Measurement of the material properties of viscous liquids using ultrasonic guided waves

The theoretical basis for a testing tool in the form of a circular waveguide for measuring both the dynamic viscosity and the longitudinal bulk velocity of viscous liquids is presented. It is based on the measurements of the attenuation of the fundamental torsional mode, T(0,1), and the fundamental longitudinal mode, L(0,1), of the waveguide when immersed in the liquid. The modeling techniques to extract the shear viscosity and the longitudinal bulk velocity are explained and experimentally verified. Results for two viscous liquids are presented: good agreement between theory and experiment was obtained.     

BEM modeling of surface water wave motion with laminar boundary layers

This study is concerned with numerical modeling of viscous surface wave motion using boundary element method (BEM). The equations of motion for thin boundary layers at the solid surfaces are coupled with the potential flow in the bulk of the fluid, and a mixed BEM-finite difference technique is used to obtain the viscosity-related quantities such as wave damping rate, shear stress, and velocity distribution inside the boundary layer. The technique is presented for standing surface wave motion. An excellent agreement is obtained between the numerical predictions and the previous results. The extension to other free surface problems is straightforward.     

An acoustic study of the relaxation properties of ZhK-1282 nematic liquid crystals in the vicinity of the nematic-isotropic phase transition

The viscous and elastic properties of a ZhK-1282 nematic liquid crystal (NLC) were studied in a temperature interval from 290 to 360 K by method of ultrasonic spectroscopy in the 3–63 MHz frequency range. The temperature dependences of the NLC density and shear viscosity are presented. The results of measurements of the velocity and attenuation of ultrasound and the shear viscosity were used to calculate the volume viscosity coefficient, the moduli of dilatation and isothermal compressibility, the relaxation times of the elastic and viscous properties, and the corresponding critical characteristics of the given NLC.     

Oscillating-cup technique for yield stress and density measurement

We discuss a possibility for simultaneous measurement of different viscometric properties by the oscillating-cup technique. The emphasis is on the following problems related to liquid metal viscometry: identification of non-Newtonian fluid flow and combined viscosity/density measurement. The cases of Bingham and Newtonian fluids are analysed in detail. The basic features of nonlinear fluid flow, viscometer oscillations, modelling of experiment and data processing are systematized and interpreted in terms of linear viscous fluids.     

Thermoviscoelastic Properties of Phenolic Resin/Polymeric Isocyanate Binder Systems

Thermoviscoelastic properties of phenolic resin/polymeric isocyanate binder systems (i.e., ISOCURE Parts I and II) are reported. The effects of blend composition and the reaction between the binders on these properties of the systems are also considered. The viscous properties of binders and their blends were measured using computer-controlled rotational viscometers (Brookfield HBDV-II+ viscometer and HAAKE Rotovisco 12 rheometer in the cone-and-plate mode). The elastic properties of the phenolic urethane polymer (the blend composition) were measured by means of a modified jet thrust technique based on measuring the thrust of a liquid jet. Although both binders are Newtonian liquids, their blends exhibit viscoelastic non-Newtonian fluid flow behavior. The viscosity of the blends increases both with time and with an increasing Part I content and may reach comparatively high values at high values of either parameter. This behavior is explained as a result of the rubbery nature of the phenolic urethane polymer, which was produced as a product of reaction between Part I and Part II. The use of the jet thrust method allowed determination of the relaxation time of various blends at different shear rates.     

Hot fluid induced temperature-dependent vibration and instability of embedded FG-CNTRC Reddy pipes

In this paper, nonlinear vibration and instability of embedded nano-composite temperature-dependent polymeric pipes conveying hot viscous fluid are investigated. The pipe is reinforced by Single-Walled Carbon NanoTubes (SWCNTs) with Uniform Distribution (UD) and three types of Functionally Graded (FG) distribution patterns. The FG-carbon nanotube reinforced composite (FG-CNTRC) pipe is located in an orthotropic temperature-dependent visco-elastomeric medium. Reddy higher-order shear deformation theory is employed to establish the governing equations. The frequency and critical fluid velocity of the structure are calculated using Differential Quadrature Method (DQM). The effects of different parameters on the nonlinear vibration and instability of the pipe are investigated.     

The measurement of bulk viscosity and the elastic-viscous analogy

Summary The motion of a liquid containing a substantial volume fraction of gas bubbles can often be calculated by considering a suitably averaged single phase continuum. This averaged material will be compressible as well as viscous and the problem arises to the determination (by experiment) of its shear and bulk viscosity coefficients. The direct measurement of bulk viscosity would be difficult, and the usual approach has been to measure an apparent elongational viscosity and then appeal to an analogy between elasticity and viscosity, claiming a connection similar to that which holds between the various elastic moduli. It is shown that this analogy does not hold in compression and that the experiments must be reinterpreted more carefully.     

Propagation of thickness-twist waves in a piezoelectric ceramic plate in contact with viscous fluids

We study theoretically the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with unattached electrodes and viscous fluids between the plate surfaces and the electrodes. Based on the theories of piezoelectricity and viscous fluids, an equation that determines the dispersion relations of the waves is obtained, showing the dependence of the phase velocity on material and geometric parameters. Due to the viscosity of the fluid, the dispersion relations are complex in general, representing damped waves with attenuation. The dispersion relations obtained can reduce to the results of a few special cases with known results. The results of the present paper are useful for developing and designing fluid sensors for measuring fluid viscosity or density.     

Viscosity measurement using drop coalescence in microgravity

We present in here validation studies of a new method for application in microgravity environment which measures the viscosity of highly viscous undercooled liquids using drop coalescence. The method has the advantage of avoiding heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Homogeneous nucleation can also be avoided due to the rapidity of the measurement using this method. The technique relies on measurements from experiments conducted in near zero gravity environment as well as highly accurate analytical formulation for the coalescence process. The viscosity of the liquid is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity for two coalescing drops. Results are presented from two sets of validation experiments for the method which were conducted on board aircraft flying parabolic trajectories. In these tests the viscosity of a highly viscous liquid, namely glycerin, was determined at different temperatures using the drop coalescence method described in here. The experiments measured the free surface velocity of two glycerin drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The liquid viscosity was determined by adjusting the computed free surface velocity values to the measured experimental data. The results of these experiments were found to agree reasonably well with the known viscosity for the test liquid used.     

Propagation properties of longitudinal leaky surface waves on lithium tetraborate

Theoretical and experimental results of longitudinal leaky surface waves with a higher phase velocity than that of ordinary leaky surface waves and a low propagation loss on lithium tetraborate (LBO) are investigated in detail. They propagate along the surface with a phase velocity close to that of longitudinal bulk wave, slightly radiating two kinds of shear bulk waves (or one shear bulk wave in the case that one of two shear wave terms is uncoupled) into the solid. Most surface components of the mode consist of a longitudinal wave term and an electromagnetic wave term. The detailed propagation properties of the longitudinal leaky surface waves on LBO with the Euler angles (phi, theta, 90 degrees ) are investigated theoretically and experimentally. The (011) cut of LBO was found to be desirable for higher frequency SAW devices. One of the reasons why that mode on LBO has a low propagation loss is also discussed.     

Properties of an elementary class of fluids with nondissipative viscous stresses

A class of fluids with both dissipative and nondissipative viscous stresses is analyzed. The class is delineated by the three assumptions, (1) the stress is isotropic, (2) the fluid admits no natural time scale, (3) the Stoke's assumption, tr(t) = − 3p, is satisfied. The constitutive relations are shown to be uniquely determined in terms of the linear bulk viscosity and the linear shear viscosity. The characteristic features of such fluids are obtained and experimental distinguishability between these fluids and the classic Navier-Stokes fluid is examined in detail. In general, it is surprisingly difficult to distinguish between the fluids considered here and the classic Navier-Stokes fluids, even though there are characteristic anomalies associated with the nondissipative stresses.     

Wall slip induced by a micropolar fluid

Lubrication theory is devoted to the study of thin-film flows, More often, the fluid can be considered as a Newtonian one and no-slip boundary conditions can be retained for the velocity at the fluid solid interface. With these assumptions it is possible to deduce from the (Navier) Stokes system a simplified equation describing the flow: the Reynolds equation. It allows to compute the pressure distribution inside the film and to obtain overall performances of a lubricated device such as load and friction coefficient. For very thin films, however, surface effects at the fluid solid interface become very important and no-slip conditions cannot be retained. Solid surfaces exert some influence on the liquid molecules and the effective shear viscosity along the boundary differs from the classical bulk shear viscosity. Moreover, the microstructure of the fluid cannot be ignored, especially the effects of solid-particle additives in the lubricant. Micropolar theory for fluids is often adopted to account of such microstructure and microrotation. In the present study, a thin micropolar fluid model with new boundary conditions at the fluid–solid interface is considered. This condition links velocity and microrotation at the interface by introducing a so-called “boundary viscosity”. By way of asymptotic analysis, a generalized micropolar Reynolds equation is obtained. Numerical results show the influence of the new boundary conditions for the load and friction coefficients. Comparisons are made with other works that retain the no-slip boundary conditions.     

An analytical model for bedload layer thickness

A theoretical study has been carried out to determine the thickness of the bedload layer in an open channel turbulent flow with non-cohesive sediment, which is very crucial in sediment transport problems as this is treated as saltation height of a sediment particle and the reference level in suspension studies. A new expression of viscous shear stress is proposed, which is a function of effective viscosity of sediment–fluid mixture, velocity gradient and volumetric concentration of sediment particles. During particle collisions, impact shear stress is generated, which is another important parameter near the sediment bed. By including both the shear stresses, an expression for the thickness of the bedload layer is developed. The predicted bedload layer thickness is a function of viscous coefficient, impact coefficient, particle diameter, relative mass density of sediment particle, maximum bed concentration and non-dimensional shear stress. It agrees reasonably well when compared with a wide class of experimental data under different hydraulic conditions.     

Flow of electro-rheological materials

Summary An electro-rheological fluid is a material in which a particulate solid is suspended in an electrically non-conducting fluid such as oil. On the application of an electric field, the viscosity and other material properties undergo dramatic and significant changes. In this paper, the particulate imbedded fluid is considered as a homogeneous continuum. It is assumed that the Cauchy stress depends on the velocity gradient and the electric field vector. A representation for the constitutive equation is developed using standard methods of continuum mechanics. The stress components are calculated for a shear flow in which the electric field vector, is normal to the velocity vector. The model predicts (i) a viscosity which depends on the shear rate and electric field and (ii) normal stresses due to the interaction between the shear flow and the electric field. These expressions are used to study several fundamental shear flows: the flow between parallel plates, Couette flow, and flow in an eccentric rotating disc device. Detailed solutions are presented when the shear response is that of a Bingham fluid whose yield stress and viscosity depends on the electric field.     

充粘性液体管材中超声导波的应力分析

对超声纵向导波在充粘液管材中的应力分布进行了分析,并讨论了用各模式检测充粘液管材的最佳频厚积范围和检测位置。分析表明,随频厚积的增加,L(0,1)和L(0,3)模式的平面内应力在管外壁上的值由负向变为正向,而L(0,2)和L(0,4)模式面内应力的值则相反,变换方向的点恰好在各模式的下一高阶模式群速度最大时的频厚积点附近;而在管内壁上,法向应力分布曲线达到零点的位置恰好在各模式群速度最大时的频厚积点附近。在各模式群速度较大的频厚积区域内,该模式在管内外表面上的平面内应力较大,而法向应力较小,因此能量泄漏较小。故在各模式群速度较大的频厚积区域内,用该模式来检测充粘液管材较合适。     

The role of viscosity in the impulse diffraction field of elastic waves induced by the acoustic radiation force

Several ultrasound-based techniques for the estimation of soft tissue elasticity are currently being investigated. Most of them study the medium response to dynamic excitations. Such responses are usually modeled in a purely elastic medium using a Green's function solution of the motion equation. However, elasticity by itself is not necessarily a discriminant parameter for malignancy diagnosis. Modeling viscous properties of tissues could also be of great interest for tumor characterization. We report in this paper an explicit derivation of the Green's function in a viscous and elastic medium taking into account shear, bulk, and coupling waves. From this theoretical calculation, 3D simulations of mechanical waves in viscoelastic soft tissues are presented. The relevance of the viscoelastic Green's function is validated by comparing simulations with experimental data. The experiments were conducted using the supersonic shear imaging (SSI) technique which dynamically and remotely excites tissues using acoustic radiation force. We show that transient shear waves generated with SSI are modeled very precisely by the Green's function formalism. The combined influences of out-of-plane diffraction, beam shape, and shear viscosity on the shape of transient waves are carefully studied as they represent a major issue in ultrasound-based viscoelasticity imaging techniques.     

Theoretical analyses and numerical simulations of the torsional mode for two acoustic viscometers with preliminary experimental tests

A rigorous analysis of the torsional modes in both a cylindrical wave guide and the associated static viscous fluid field has been conducted from the solid and the fluid wave equations and the coupled boundary conditions. As a result, two acoustic viscometer models, along with four independent equations connecting the density and the viscosity of the fluid with the attenuation and the phase velocity of the torsional wave in the wave guide, have been developed. The analysis shows that the product of the viscosity and the density of the fluid can be measured from the end reflection coefficient of the torsional wave in the wave guide and that both the viscosity and the density can be determined simultaneously from either the phase velocity or the attenuation of the torsional wave in a single cylindrical wave guide. For the simultaneous measurements of the viscosity and the density, the independent equations have to be solved numerically, for example, using Matlab (The MathWorks, Natick, MA), given either the attenuation or the phase velocity in the wave guide that is surrounded by the fluid. To demonstrate the technical feasibility, numerical simulations have been conducted to discern viscosity, phase velocity, and density, all versus attenuation, at different frequencies, and with variable dimension of a molybdenum rod, so that both the advantages and the disadvantages of the simultaneous measurements can be explored. In the end, to test the two models, preliminary experiments on two viscous standards were conducted at 23 degrees C, and good agreements have been achieved between the viscosities measured from both models and for both standards.     

Monochromatic heterodyne fiber-optic profile sensor for spatially resolved velocity measurements with frequency division multiplexing

Investigating shear flows is important in technical applications as well as in fundamental research. Velocity measurements with high spatial resolution are necessary. Laser Doppler anemometry allows nonintrusive precise measurements, but the spatial resolution is limited by the size of the measurement volume to approximately 50 microm. A new laser Doppler profile sensor is proposed, enabling determination of the velocity profile inside the measurement volume. Two fringe systems with contrary fringe spacing gradients are generated to determine the position as well as the velocity of passing tracer particles. Physically discriminating between the two measuring channels is done by a frequency-division-multiplexing technique with acousto-optic modulators. A frequency-doubled Nd:YAG laser and a fiber-optic measuring head were employed, resulting in a portable and flexible sensor. In the center of the measurement volume of approximately 1-mm length, a spatial resolution of approximately 5 microm was obtained. Spatially resolved measurements of the Blasius velocity profile are presented. Small velocities as low as 3 cm/s are measured. The sensor is applied in a wind tunnel to determine the wall shear stress of a boundary layer flow. All measurement results show good agreement with the theoretical prediction.     

Numerical 2D models of consolidation of dense flocculated suspensions

A mathematical 2D model for a consolidation process of a highly concentrated, flocculated suspension is developed. The suspension is treated as a mixture of a fluid and solid particles by an Eulerian two-phase fluid model. The suspension is characterized by constitutive relations correlating the stresses, interaction forces, and inter-particle forces to concentration and velocity gradients. This results in three empirical material functions: a permeability, a non-Newtonian viscosity and a non-reversible particle interaction pressure. Parameters in the models are fitted to experimental data. A simulation program using finite difference methods both in time and space is applied to one and two dimensional test cases. The effect of different viscosity models as well as the effect of shear on consolidation rate is studied. The results show that a shear thinning viscosity model yields a higher consolidation rate compared to a model that only depends on the volume fraction. It is also concluded that the size of the viscosity influences the time scale of the process and that the expected effect of shear on the process is not weil reproduced with any of the models.     

Viscosity measurement of Newtonian liquids using the complex reflection coefficient

This work presents the implementation of the ultrasonic shear reflectance method for viscosity measurement of Newtonian liquids using wave mode conversion from longitudinal to shear waves and vice versa. The method is based on the measurement of the complex reflection coefficient (magnitude and phase) at a solid-liquid interface. The implemented measurement cell is composed of an ultrasonic transducer, a water buffer, an aluminum prism, a PMMA buffer rod, and a sample chamber. Viscosity measurements were made in the range from 1 to 3.5 MHz for olive oil and for automotive oils (SAE 40, 90, and 250) at 15 and 22.5degC, respectively. Moreover, olive oil and corn oil measurements were conducted in the range from 15 to 30degC at 3.5 and 2.25 MHz, respectively. The ultrasonic measurements, in the case of the less viscous liquids, agree with the results provided by a rotational viscometer, showing Newtonian behavior. In the case of the more viscous liquids, a significant difference was obtained, showing a clear non-Newtonian behavior that cannot be described by the Kelvin-Voigt model.