped resonant torsional acoustic mode of the cylinder.

Description

[0001] HOLLOW CYLINDRICAL VISCOMETER EMPLOYING TRAPPED TORSIONAL MODES

[0002] Related Applications

[0003] This application claims the benefit of U.S. Provisional Patent Application Serial No. 63 / 602,494 (filed November 24, 2023), which is herein incorporated by reference in its entirety.

[0004] Federally-Sponsored Research and Development

[0005] This invention was made with United States Government support from the National Institute of Standards and Technology (NIST), an agency of the United States Department of Commerce. The Government has certain rights in this invention.

[0006] Field of Invention

[0007] The present invention relates generally to the use of vibrational modes in sensing, and more particularly to a viscometer employing trapped torsional modes to sense viscosity.

[0008] Background

[0009] A viscometer (also called viscosimeter) is an instrument used to measure the viscosity of a fluid. Vibrational viscometers operate by measuring the damping or shift in frequency of an oscillating electromechanical resonator immersed in a fluid whose viscosity is to be determined. The resonator generally oscillates in torsion or transversely (as a cantilever beam or tuning fork). The higher the viscosity, the larger the damping or shift in frequency imposed on the resonator.

[0010] Summary of Invention

[0011] Exemplary embodiments include a class of devices for measuring viscosity of fluids in industrial, consumer, and research settings. An exemplary embodiment includes a hollow cylinder with dimensional and / or compositional variations along the length that localize resonant torsional modes in a central section and hardware for exciting / detecting these modes through piezoelectric or electromagnetic-acoustic transduction. Advantages of exemplary devices over conventional viscometers include non-invasive measurement of fluids in pipes during industrial production and elimination of measurement errors and uncertainty associated with mechanical contact.

[0012] According to one aspect of the invention, a viscometer for determining a viscosity of a fluid in an interior chamber of the viscometer includes: a hollow cylindrical resonator with an axially varying vibrational property configured to axially localize a resonant torsional acoustic mode; a torsional vibration exciter configured to excite higher-order torsional modes in the cylindrical resonator; and a detection unit configured to determine the viscosity of fluid in the cylindrical resonator based on measured fluid-induced changes in one or more of acoustic loss or frequency of a trapped resonant torsional acoustic mode of the cylinder.

[0013] Optionally, the axially varying vibrational property is wall thickness.

[0014] Optionally, the hollow cylindrical resonator includes a hollow cylinder wherein the axially varying vibrational property is a surface film or sleeve on an axial ly-central portion of an outer surface of the hollow cylinder.

[0015] Optionally, the hollow cylinder is nonconductive and the surface film or sleeve is metallic.

[0016] Optionally, the surface film or sleeve is a piezoelectric layer having a predominant crystallographic alignment that leads to in-plane shear displacements in the presence of an in-plane electric field.

[0017] Optionally, the surface film or sleeve is multiple azimuthally separated piezoelectric layers having a predominant crystallographic alignment that leads to in-plane shear displacements in the presence of an in-plane electric field.

[0018] Optionally, the surface film or sleeve includes metallic layer(s) and a piezoelectric layer having a predominant crystallographic alignment that leads to in-plane shear displacements in the presence of a normal electric field.

[0019] Optionally, the hollow cylindrical resonator includes a first metal layer; a piezoelectric layer with predominant crystallographic alignment that leads to shear displacements in the presence of a surface-normal electric field; and a second metallic layer.

[0020] Optionally, the axially varying vibrational property is material composition causing lower acoustic shear velocity in an axially central portion of the hollow cylindrical resonator.

[0021] Optionally, the torsional vibration exciter excites via electromagnetic- acoustic transduction.

[0022] Optionally, a frequency of an oscillating driving voltage across an electroacoustic transduction device of the torsional vibration exciter is equal to a resonant frequency of a torsional mode that is localized in and / or near an axially central portion of the cylindrical resonator.

[0023] Optionally, the torsional vibration exciter includes an electroacoustic transduction device, and the detection unit includes the same electroacoustic device.

[0024] Optionally, the viscometer includes an electroacoustic transducer having: a coil with axially aligned wire segments adjacent to an outer surface of the cylindrical resonator, the coil wound in a meander pattern such that an axial direction of current passing through the coil alternates as a function of azimuthal angle; and a plurality of magnets spaced around a circumference of the cylindrical resonator with alternating polarity matching that of the coil and magnetic fields predominantly perpendicular to portions of the outer surface of the resonator adjacent each section of wire.

[0025] Optionally, the viscometer includes an electroacoustic transducer configured to employ lateral-field piezoelectric transduction with oscillating azimuthal electric fields inductively generated by a solenoid coil surrounding the cylindrical resonator.

[0026] Optionally, the viscometer is configured to employ surface-normal electric fields generated by voltages applied between the first and second metal layers.

[0027] Optionally, the surface film or sleeve is a piezoelectric film, and the viscometer further includes an electrical coil circumferentially wrapped around the piezoelectric film and configured to excite the piezoelectric film with oscillating inductively-generated azimuthal electric fields to generate torsional modes in the viscometer that are trapped at the portion of the cylinder wrapped with the piezoelectric film.

[0028] Optionally, the viscometer includes an electroacoustic transducer configured to employ lateral-field piezoelectric transduction with oscillating predominantly azimuthal electric fields generated by electrodes that are axially aligned with edges of each section of piezoelectric film and provide the same azimuthal electric-field polarity in all piezoelectric films in each cross section.

[0029] Optionally, the surface film or sleeve includes a piezoelectric film between a conducting surface of the cylinder or, optionally, first metal film and a second metal film and the viscometer is configured to excite azimuthal shear displacements in the piezoelectric film with oscillating normal electric fields generated by voltages applied between the cylinder or first film and the second metal film.

[0030] According to another aspect of the invention, a method of operating a hollow cylindrical torsional viscometer at a selected temperature T and fluid pressure P without knowledge of material properties, dimensions, or detailed vibrational displacement pattern of the resonator includes the steps of: measuring logarithmic decrement do of a selected resonant torsional mode in vacuum at the selected temperature; measuring logarithmic decrement 3 and resonant frequency A of the selected mode with the interior of the resonator filled with a reference fluid of known viscosity 77 and density p at the selected temperature and pressure; and inserting the measured values of <5o, 3, and p into equations 5 and 6, below, to determine a value of the function g(T,P) for the selected resonant mode, T and fluid pressure P.

[0031] Optionally, the method also includes the steps of: determining a density p of a sample fluid at the selected temperature and pressure; measuring a logarithmic decrement <5o of a selected resonant mode in vacuum at the selected temperature; measuring a resonant frequency f and logarithmic decrement 3 of the selected resonant mode with the sample fluid present at the selected temperature and pressure; and determining the viscosity 77 of the sample fluid from the equations. The foregoing and other features of the invention are hereinafter described in greater detail with reference to the accompanying drawings.

[0032] Brief Description of the Drawings

[0033] FIG. 1 shows a schematic representation of an exemplary viscometer;

[0034] FIG. 2 shows an exemplary viscometer including an axially-arranged coil surrounding a central section of hollow cylindrical trapped-mode resonator with an arrangement of radially-extending magnets arranged circumferentially around the coil.

[0035] FIG. 3 shows an exemplary viscometer including a cylindrical coil (solenoid) surrounding a central section of a hollow cylindrical trapped-mode resonator with a piezoelectric layer on the surface. The coil may be supported by a thin-walled nonconducting tube (not shown), for example.

[0036] FIG. 4 shows an exemplary viscometer including a hollow cylindrical trapped-mode resonator with multiple separated piezoelectric layers on the surface. Electrodes are arranged axially adjacent the edges of the piezoelectric layers such that voltages applied to the electrodes produce electric fields predominantly parallel to the plane of each piezoelectric layer.

[0037] FIG. 5 shows a block diagram of an exemplary method of using an exemplary viscometer.

[0038] Detailed Description

[0039] Exemplary embodiments can measure the viscosity of fluids inside pipes / tubes in industrial processing / transport and other commercial applications, potentially including sensing of oil viscosity in internal combustion engines. Exemplary embodiments can provide enhanced resolution and repeatability of viscosity measurements in commercial and research / development settings.

[0040] Referring first to FIG. 1 a schematic representation of an exemplary viscometer is shown at 100. The viscometer includes a hollow cylinder 110 with an axially varying physical property or dimension that effects its vibrational response characteristics such as, e.g., wall thickness, surface films, and / or composition that lead to axial localization of resonant torsional acoustic modes. The area of this vibrational property variance is shown at 115. The viscometer also includes a torsional vibration exciter 120 for exciting higher-order torsional modes in the cylinder 110 through, e.g., electromagnetic-acoustic or piezoelectric transduction, and a detection unit 130 that includes a method for determining the viscosity of the fluid inside the cylinder 110 from measured fluid- induced changes in acoustic loss or frequency of a trapped resonant torsional mode of the cylinder 110.

[0041] In some embodiments, the torsional vibration exciter 120 may include a transduction device and a unit that drives the transduction device with an oscillating voltage at a resonant torsional frequency of the cylinder. In an exemplary embodiment, the transduction device is an electroacoustic transducer that produces oscillating azimuthal forces on near-surface regions of the resonator when oscillating voltages are applied to the device.

[0042] In some embodiments, the detection unit 130 includes a transduction device for detecting acoustic vibrations (receiving transduction device) and a signal processing unit. In an exemplary embodiment, the receiving transduction device is an electroacoustic transducer that generates oscillating voltages across electrical leads when oscillating near-surface azimuthal displacements are present in the cylindrical resonator.

[0043] In some embodiments, the torsional exciter 120 and detection unit 130 are a single device with multiple components.

[0044] Referring now to FIG. 2, an exemplary viscometer is shown at 200. The viscometer 200 shares many similarities to the above-referenced viscometer 100, and consequently the same reference numerals but indexed by 100 are used to denote structures corresponding to similar structures in the viscometers. In addition, the foregoing description of the viscometer 100 is equally applicable to the viscometer 200 except as noted below. Moreover, it will be appreciated upon reading and understanding the specification that aspects of the viscometers may be substituted for one another or used in conjunction with one another where applicable. For example, FIG. 2 does not depict a torsional exciter 120 or detection unit 130, but it should be understood by those skilled in the art that these schematic units have been omitted for visual clarity and concision but are equally useful and operable with the depicted portions of viscometer 200. The viscometer 200 includes a plurality of (preferably permanent) magnets 222 mounted around the cylinder 210 at equally spaced intervals (although the magnets may be unequally spaced in alternative embodiments). These magnets and / or other components of the torsional vibration exciter (not shown) may reside within an optional housing 226, which may be ferromagnetic. The polar ends 222a and 222b of the magnets 222 are adjacent the cylinder 210, and each part of adjacent magnets 222 has ends 222a and 222b of opposite polarity. The viscometer 200 also has at least one wire coil 224 which is also mounted adjacent the cylinder, between the cylinder 210 and the magnets 222. The individual wire segments 224a and 224b of the wire coil 224 are mounted adjacent to the polar ends 222a and 222b of the plurality of magnets 222, and are arranged in a meander pattern wherein the wire segments 224a and 224b extend back and forth along the axial direction of the cylinder 210 (i.e. into and out of the page) and are alternately connected at the ends. If an electrical current is passed through this meander coil, the axial direction of the current in the wire segments 224a marked with an X in the center is opposite to the direction of the current in the wire segments 224b marked with a dot in the center.

[0045] When a time-dependent electrical voltage is applied to the torsional vibration exciter, a time-dependent current flows through the wire coil 224 and this leads to induction of time-dependent eddy currents of opposite sign in the cylinder material next to each section of wire (following Ampere’s, Faraday’s, and Lenz’s laws of electromagnetism). These eddy currents, in the presence of the magnetic field, lead to time-dependent near-surface Lorentz forces on the cylinder 210 and / or sleeve 215 that are primarily in one azimuthal direction around the circumference at each instant of time, because of the matching periodicities of the magnetic field and meander coil.

[0046] If the frequency of the time-varying voltage applied to the wire coil 224 matches a resonant torsional vibrational frequency of the cylinder 210, the viscometer 200 will acoustically resonate at this frequency.

[0047] Another exemplary viscometer is shown at 300. The viscometer 300 shares many similarities to the above-referenced viscometers 100, 200, and consequently the same reference numerals but indexed by 100 are used to denote structures corresponding to similar structures in the viscometers. In addition, the foregoing description of the viscometers 100, and 200 are equally applicable to the viscometer 300 except as noted below. Moreover, it will be appreciated upon reading and understanding the specification that aspects of the viscometers may be substituted for one another or used in conjunction with one another where applicable. For example, FIG. 3 does not depict a torsional exciter 120, detection unit 130, or optional housing but it should be understood by those skilled in the art that these schematic units have been omitted for visual clarity and concision but are equally useful and operable with the depicted portions of viscometer 300.

[0048] Viscometer 300 includes a combination of i) a nominally homogeneous nonconducting (e.g., ceramic or amorphous) cylinder 310 with uniform inner and outer diameters and ii) a thin piezoelectric layer 315 covering a central section of the outer surface of the cylinder 310. An alternating current / passed through the solenoid coil 324 produces azimuthal electric fields in the piezoelectric layer, generating azimuthal shear displacements in the film 315 and underlying cylinder 310.

[0049] Referring now to FIG. 4, another exemplary viscometer is shown at 400. The viscometer 400 shares many similarities to the above-referenced viscometers 100, 200, 300, and consequently the same reference numerals but indexed by 100 are used to denote structures corresponding to similar structures in the viscometers. In addition, the foregoing description of the viscometers 100, 200, 300 are equally applicable to the viscometer 400 except as noted below. Moreover, it will be appreciated upon reading and understanding the specification that aspects of the viscometers may be substituted for one another or used in conjunction with one another where applicable. For example, FIG. 4 does not depict a torsional exciter 120 or detection unit 130, but it should be understood by those skilled in the art that these schematic units have been omitted for visual clarity and concision but are equally useful and operable with the depicted portions of viscometer 400.

[0050] The hollow cylinder 410 may be made from a nonconducting material. The viscometer 400 includes separate sections of piezoelectric layers 420 with regular or irregular spacing around the circumference of cylinder 410. The piezoelectric layers have a predominant crystallographic alignment that leads to shear displacement gradients in each layer and the cylinder substrate beneath each layer that are primarily perpendicular to the surface (i.e. , in the radial direction) when an electric field is applied parallel to the surface of the layer. The corresponding displacements in the layer and the cylinder are primarily parallel to the electric field. The physical mechanism in this transduction effect is the same as that employed in conventional lateral-field excitation of piezoelectric films with c-axis (crystallographic hexagonal axis of the piezoelectric material) oriented primarily perpendicular to a planar substrate.

[0051] Electrodes 424 and 425 in FIG. 4 extend along the edges of each piezoelectric layer 420 in the direction of the cylindrical axis (i.e., into the page). These electrodes are optionally mounted on a housing 426. A voltage with opposite polarities across electrodes labeled “+” and (424 and 425, respectively) will produce an electric field primarily in the plane of each piezoelectric layer and in the same azimuthal direction in all of the layers. Therefore, such a voltage will induce displacements in the cylinder with a substantial torsional component. If the voltage is alternating at a frequency matching that of a resonant torsional mode of cylinder 410, this resonant mode will be excited.

[0052] Referring back to Fig. 1 , central region 115 may optionally be covered in part or entirely by a first metal layer, a piezoelectric layer, and a second metal layer, with the piezoelectric material having a primary crystallographic orientation that leads to azimuthal shear displacements in the presence of a surface-normal electric field. If the cylinder is conducting, the first metal layer is optional. Application of an oscillating voltage between the first metal layer (or conducting cylinder) and the second metal layer excites a torsional mode of the cylinder, if the excitation frequency matches the resonant frequency of that mode. Examples of piezoelectric layers with crystallographic orientation that may be effective for this type of excitation include materials such as ZnO with hexagonal crystal symmetry and crystallographic c-axis inclined azimuthally away from normal.

[0053] The basic physical mechanism employed in embodiments of the invention to determine viscosity may be the same as that employed in conventional torsional quartz viscometry (TQV): a viscous fluid in contact with a solid acoustic resonator introduces viscoelastic loss to resonant modes that have in-plane shear displacements at the fluid / solid interface, and measurements of this increase in loss or associated shift in resonant frequency enable a determination of the fluid viscosity. Differences between the invention and conventional TQV may include:

[0054] • Resonator geometry and materials;

[0055] • Surface of the resonator that is in contact with the fluid (inner, rather than outer);

[0056] • Use of localized (“trapped”) torsional modes with negligible vibrational amplitudes outside of a central section of the resonator, rather than approximately torsional modes with maximal displacements at the ends of the resonator; and / or

[0057] • Methods of electroacoustic transduction.

[0058] In conventional TQV systems in research environments, the resonator is a single-crystal solid cylinder of quartz in which vibrations are excited by alternating electric fields that are generated by electrodes close to the surface of the cylinder. In an exemplary device, the geometric and material configuration of the hollow cylindrical trapped-mode resonator may be one or more of the following:

[0059] 1 . A metal cylinder with nominally homogeneous composition and slightly greater wall thickness (i.e., greater outer diameter and / or smaller inner diameter) in a central section of the cylinder,

[0060] 2. A combination of i) a nominally homogeneous nonconductiong (e.g., ceramic or amorphous) cylinder with uniform inner and outer diameters and ii) a thin metallic layer covering a central section of the outer surface of the cylinder.

[0061] 3. A combination of i) a nominally homogeneous nonconducting (e.g., ceramic or amorphous) cylinder 310 with uniform inner and outer diameters and ii) a thin piezoelectric layer 315 covering a central section of the outer surface of the cylinder 310 as shown in FIG. 3. At each point on the surface, the piezoelectric layer 315 has a predominant crystallographic alignment that leads to in-plane shear displacements in the presence of an in-plane electric field. Examples of such piezoelectric layers are ZnO, AIN, and doped AIN with c-axis crystallographic orientation predominantly perpendicular to the surface.

[0062] 4. A metal cylinder with constant inner and outer diameters and variation in composition along the length that provides lower shear velocity in a central section.

[0063] Materials selected for each of these exemplary device configurations should have relatively low intrinsic acoustic loss to avoid degradation of device resolution and range. Therefore, materials that are substantially viscoelastic, such as rubber and plastics, would be poor choices. Significant azimuthal dependence of elastic constants (transverse acoustic anisotropy) of the cylinder material should also be avoided, since this would introduce surface-normal displacements of resonant modes at the inner surface and associated radiation of acoustic energy into any enclosed fluid. Such anisotropy is a limitation of conventional TQV with single-crystal quartz cylinders.

[0064] With appropriate choices for dimensions, each of these geometric / material configurations — or combinations of these configurations — will effectively localize (trap) higher-order torsional modes within and near (in and adjacent) a central section of the resonator. With such localization, each on the above Geometry / Material Configurations can be extended by the incorporation of dimensional variations at the ends, such as flanges or threads, that facilitate coupling to adjacent hardware (e.g., fluid-carrying pipes), and such additions will have negligible effect on the trapped modes.

[0065] Potential embodiments of the above geometric / material configurations are effectively unlimited with respect to specific dimensional and material parameters. Effective and practical device parameters are dependent on requirements of specific applications, such as required fluid volume in the cylinder, lack of chemical reactivity, mechanical strength, and resolution or range of viscosity measurements. This document does not limit the range of applications or specific associated geometric / material parameters of embodiments of the invention. For any application, dimensional / material parameters of an embodiment of the invention must localize resonant vibrations to the extent that the vibrational amplitudes at the ends of the device that are attached to other structures are negligible. This localization must be greater in applications that require greater resolution and associated low background acoustic loss. The degree to which localization is achieved for a specific embodiment can be assessed with a piezoelectric or electromagnetic-acoustic receiving transducer placed on the outer surface at a series of locations along the length. Qualitative information on localization also can be obtained by measuring changes in acoustic loss while pressing a viscoelastic object against the outer surface of the resonator at a series of positions along the length. Such tests can be employed to determine appropriate choices for dimensional / material parameters among those of a set of fabricated devices by those skilled in the art upon reading and understanding the disclosures herein.

[0066] Guidance in selecting dimensional / material parameters of embodiments can be provided by numerical modeling of resonant vibrational displacements (e.g., finite-element calculations) in the absence of fluid. Predictions of the degree of vibrational trapping can also be provided through the use of approximate analytical expressions similar to those for trapped torsional modes in solid cylinders presented by Johnson et al. [J. Acoust. Soc. Am. 100, pp. 285- 293 (1996)], the contents of which is hereby incorporated herein in its entirety.

[0067] A translation of the analytical approach of Johnson et al. to hollow trapped-mode cylinders of a single isotropic material begins with equations for angular resonant frequencies w of torsional modes of a cylinder with uniform inner diameter a, outer diameter b, and shear velocity v where y is the axial wavenumber and 3 satisfies the relation where J2 and Y2 are Bessel’s functions of second order of the first and second kind, respectively [D. C. Gazis, J. Acoust. Soc. Am. 30, pp. 786-794; D. C. Gazis, J. Acoust. Soc. Am. 31 , pp. 568-578 ]. Innumerable values of (3 satisfy Eq. 2, each with a unique number of radial nodes in the corresponding displacement pattern. For each value of 3, y is found from Eq. 1 to be, respectively, real or imaginary when co is greater or less than a “cutoff’ frequency equal to v3. Therefore, vibrational displacements for a given value of 3 are sinusoidal or exponential functions of the axial coordinate z when w is, respectively, above or below the cutoff frequency.

[0068] For a hollow cylinder with slightly greater diameter in a central section (denoted Section 1) and a specified number of radial nodes, the cutoff frequency wi in this section is slightly lower than the cutoff frequency W2 in the smaller diameter sections (Sections 2 and 3). Therefore, resonant modes with frequencies between wi and W2 will have sinusoidal dependence on z in Section 1 and decay exponentially towards the ends in Sections 2 and 3. Such localized (trapped) modes are a focus of this invention.

[0069] For the purpose of estimating the rate of decay of vibrational displacements towards the ends with specific dimensions, displacement functions with sinusoidal dependence on z in Section 1 and exponential dependence on z in Sections 2 and 3 are approximated as having the same dependence on the radial coordinate at the interfaces between sections. Solutions for the resonant modes are obtained from the requirement that displacements and traction forces be continuous across the interfaces. For modes with displacements that are even functions of z (with z defined as zero at the center of Section 1 ) the resonant torsional frequencies w are given by where / is the length of Section 1 and wi and W2 are, respectively, the cutoff frequencies given by Eq. 2 for Sections 1 and 2. Similarly, resonant frequencies of trapped modes that are odd functions of z are given by

[0070] Once solutions for wi, W2, and w are determined from Eq. 2 and Eq. 3 or 4 for a selected number of radial nodes in the displacements and corresponding values of (3, these angular frequencies can be inserted into Eq. 1 to determine yi and the associated degree of vibrational trapping. Such calculations can be quickly employed with a range of dimensional parameters to guide users of the invention towards effective configurations in the absence of fabrication and testing of multiple embodiments.

[0071] For hollow cylinders with a constant diameter and a central Section 1 composed of a different material than that of Sections 2 and 3 (geometric / material configuration 4 listed above), Eqs. 1 and 2 remain valid for each section with corresponding shear velocity (vi or 1 / 2) and density (pi or 2). Equations 3 and 4 are modified for this configuration by a factor of pi / p multiplying the left sides of these equations.

[0072] Eq. 1 & 2 may be modified by those skilled in the art as appropriate to be applicable to geometric / material configurations with radially varying material properties. Numerical methods such as FEM can be used to guide the identification of effective dimensional parameters as described above.

[0073] The electro-acoustic transduction configuration / mechanism incorporated in exemplary embodiments may be one of the following: :

[0074] 1 . Electromagnetic-acoustic transduction with i) a coil with axially aligned wires close to the outer metal surface of a cylinder and ii) a static magnetic B-field with direction predominantly perpendicular to the surface of the cylinder beneath each section of wires. An alternating electrical current passed through the coil induces near-surface eddy currents and azimuthal Lorentz forces in the metal surface. This configuratioin is illustrated in FIG. 2.

[0075] 2. Piezoelectric transduction with a solenoid coil 324 surrounding a central trapped-mode section 315 of a cylinder 310 with Geometry / Material Configuration 3. This configuration is illustrated in FIG. 3. An alternating current / passed through the coil inductively produces azimuthal electric fields in the piezoelectric layer with radial c-axis orientation, generating azimuthal shear displacements in the film 315 and underlying cylinder 310.

[0076] 3. Piezoelectric transduction with electrodes axially aligned with edges of sections of piezoelectric films 420 with radial c-axis orientation on the surface of cylinder 410. This configuration is illustrated in FIG. 4. Voltages applied to the electrodes directly introduce azimuthal electric fields in the films and piezoelectrically generate azimuthal shear displacements. More than one of each of the above electro-acoustic transduction configurations can be implemented on a single cylindrical trapped-mode resonator. In other words, multiple sections of a resonator and surrounding transduction hardware could have cross sections similar to those depicted in Figs. 2, 3, or 4, with separate electrical connections in each section and optionally different polarities of voltages, currents, and / or magnetic fields. If two sections of transduction hardware are employed, the functions of excitation and reception can be separately handled by two devices (as represented schematically in Fig. 1). Different polarities in two sections on opposite sides of the axial center of a resonator could optionally be employed to preferentially excite resonant torsional modes with acoustic displacements that are odd functions of the axial coordinate.

[0077] An operating equation for determining the viscosity r) of a fluid from measurements of a trapped torsional mode of an embodiment of the invention is where is the resonant frequency with fluid present, p is the independently determined density of the fluid,cyi(z) is the density of the resonator at point z, v(z) is the maximal velocity of vibrational displacements in the resonator at point z during an arbitrary vibrational cycle, and df is the fluid contribution to the logarithmic decrement (acoustic loss): where do and d are values of the logarithmic decrement of the selected resonant mode measured with nothing in the cylinder (in vacuum) and with fluid present, respectively. The integrals in the numerator and denominator of Eq. 5 are respectively performed over the volume \ / of the resonator and the inner surface S of the resonator in contact with fluid. This equation is a generalization, allowing for variations in density (multiple materials), of an equation given by P. R. Heyliger, C. Junker, K. Meier, and W. L. Johnson, “Effects of crystalline anisotropy on resonant acoustic loss of torsional quartz viscometers,” J. Acoust. Soc. Am. 151 , 2135-2148 (2022) (hitps: / / dGrorq / 10.1121 / 10 0009825). the content of which is hereby incorporated herein by reference in its entirety. Unlike the equation of Heyliger et al., Eq. 5 does not include normal displacements of resonator surfaces in contact with the fluid, which exist in conventional solid cylindrical quartz torsional viscometers because of anisotropic crystal properties.

[0078] An alternate operating equation can be expressed in terms of a measured downward shift in resonant frequency that accompanies the acoustic loss introduced by a fluid. However, as explained in the above-cited reference by Heyliger et al., measurements of resonant frequency shifts for determining viscosity have been found to be less reliable than measurements of acoustic loss in conventional torsional quartz viscometry because of high sensitivities of frequencies to drifting temperature.

[0079] The term in square brackets in Eq. 5 is dependent only on the selected resonant torsional mode and the geometry and material properties of the resonator. Therefore, at a specified temperature and pressure, this term is a constant (independent of fluid properties) for each resonant mode that is employed for viscosity measurements with a specific embodiment of the invention.

[0080] Referring now to Fig. 5, a method of use of an embodiment of the invention for determining viscosity of a fluid with a selected resonant mode is shown in block-diagram form at 500.

[0081] At optional block 510, the device may be calibrated.

[0082] Calibration may include using a reference fluid for which the viscosity and density are known at a selected temperature and pressure. An exemplary reference fluid is toluene at 293.15 K and 0.1 MPa (approximately atmospheric pressure at sea level), which has previously served as a reference in comparisons of values of viscosity determined with various measurement techniques. An application of Eq. 5 to measurements of do in the absence of fluid and f and 8 with the reference fluid present may provide a value for the quantity in square brackets in this equation for the selected resonant mode, and this can then be used in Eq. 5 to determine viscosities from similar measurements of other fluids with this embodiment at the calibrated temperature and pressure. Values of b and 80 can be determined from the rate of change of phase and amplitude of the signal measured with a phase-sensitive receiver during resonant ringdown after tone-burst excitation [Johnson, Mechanical Systems and Signal Processing 168 (2022) 108631], the content of which is hereby incorporated herein in its entirety. These values can alternately be determined from established scanned-frequency or pulsed / FFT measurements of signal amplitude vs. frequency and the general relationship of the logarithmic decrement to the width of a resonant peak.

[0083] An embodiment may be calibrated at multiple temperatures and pressures to optimize the accuracy of measurements of fluid viscosities at these temperatures and pressures. Effects of varying temperature on the term in square brackets in Eq. 5 may include changes in density, which are typically on the order of 10 ppm / °C for most materials. Effects of varying pressure may include changes in resonator dimensions a and / or b that affect the vibrational displacement pattern and associated v(z) in Eq. 5.

[0084] At block 520, the density of the fluid at the selected temperature and pressure is determined.

[0085] At block 530, measure <5o with the resonator in vacuum at the selected temperature and measure fand d with the fluid present at the selected temperature and pressure.

[0086] As described above, these measurements can be performed with either a time-domain technique with single-frequency tone-burst excitation or frequencydomain technique with stepped-frequency of pulse excitation employing the general relationship between resonant peak width and logarithmic decrement.

[0087] At block 540, the viscosity 77 of the fluid is determined by inserting the measured values <5o, f, and b into Eqs. 5 and 6 with the calibrated value of the expression in square brackets inserted into Eq. 5. The detection unit 130 may be adjusted as appropriate based on these results.

[0088] Conventional devices for continuous in-line measurement of viscosity of fluids in pipes employ sensors that either project directly into the fluid through pipe walls or are configured in a closed-end side port into which fluid can enter from the main fluid channel. Devices projecting through pipe walls can be vulnerable to damage associated with fluid flow and pressure variations (including water hammer), and damaged probes can introduce risks of fluid contamination and secondary damage to equipment. Devices configured in side ports are less sensitive to rapid changes in viscosity of fluid passing through the pipe and more vulnerable to fouling. All of these potential problems are absent with exemplary devices, which enables sensing of the viscosity without altering the cylindrical geometry of the fluid passageway.

[0089] Commercial in-line viscometers typically have minimal measurable viscosities on the order of 1 mPa*s with ranges on the order of 1000 mPa*s. Therefore, most commercial devices are ineffective at accurately measuring viscosities of fluids less viscous than water. For viscometers that employ measurements of damping of a resonant torsional mode, resolutions are partly limited by background loss arising from mechanical support of the sensor. This contribution to the background loss is effectively eliminated in exemplary embodiments by trapping of vibrations away from areas of mechanical support.

[0090] In contrast to commercial devices for in-line sensing, torsional quartz viscometers in research settings can employ much less robust mechanical contact and achieve accuracies that are orders of magnitude greater than commercial devices. For example, conventional torsional quartz viscometers may employ thin wires to support resonating quartz cylinders. Nevertheless, uncertainties introduced by even such delicate support are a concern. Exemplary devices eliminate such uncertainties in research instruments by vibrational trapping.

[0091] The processes described herein may be embodied in, and fully automated via, software code modules executed by a computing system that includes one or more general purpose computers or processors. The code modules may be stored in any type of non-transitory computer-readable medium or other computer storage device. Some or all the methods may alternatively be embodied in specialized computer hardware. In addition, the components referred to herein may be implemented in hardware, software, firmware, or a combination thereof. Many other variations than those described herein will be apparent from this disclosure. For example, depending on the embodiment, certain acts, events, or functions of any of the algorithms described herein can be performed in a different sequence, can be added, merged, or left out altogether (e.g., not all described acts or events are necessary for the practice of the algorithms). Moreover, in certain embodiments, acts or events can be performed concurrently, e.g., through multi-threaded processing, interrupt processing, or multiple processors or processor cores or on other parallel architectures, rather than sequentially. In addition, different tasks or processes can be performed by different machines and / or computing systems that can function together.

[0092] Any logical blocks, modules, and algorithm elements described or used in connection with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, and elements have been described above 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. The described functionality can be implemented in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the disclosure.

[0093] The various illustrative logical blocks and modules described or used in connection with the embodiments disclosed herein can be implemented or performed by a machine, such as a processing unit or processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A processor can be a microprocessor, but in the alternative, the processor can be a controller, microcontroller, or state machine, combinations of the same, or the like. A processor can include electrical circuitry configured to process computerexecutable instructions. In another embodiment, a processor includes an FPGA or other programmable device that performs logic operations without processing computer-executable instructions. A processor can also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. Although described herein primarily with respect to digital technology, a processor may also include primarily analog components. For example, some or all of the signal processing algorithms described herein may be implemented in analog circuitry or mixed analog and digital circuitry. A computing environment can include any type of computer system, including, but not limited to, a computer system based on a microprocessor, a mainframe computer, a digital signal processor, a portable computing device, a device controller, or a computational engine within an appliance, to name a few.

[0094] The elements of a method, process, or algorithm described in connection with the embodiments disclosed herein can be embodied directly in hardware, in a software module stored in one or more memory devices and executed by one or more processors, or in a combination of the two. A software module can reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of non-transitory computer-readable storage medium, media, or physical computer storage known in the art. An example storage medium can be 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 can be integral to the processor. The storage medium can be volatile or nonvolatile.

[0095] While one or more embodiments have been shown and described, modifications and substitutions may be made thereto without departing from the spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustrations and not limitation. Embodiments herein can be used independently or can be combined.

[0096] All ranges disclosed herein are inclusive of the endpoints, and the endpoints are independently combinable with each other. The ranges are continuous and thus contain every value and subset thereof in the range. Unless otherwise stated or contextually inapplicable, all percentages, when expressing a quantity, are weight percentages. The suffix (s) as used herein is intended to include both the singular and the plural of the term that it modifies, thereby including at least one of that term (e.g., the colorant(s) includes at least one colorants). Option, optional, or optionally means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event occurs and instances where it does not. As used herein, combination is inclusive of blends, mixtures, alloys, reaction products, collection of elements, and the like.

[0097] As used herein, a combination thereof refers to a combination comprising at least one of the named constituents, components, compounds, or elements, optionally together with one or more of the same class of constituents, components, compounds, or elements.

[0098] All references are incorporated herein by reference.

[0099] The use of the terms “a,” “an,” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. It can further be noted that the terms first, second, primary, secondary, and the like herein do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. It will also be understood that, although the terms first, second, etc. are, in some instances, used herein to describe various elements, these elements should not be limited by these terms. For example, a first current could be termed a second current, and, similarly, a second current could be termed a first current, without departing from the scope of the various described embodiments. The first current and the second current are both currents, but they are not the same condition unless explicitly stated as such.

[0100] The modifier about used in connection with a quantity is inclusive of the stated value and has the meaning dictated by the context (e.g., it includes the degree of error associated with measurement of the particular quantity). The conjunction or is used to link objects of a list or alternatives and is not disjunctive; rather the elements can be used separately or can be combined together under appropriate circumstances. Although the invention has been shown and described with respect to a certain embodiment or embodiments, it is obvious that equivalent alterations and modifications will occur to others skilled in the art upon the reading and understanding of this specification and the annexed drawings. In particular regard to the various functions performed by the above described elements (components, assemblies, devices, compositions, etc.), the terms (including a reference to a "means") used to describe such elements are intended to correspond, unless otherwise indicated, to any element which performs the specified function of the described element (i.e., that is functionally equivalent), even though not structurally equivalent to the disclosed structure which performs the function in the herein illustrated exemplary embodiment or embodiments of the invention. In addition, while a particular feature of the invention may have been described above with respect to only one or more of several illustrated embodiments, such feature may be combined with one or more other features of the other embodiments, as may be desired and advantageous for any given or particular application.

Claims

ClaimsWhat is claimed is:1 . A viscometer for determining a viscosity of a fluid in an interior chamber of the viscometer, comprising: a hollow cylindrical resonator with an axially varying vibrational property configured to axially localize a resonant torsional acoustic mode; a torsional vibration exciter configured to excite higher-order torsional modes in the cylindrical resonator; and a detection unit configured to determine the viscosity of fluid in the cylindrical resonator based on measured fluid-induced changes in one or more of acoustic loss or frequency of a trapped resonant torsional acoustic mode of the cylinder.

2. The viscometer of claim 1 , wherein the axially varying vibrational property is wall thickness.

3. The viscometer of claim 1 , wherein the hollow cylindrical resonator includes a hollow cylinder and wherein the axially varying vibrational property is a surface film or sleeve on an axially-central portion of an outer surface of the hollow cylinder.

4. The viscometer of claim 3, wherein the hollow cylinder is nonconductive, and the surface film or sleeve is metallic.

5. The viscometer of claim 3, wherein the surface film or sleeve is a piezoelectric layer having a predominant crystallographic alignment that leads to in-plane shear displacements in the presence of an in-plane electric field.

6. The viscometer of claim 3, wherein the surface film or sleeve is multiple azimuthally separated piezoelectric layers having a predominant crystallographic alignment that leads to in-plane shear displacements in the presence of an in-plane electric field.

7. The viscometer of claim 3, wherein the hollow cylindrical resonator includes: a first metal layer; a piezoelectric layer with predominant crystallographic alignment that leads to shear displacements in the presence of a surface-normal electric field; and a second metallic layer.

8. The viscometer of claim 1 , wherein the axially varying vibrational property is material composition causing lower acoustic shear velocity in an axially central portion of the hollow cylindrical resonator.

9. The viscometer of any preceding claim, wherein a surface of the resonator is metallic, and the torsional vibration exciter excites via electromagnetic-acoustic transduction.

10. The viscometer of any preceding claim, wherein a frequency of an oscillating driving voltage across an electroacoustic transduction device of the torsional vibration exciter is equal to a resonant frequency of a torsional mode that is localized in and / or near an axially central portion of the cylindrical resonator.11 . The viscometer of any preceding claim, wherein the torsional vibration exciter includes an electroacoustic transduction device, and the detection unit includes the same electroacoustic device.

12. The viscometer of any one of claims 1 -4 or 7-11 , further comprising an electroacoustic transducer having: a coil with axially aligned wire segments adjacent to an outer surface of the cylindrical resonator, the coil wound in a meander pattern such that an axial direction of current passing through the coil alternates as a function of azimuthal angle; anda plurality of magnets spaced around a circumference of the cylindrical resonator with alternating polarity matching that of the coil and magnetic fields predominantly perpendicular to portions of the outer surface adjacent each section of wire, and wherein a surface of the resonator is metallic.

13. The viscometer of claim 5, further comprising an electroacoustic transducer configured to employ lateral-field piezoelectric transduction with oscillating azimuthal electric fields generated by a solenoid coil surrounding the cylindrical resonator.

14. The viscometer of claim 6, further comprising an electroacoustic transducer configured to employ lateral-field piezoelectric transduction with oscillating predominantly azimuthal electric fields generated by electrodes that are axially aligned with edges of each section of piezoelectric film and provide the same azimuthal electric-field polarity in all piezoelectric films in each cross section.

15. The viscometer of claim 7 configured to employ surface-normal electric fields generated by voltages applied between the first and second metal layers.

16. The viscometer of claim 3, wherein the surface film or sleeve is a piezoelectric film, and the viscometer further comprising: an electrical coil circumferentially wrapped around the piezoelectric film and configured to excite the piezoelectric film with inductively-generated in-plane electric fields to generate torsional modes in the viscometer that are trapped at the portion of the cylinder wrapped with the piezoelectric film.

17. A method of operating a hollow cylindrical torsional viscometer at a selected temperature T and fluid pressure P without knowledge of material properties, dimensions, or detailed vibrational displacement pattern of the resonator, the method comprising:measuring logarithmic decrement <5o of a selected resonant torsional mode in vacuum at the selected temperature; measuring logarithmic decrement 3 and resonant frequency A of the selected mode with the interior of the resonator filled with a reference fluid of known viscosity 77 and density p at the selected temperature and pressure; and inserting the measured values of <5o, 3, and p into the following equations to determine a value of the function g(T,P) for the selected resonant mode, T and fluid pressure P18. The method of claim 17, further comprising the steps of: determining a density p of a sample fluid at the selected temperature and pressure; measuring a logarithmic decrement <5o of a selected resonant mode in vacuum at the selected temperature; measuring a resonant frequency fand logarithmic decrement 3 of the selected resonant mode with the sample fluid present at the selected temperature and pressure; and determining the viscosity 77 of the sample fluid from the equations.

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