Measuring static yield stress of electrorheological fluids using the slotted plate device

An electrorheological (ER) response is defined as the dramatic change in rheological properties of a suspension of small particles due to the application of a large electric field transverse to the direction of flow. ER fluids are typically composed of nonconducting or semiconducting particles dispersed in a nonconducting continuous phase. A sufficiently large electric field will cause ER fluids to solidify, giving rising to a yield stress. Many applications in torque and stress transfer devices were proposed employing the reversible yielding behavior of ER fluids. Successful applications depend on a large yield stress of ER fluids and therefore accurate measurements of the yield stress of ER fluids are required. Reported experimental yield stresses of ER fluids have been dynamic yield stresses obtained by extrapolating the shear stress–shear rate data to zero-shear rate. It would be very helpful to the understanding of ER behaviors and the applications of ER fluids to be able to measure the static yield stress of ER fluids accurately. The slotted plate technique has been shown to be a successful method to determine the static yield stress of suspensions. The values obtained via the slotted plate method are static yield stress as the platform is designed for extremely low-speed motion. In this study, we modified the slotted plate device for the application of large electric fields and measured the static yield stress of TiO₂ ER fluids under various electric fields. The measured static yield stress values are also compared with the static yield stress values from a commercial rheometer.     

Viscoelastic plastic rheological model for particle filled polymer melts

A viscoelastic plastic model for suspension of small particles in polymer melts has been developed. In this model, the total stress is assumed to be the sum of stress in the polymer matrix and the filler network. A nonlinear viscoelastic model along with a yield criterion were used to represent the stresses in the polymer matrix and the filler network, respectively. The yield function is defined in terms of differential equations with an internal parameter. The internal parameter models the evolution of structure changes during floc rupture and restoration. The theoretical results were obtained for steady and oscillatory shear flow and compared with experimental data for particle filled thermoplastic melt. The experimental data included the steady state shear strress over a wide range of shear rates, the transient stress in a start up shear flow, stress relaxation after cessation of a steady state shear flow, the step shear and the oscillatory shear flow at various amplitudes.     

用电化学方法测试动脉模型壁面剪应力

应用电化学方法,对动脉模型Ｔ型分叉部位流场壁面剪应力进行测试研究。测试了对于现有理论分析和数值计算都比较困难的高雷诺数（ＲＥ＝１０００－２０００）流动流场的壁面剪应力,并且对苦干不同雷诺数及不同支管分流情况进行了系列测试。通过实验发现,此部痊同时存在高剪应力区和低剪应力区,确定了它们的位置和剪应力的大上。系列测试还显示：随着雷诺数的变化,无量纲管应力有一定的变化;而当支管分流变化时,无量纲剪应力的     

Determination of yield stress fluid behaviour from inclined plane test

The aim of this paper is to determine precisely under which conditions an inclined plane can be used as a rheometer, which could represent a practical and rapid technique for various types of industrial or natural viscoplastic coarse suspensions. We first examine its efficiency and relevancy for determining fluid yield stress in a straight way by measuring the deepest fluid layer able to stay on the inclined plane. We have made experiments with different materials (clay-water suspensions) whose yield stress ranged from 35 to 90 Pa, using 1 m long open rectangular channels with a slope ranging from 10 to 30° and a width ranging from 5 to 25 cm. Our procedure involved measuring the final fluid depth far from edges a long time after the end of the slow gravity-induced emptying of a dam placed upstream. The fluid yield stress was also estimated independently by fitting a Herschel-Bulkley model to simple shear rheometry data obtained within a relatively wide shear rate range. A good agreement between inclined rectangular channel tests and independent usual rheometrical tests is obtained even for aspect ratios (flow depth to channel width ratio) as large as 1 when one assumes that, when the fluid has stopped, the side and bottom wall shear stresses are equal to the fluid yield stress. These results prove the efficiency of the inclined plane test for determining yield stress when appropriate experimental precautions are taken for both tests. In addition we examine the possibility of determining the simple shear flow curve of a mud suspension from fluid depth, velocity and discharge measurements of different steady flows in a wide open channel (8 m long; 60 cm wide) equipped with a recirculating system. The results obtained from inclined plane tests are in good agreement with independent rheometrical data (with torsional geometries). However it is technically difficult to cover a wide shear rate range from the inclined plane technique since this requires a rather wide channel flow rate range.     

Characterization of yield stress fluids with concentric cylinder viscometers

The methods normally employed for shear rate calculations from concentric cylinder viscometer data generally are not applicable for fluids with a yield stress. In cylindrical systems with large radius ratios, as usually is the case with suspensions, the yield stress induces two possible flow regimes in the annulus. Unless the yield value is exceeded everywhere in the gap only part of the fluid can be sheared while the remaining region behaves like a solid plug. A correct calculation of the shear rate must take into account the presence of a variable effective gap width determined by the extent of the sheared layer. For time-independent yield stress fluids, a two-step procedure, which does not require any specific flow model, is proposed for analysing the experimental torque-speed data. Under the partially sheared condition, the shear rate can be computed exactly, whereas for the fully sheared flow the Krieger and Elrod approximation is satisfactory. The method is assessed by examining both semi-ideal data generated with a Casson fluid with known properties, and experimental data with an industrial suspension. A more complicated problem associated with characterization of time-dependent yield stress fluids is also identified and discussed. An approximate procedure is used to illustrate the dependence of the shear rate on time of shear in constant-speed experiments.     

An experimental investigation into the kinematics of a concentrated hard-sphere colloidal suspension during Hopkinson bar evaluation at high stresses

The behavior of a concentrated, hard-sphere colloidal suspension is evaluated using the split Hopkinson pressure bar (SHPB) experimental technique. The composition of the suspension is measured using thermograviometric analysis before and after loading. This, combined with recorded pressure distributions, result in the conclusion that the suspension undergoes high rate squeezing flow. Experimental results demonstrate that the suspension exhibits shear thickening consistent with that observed in standard rotational rheometry. At sufficiently high stresses the suspension exhibits a second regime of shear thinning behavior that is consistent with elastohydrodynamic theory that incorporates the shear modulus of the particles themselves. Further increases in stress result in irreversible behavior, i.e., rather than fracturing or crushing, the particles form non-reversible agglomerates during testing. This fact is demonstrated through the use of dynamic light scattering and electron microscopy. This behavior occurs within a regime of viscous material response which is seen to occur at normal strain rates and stresses over 10⁴ s^?1 and 40 MPa, respectively.     

Rheo-PIV of a yield-stress fluid in a capillary with slip at the wall

An analysis of the yielding and flow behavior of a model yield-stress fluid, 0.2 wt% Carbopol gel, in a capillary with slip at the wall has been carried out in the present work. For this, a study of the flow kinematics in a capillary rheometer was performed with a two-dimensional particle image velocimetry (PIV) system. Besides, a stress-controlled rotational rheometer with a vane rotor was used as an independent way to measure the yield stress. The results in this work show that in the limit of resolution of the PIV technique, the flow behavior agrees with the existence of a yield stress, but there is a smooth solid?Cliquid transition in the capillary flow curve, which complicates the determination of the yield stress from rheometrical data. This complication, however, is overcome by using the solely velocity profiles and the measured wall shear stresses, from which the yield-stress value is reliably determined. The main details of the kinematics in the presence of slip were all captured during the experiments, namely, a purely plug flow before yielding, the solid?Cliquid transition, as well as the behavior under flow, respectively. Finally, it was found that the slip velocity increases in a power-law way with the shear stress.     

Magnetorheology in viscoplastic media

Suspensions of iron particles in media with yield stresses were investigated to determine the effect of the continuous phase yield stress on the magnetorheological (MR) response. The steady-shear MR response was independent of the continuous phase yield stress for yield stresses in the range 0.9–37 Pa. The field-induced suspension yield stress increased sub-quadratically with the flux density. The small amplitude oscillatory shear response exhibited history dependence. The storage modulus depended not only on the magnitude of the applied magnetic field, but also on its history. This history dependence can be explained in terms of the field-dependent evolution of the suspension microstructure. Received: 24 February 1999 Accepted: 12 July 1999     

On the mechanical properties of soil as they affect traction

In order to explore some of the controversies encountered in soil testing, the author conducted numerous tests with the purpose of determining soil shear strength and the factors influencing it. Five different representative soil types were used, and the influence of void ration and moisture content on cohesion and internal friction was examined. A suitable parameter employed in soil physics was found by means of which the measured mechanical characteristics were arranged into a multi-variable system. The author determined that the interpretation of their meaning contradict the classical soil mechanics definition of shear stresses. The contradiction is eliminated by the author's new interpretation of the shear diagram which is in consonance with the tenets of classical soil mechanics.     

Shear and squeeze rheometry of suspensions of magnetic polymerized chains

We present the first experimental results on the magnetorheology of suspensions of non-Brownian magnetic ellipsoidal particles. These particles are made of spherical iron particles linked by polymers and are called polymerized chains. Steady shear, oscillatory shear, and oscillatory squeeze rheological tests have been performed. The rheological properties of the suspension of polymerized chains have been compared with those of the suspension of spherical iron particles. In shear flow, both suspensions develop nearly the same yield stress, while in squeeze flow, the yield stress is several times higher for the suspension of polymerized chains. We show that the squeezing force of a suspension of spherical particles is an increasing function of the magnetic field intensity at low magnetic fields but decreases dramatically at higher fields. Surprisingly, this phenomenon, attributed to cavitation or air entrainment, does not occur in the suspension of polymerized chains.     

Numerical study of particulate suspension flow through wavy‐walled channels

The particulate suspension flow in a channel whose walls describe a travelling wave motion is examined numerically. A perturbation method is employed and the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first‐order perturbation quantities are numerically determined by solving the governing system of ordinary differential equations by shooting technique. The present approach does not impose any restriction on the Reynolds number of the flow and the wave number and frequency of the wavy‐walled channel, although it is limited by the linear analysis. The wall shear stress and the positions of flow separation and reattachment points are computed and the influence of the volume fraction density of the particles is examined. The variations of velocity and pressure of the particulate suspension flow with frequency of excitation are also presented. Copyright © 2005 John Wiley & Sons, Ltd.     

颗粒增强复合材料的屈服极限

基于渐近均匀化方法,导出了颗粒增强复合材料的屈服准则,给出了初始屈服应力的解析表达式。因为颗粒增强体的弹性模量远比弹塑性基体的弹性模量高,这个模量差在增强体和基体中产生了装配刚度。解局部问题可以得到该装配刚度。从屈服应力的表达式可以看出,增强体和基体两者的平均装配刚度和剪切模量之比决定了屈服应力的提高程度。给出了两个数值算例。采用菱形十二面体单胞求解了局部问题。取单胞形状为菱形十二面体的优点是增强体的体积比可以高达74%。     

Finite deformation crack-line fields in a thin elasto-plastic sheet

Finite deformation in the crack-tip zone of plastic deformation is investigated for Mode-I opening of a crack in a thin sheet of elasto-plastic material. The material obeys the von Mises yield criterion in the true stresses, and the stretching tensor satisfies a flow law of the Prandtl-Reuss type. Incompressibility and a state of generalized plane stress are assumed. It is assumed that linearized elasticity applies outside the zone of plastic deformation. On the crack-line between the crack-tip and the elastic—plastic boundary, two distinct regions have been recognized: the near-tip zone and the intermediate region. In the near-tip zone the fields are controlled by the radius of curvature of the blunted crack-tip. Here the stress field has been approximated by classical plane stress results. It has been assumed that the crack-line stresses may be taken as uniform in the intermediate region. In each region, deformation variables have been determined by the use of the constitutive relations, and the results have been matched to the corresponding quantities in the neighboring region(s). In this manner expressions have been constructed for the deformation gradients on the crack-line, in terms of the distance to the crack-tip in the deformed configuration, the yield stress in shear, and the stress intensity factor of linear elastic fracture mechanics.     

Quiescent and shear-induced crystallization of polyprophylenes

In this paper, the effect of shear on the flow-induced crystallization (FIC) of several polypropylenes of various macrostructures was studied using rheometry combined with polarized microscopy. Generally, an increase in strain and strain rate or decrease of temperature is found to decrease the thermodynamic barrier for crystal formation and thus enhancing crystallization kinetics at temperatures between the melting and crystallization points. Secondly, popular models based on suspension theory which are used to relate the degree of crystallinity to normalized rheological functions (such as viscosity) are validated experimentally. For this purpose, the space filling of crystals in the polarized micrographs determined from image processing was plotted as a function of normalized viscosity under various shear rates. It is found that the constant(s) of various suspension models should be dependent on the flow parameters in order for the suspension models to describe the effect of shear on FIC, particularly at higher shear rates.     

Effect of void fraction and friction factor models on the prediction of pressure drop of R134a during downward condensation in a vertical tube

The theoretical flow models of homogeneous and separated flow are applied to in-tube condensation to predict the pressure drop characteristics of R134a. The homogeneous flow model is modified by ten different dynamic viscosity correlations and various alternative correlations of total, frictional and momentum pressure drops to take account of the partial condensation inside the tube. Numerical analyses were performed to determine the average and local homogeneous wall shear stresses and friction factors by means of a CFD program. The equivalent Reynolds number model is modified by six different two-phase friction factors to determine the total condensation pressure drop in the separated flow model. The refrigerant side total pressure drops, frictional pressure drops, friction factors and wall shear stresses are determined within a ±30% error band. The importance of using the alternative total, momentum and frictional pressure drop correlations for the homogeneous flow model is also shown.     

Extensional rheology of concentrated poly(ethylene oxide) solutions

The shear and extensional rheology of three concentrated poly(ethylene oxide) solutions is examined. Shear theology including steady shear viscosity, normal stress difference and linear viscoelastic material functions all collapse onto master curves independent of concentration and temperature. Extensional flow experiments are performed in fiber spinning and opposed nozzles geometries. The concentration dependence of extensional behavior measured using both techniques is presented. The zero-shear viscosity and apparent extensional viscosities measured with both extensional rheometers exhibit a power law dependence with polymer concentration. Strain hardening in the fiber spinning device is found to be of similar magnitude for all test fluids, irrespective of strain rate. The opposed nozzle device measures an apparent extensional viscosity which is one order of magnitude smaller than the value determined with the fiber spinline device. This could be attributed to errors caused by shear, dynamic pressure, and the relatively small strains developed in the opposed nozzle device. This instrument cannot measure local kinematics or stresses, but averages these values over the non-homogenous flow field. These results show that it is not possible to measure the extensional viscosity of non-Newtonian and shear thinning fluids with this device. Fiber spin-line experiments are coupled with a momentum balance and constitutive model to predict stress growth and diameter profiles. A one-mode Giesekus model accurately captures the plateau values of steady and dynamic shear properties, but fails to capture the gradual shear thinning of viscosity. Giesekus model parameters determined from shear rheology are not capable of quantitatively predicting fiber spinline kinematics. However, model parameters fit to a single spinline experiment accurately predict stress growth behavior for different applied spinline tensions.     

Elastico-viscous squeeze films: Part 3. the torsional-balance rheometer

The observation made in Part 2 that squeezing flow with a superimposed rotation results in an equilibrium situation with the applied load just balancing the normal stresses generated in the test fluid is used to develop a new technique (the Torsional-Balance Rheometer) for measuring the viscometric functions of elastic liquids.The Rheometer utilizes conventional torsional flow and its novel feature is that the applied load is fixed and the associated shear rate at the rim determined, in contrast to the usual situation where the shear rate is fixed and the total normal force measured.It is argued that the Torsional Balance has significant advantages over other rheometers in the very high shear-rate range, since the normal stresses being measured themselves supply a mechanism for keeping the top plate (which is free to float on the test fluid) at a constant separation from the rotating bottom plate, hence allowing very small gaps to be considered. Consistent data are shown to be possible for shear rates in excess of 10⁵ s^?1.     

A cell model theory of the shear viscosity of a concentrated suspension of interacting spheres in a non-Newtonian fluid

A theoretical approach to the shear viscosity of concentrated suspensions of small particles in a non-Newtonian fluid has been developed using a cell theory model involving particle-particle interaction. The cell theory of Frankel and Acrivos was first generalized to power-law fluid matrices without particle interaction. Particle-particle interaction was then taken into consideration. The theory suggests that the flow behavior of such systems at low shear rates is chiefly dependent upon non-hydrodynamics interparticle interaction such as van der Waals—London and electrostatic forces which induce flocculation and yield stresses. The flow properties at high shear rates are determined by hydrodynamics interaction essentially dependent upon particle concentration and shape.     

Non-linear viscoelasticity and temporal behavior of typical yield stress fluids: Carbopol, Xanthan and Ketchup

The viscoelastic properties of yield stress fluids are difficult to measure outside the linear viscoelastic regime, in particular above their yield stress. These properties are investigated for several common yield stress fluids using inertio-elastic oscillations. From this coupling between the instrument’s inertia and the viscoelasticity of the materials, the complete simple shear rheology can be determined, including viscoelasticity under flow. Findings show that the tested materials have an almost constant elasticity below and above the yield stress, even for applied stresses several times larger than the yield stress. Moreover, the temporal behavior of the materials is unambiguously determined. Concentrated Xanthan is shown to be thixotropic, while Ketchup mainly shows retarded viscoelasticity. Carbopol does not show long-term temporal dependance but apparently exhibits fracturation.     

Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.