Showing papers in "Journal of Rheology in 1991"

Wall slip of molten high density polyethylene. I. Sliding plate rheometer studies

Abstract: Experiments were performed in a sliding plate rheometer with a high density polyethylene to determine the conditions for the onset of slip and the relationship between slip velocity and shear stress. It was found that melt slip occurs at a critical shear stress of approximately 0.09 MPa in both steady and transient shear tests. The effect of the presence of a layer of fluorocarbon at the interface on both the slip velocity and the critical shear stress for the onset of slip, was also studied. Exponential shear was used to study the effect of shear history on slip. Both steady state and dynamic models for the slip velocity are proposed that are consistent with the experimental observations. Results of oscillatory shear experiments suggest that melt slip is a physicochemical process in which the polymer–wall interface undergoes continuous change during successive cycles.

Dynamic mechanical studies of electrorheological materials: Moderate frequencies

Abstract: An ER material composed of alumino‐silicate particles in paraffin oil is studied for its response to sinusoidally oscillating shear strains at frequencies in the range of 10–50/s. The response of the material may be discussed in terms of three rheological regions; pre‐yield, yield, and post‐yield. Within each region there is a different mode of deformation; viscoelastic in the pre‐yield, viscoelastic plastic in the yield, and plastic in the post‐yield. The deformation modes are dependent on applied electric field strength, strain amplitude, and strain frequency. Furthermore, the energy dissipated by the ER material is analyzed as related to strain amplitude and electric field. The energy dissipated by the ER material is proportional to the strain raised to the second power when the material is deformed in the pre‐yield region, varies between the strain raised to the second power and raised to the first power during deformation in the yield region, and the energy is proportional to the strain raised to the...

On the viscosity‐concentration dependence of immiscible polymer blends

Abstract: Upon addition of small quantities of a second phase the mixture shows a droplet/matrix structure, changing into a co‐continuous one at the percolation threshold, φc≂0.16. The level of phase co‐continuity reaches a maximum at the phase inversion concentration, φ2I, where the viscosities of a system in which polymer‐1 is dispersed in polymer‐2 and the other where polymer‐2 is dispersed in polymer‐1 are equal. Thus φ1I can be expressed as function of viscosity ratio, λ=η1/η2, with intrinsic viscosity and maximum packing volume fraction as parameters. Next, it was postulated that in immiscible polymer blends the viscosity‐concentration dependence is determined by two mechanisms: an interlayer slip and the emulsionlike viscosity increase culminating at the inversion concentration, φ2I. The derived two‐parameter equation was found to describe the observed η versus φ dependence quite well. The parameters, calculated from the least‐squares regression fit of experimental data to the two‐parameter equation, were fo...

Experimental observations of particle migration in concentrated suspensions: Couette flow

Abstract: Nuclear magnetic resonance (NMR) imaging was used to observe the evolution of radial concentration and velocity profiles of initially well‐mixed concentrated suspensions of spheres in viscous Newtonian liquids undergoing flow between rotating concentric cylinders (wide‐gap, annular Couette flow). In Couette flow, particles migrate from the high shear‐rate region near the inner rotating cylinder to the low shear‐rate region at the outer wall. The particle concentration near the outer wall approaches maximum packing for randomly distributed spheres at steady state, and velocity profiles reveal that the suspension is almost stagnant in these regions. For unimodal suspensions of spheres, the shear‐induced migration of large particles results in concentric two‐dimensional, circular sheets of particles arranged in hexagonal close‐packed arrangements extending inward from the outer wall. This paper examines the functional dependence of particle migration in concentrated suspensions undergoing shear flow in a wid...

The Cox-Merz rule extended: A rheological model for concentrated suspensions and other materials with a yield stress

Abstract: A nonlinear rheological model combining elastic, viscous, and yielding phenomena is developed in order to describe the rheological behavior of materials which exhibit a yield stress. A key feature of the formulation is the incorporation of a recoverable strain; it has a maximum value equal to the critical strain at which the transition from an elastic solid‐like response to a viscous shear thinning response occurs. An analysis is presented to enable determination of all the model parameters solely from dynamic measurements which are easily accessible experimentally. A rigorous correlation, analogous in form to the Cox–Merz rule, is shown to exist between the steady shear viscosity and the complex dynamic viscosity in terms of a newly defined ‘‘effective shear rate.’’ Experimental data obtained for a 70 vol % suspension of silicon particles in polyethylene indicate agreement with theoretical predictions for both the dynamic and steady shear behavior.

Mesoscopic domain theory for textured liquid crystalline polymers

Abstract: Here we present a mesoscopic theory of the low‐flow‐rate rheological properties of textured or polydomain samples of liquid crystalline polymers. In this theory, the Leslie–Ericksen equations are assumed to apply to each domain; these equations are averaged over a spatial region, large compared to a single domain, yet small compared to bulk dimensions. Along with these averaged equations, phenomenological expressions are postulated that allow us to obtain a relatively simple set of coupled equations for the domain size and the mesoscopic orientation and stress tensors. The values of the Leslie–Ericksen viscosities that appear in the equations are obtained from the Doi theory for nematic polymers. We apply the theory to several shear flows, namely recoverable shear after cessation of steady shearing, and step reversal and step increase of shear rate. In each case promising agreement is found between the predictions of the mesoscopic theory and measurements on lyotropic liquid crystalline polymers.

Rheology of extremely shear thickening polymer dispersionsa) (passively viscosity switching fluids)

Abstract: The flow properties of concentrated polymer dispersions which exhibit extreme shear thickening have been investigated in steady and transient shearing flows using various types of rheometers. A phenomenological characterization based on few fluid parameters is proposed and pertinent test modes for their determination are discussed. The dispersions consist of monodisperse, electrostatically stabilized, solid spherical particles (diameter <0.5 μm) dispersed in glycols. They show a reversible steplike viscosity transition of nearly three powers of ten when an apparent critical shear rate γc is exceeded. This jump from a low to a high viscosity state shows typical features of a shear‐rate‐induced phase transition, including hysteresis and the existence of a metastable low viscosity state above γc. The viscosity step can be traced continuously by using stress controlled rheometers. Pronounced fluctuations of the rate of deformation with time are observed at the critical shear rate. The apparent critical shea...

Velocity and concentration measurements of suspensions by nuclear magnetic resonance imaging

Abstract: Nonuniform velocity and concentration distributions have been measured for suspensions of small, negatively buoyant particles flowing in horizontal tubes. All measurements were performed during statistically steady flow conditions with average fluid velocities up to 25 cm/s. The mean particle concentration φs ranged between 0.0≤φs≤0.39. Time‐averaged measurements were recorded noninvasively by using a three‐dimensional, flow‐compensating, nuclear magnetic resonance technique. This method spatially resolves both the fluid velocity and particle concentration distributions from a single imaging experiment and permits detailed analysis of the flow‐induced structure of nondilute suspensions.

NMR flow imaging of fluids and solid suspensions in Poiseuille flow

Abstract: The application of nuclear magnetic resonance (NMR) flow imaging to the study of Poiseuille flows of single‐phase fluids and solid/liquid suspensions is demonstrated and investigated Two fluids were studied: a mixture of a low‐molecular‐weight polyether oil and water which is Newtonian and an aqueous solution of a high‐molecular‐weight polymer which is non‐Newtonian The velocity profiles of these fluids in Poiseuille flow measured by NMR are in excellent agreement with those predicted from viscometric data using a power law model The suspensions investigated consisted of density‐matched compositions of solid poly(methyl methacrylate) beads of various concentrations up to 52% in a Newtonian, polyether‐based liquid At particle loadings above 40% these suspensions exhibited rheological behavior akin to what has been reportedly observed for some solid‐rocket motor propellant compositions NMR‐derived flow velocities of these suspensions at high particle loadings show clear deviations from the Newtonian parabolic behavior and some unusual intensity features which are not yet fully understood The capabilities and limitations of NMR flow imaging as well as considerations for data interpretation in the special case of highly filled suspensions is discussedThe application of nuclear magnetic resonance (NMR) flow imaging to the study of Poiseuille flows of single‐phase fluids and solid/liquid suspensions is demonstrated and investigated Two fluids were studied: a mixture of a low‐molecular‐weight polyether oil and water which is Newtonian and an aqueous solution of a high‐molecular‐weight polymer which is non‐Newtonian The velocity profiles of these fluids in Poiseuille flow measured by NMR are in excellent agreement with those predicted from viscometric data using a power law model The suspensions investigated consisted of density‐matched compositions of solid poly(methyl methacrylate) beads of various concentrations up to 52% in a Newtonian, polyether‐based liquid At particle loadings above 40% these suspensions exhibited rheological behavior akin to what has been reportedly observed for some solid‐rocket motor propellant compositions NMR‐derived flow velocities of these suspensions at high particle loadings show clear deviations from the Newtonian pa

Note: NMR imaging of shear‐induced diffusion and structure in concentrated suspensions undergoing Couette flow

Abstract: This note describes nuclear magnetic resonance (NMR) imaging of two concentrated suspensions undergoing flow between rotating concentric cylinders (wide‐gap, annular Couette flow). Suspensions of both monodisperse (50% by volume) and bidisperse (60% by volume) spheres are studied. We find that particles migrate from the higher shear rate regions near the rotating inner cylinder to the lower shear rate regions near the stationary outer wall, establishing large concentration gradients after only a short time. In addition, the large particles in the bimodal suspension form concentric cylindrical sheets, parallel to the axis of the Couette device, which rotate relative to each other. In the Couette devices used in these studies, no significant axial migration of the particles is observed: the dispersion of particles is almost entirely in the radial direction. This particle migration and structure formation is believed responsible for torque reductions and other anomalous behavior witnessed during rheological ...

ER fluid requirements for automotive devices

Abstract: The requirements necessary for electrorheological fluids to be used in automotive devices are discussed along with the necessary fluid design data. As part of this discussion the following four devices were analyzed assuming three different levels of fluid properties: engine damper, vehicle shock absorber, alternator variable speed drive, and engine accessory variable speed drive. The analysis was done using ‘‘current fluids,’’ ‘‘near term fluids,’’ and ‘‘long range fluids.’’ The feasibility of each device with each fluid level was determined, and, for those cases predicted as unfeasible, methods that could be used to make them feasible are discussed.

The study of the glass transition of glutenin using small amplitude oscillatory rheological measurements and differential scanning calorimetry

Abstract: Hydrated glutenin was studied using mechanical spectrometry and differential scanning calorimetry (DSC). Small amplitude oscillatory measurements showed, as a function of temperature, that hydrated glutenin between 4% and 14% moisture content showed glass transition temperatures between 132 and 22 °C. Over the same moisture range, glutenin samples had glass transitions temperatures between 110 and 21 °C as measured by DSC. Both techniques showed that the glass transition temperature of glutenin shifted to lower temperatures with increasing moisture content. Linear approximations of the glass transition temperatures obtained by DSC vs moisture content showed a depression of about 9 °C/wt. %. Both methods showed that glutenin was very sensitive to the plasticizing effect of water in the moisture range studied and appears to be an amorphous, water plasticizable polymer.

The measurement and description of the yielding behavior of waxy crude oil

Abstract: Statically cooled samples of waxy crude oil possess a complex yielding behavior that cannot be described by existing yield stress fluid models nor by the description and modeling of thixotropic materials. Three distinct characteristics of the yielding process, namely, a solid (Hookean) behavior, a slow deformation (creep), and a sudden failure of the sample that closely resembles the brittle or ductile fracture of solids, have been identified by four different techniques−the vane technique, the cone and plate viscometer (constant rotation), constant stress rheometry, and oscillatory (dynamic) testing. A capillary viscometer or pilot scale pipeline presents technical difficulties which make it unsuitable for investigating the yielding behavior of waxy crude oils. The shear stress at fracture is the value of most interest to pipeline designers and the one most often taken as the yield point. Means of obtaining reproducible yield stress and fracture stress data are discussed.

Viscoelastic behavior among HEUR thickeners

Abstract: The viscoelastic behavior of commerical and model hydrophobically modified, ethoxylated urethane (HEUR) polymers is examined in aqueous solutions, alone and in the presence of sodium dodecylsulfate (SDS). An unmodified poly(oxyethylene) and a linear model HEUR thickener without internal hydrophobes are compared with three commercial HEUR thickeners, one of low molecular weight comparable with the model HEUR and two of higher molecular weight, comparable to the unmodified poly(oxyethylene). Shear thickening in the viscosity‐shear rate profile, storage and loss moduli, die swell, and dynamic uniaxial extensional viscosity behaviors are examined. There is general agreement among the elastic functions for the low molecular weight commercial HEUR which is primarily inelastic and for one of the higher molecular weight commercial HEUR thickeners, which exhibits a strongly elastic behavior. The addition of SDS to aqueous HEUR solutions increases solutionviscosity; in one of the high MW HEUR thickeners this increase is associated with an increase in the elasticity of the solution. In the lower molecular weight HEUR, the increases in solutionviscosity observed with SDS are not associated with a notable change in the elasticity of the solution. The difference in rheological response is interpreted not in terms of ‘‘real’’ molecular weight differences, but in terms of competition between intra‐ and interhydrophobe associations. Other differences are discussed and compared with the rheological response of a low molecular weight model HEUR thickener without internal hydrophobic linkages.

Fiber–fiber interactions in homogeneous flows of nondilute suspensions

Abstract: A theoretical model for calculating the average interfiber spacing in nondilute short fiber suspensions is presented. The approach adopts the Doi–Edwards theory to model spacing between rigid rod‐like polymer molecules to determine the interfiber spacing. Modifications have been introduced to the Doi–Edwards theory in order to obtain accurate estimates of interfiber spacing at all orientation states and for fibers of finite diameter. A parametric study has been conducted to explore the influence of the relevant dimensionless parameters: the fiber volume fraction, the fiber aspect ratio, and the probability distribution function of the fiber orientation state on the average spacing between the fibers. An approach has been suggested to use this spacing to characterize fiber–fiber interactions in flowing suspensions. Numerical predictions of flow‐induced fiber orientation based on this approach are presented.

Rheological properties of copolymer modified polyethylene/polystyrene blends

Abstract: In this study, the effect of hydrogenated styrene butadiene diblock copolymers on the rheological properties of high‐density polyethylene (HDPE)/high impact polystyrene (HIPS) blends is investigated. The blends were prepared in the melt state at 180 °C for 5 min in a batch mixer. The results show that the rheological properties of the blends were very sensitive to the copolymer concentration present in the blend mainly in the low frequency region. At low copolymer content (e.g., 1 wt. %), an important decrease of the zero‐shear viscosity (η0) was observed in the case of HIPS rich blends. For the HDPE rich blends, this decrease was not observed when modified with the pure diblock copolymer. As the copolymer content increases, and depending on the copolymer structure, an increase or a further decrease of η0 was obtained. This behavior was interpreted as due to the change in the copolymer state in the blend, i.e., saturation of the interface and micelles formation. Predictions of an emulsion model of two viscoelastic liquids including an interfacial tension (σ) contribution to the elastic properties were close to the experiments for the 90/10 and 20/80 HDPE/HIPS unmodified blends, but unsatisfactory in the other cases. According to the general features of polymer suspensions and to the predictions of this model, it is concluded that phase interactions as produced by the addition of the copolymer are very important. This aspect must be included in any rheological model for copolymer modified immiscible blends.

Transient shear behavior of a thermotropic liquid crystalline polymer in the nematic state

Abstract: Transient shear experiments show that a thermotropic liquid crystalline polymer (TLCP) in its nematic state behaves linear viscoelastically as long as the shear does not exceed a characteristic stress of 2×104 Pa or a characteristic strain of approximately γ=2, whichever is reached first. The relaxation modes, as determined in dynamic mechanical experiments, are sufficient for describing the linear viscoelastic behavior in step strain and start‐up at constant rate. Beyond this linear region, the behavior deviates drastically from that of conventional homopolymers: Negative first normal stress differences are measured during steady shear at rates below 0.5 s−1; long relaxation modes are more affected in a large step strain experiment than short relaxation modes [thus no factorization of G(t,γ) into separate time and strain functions]; no zero shear viscosity is detected in the accessible range; the normal stress relaxes faster than the shear stress; in a start‐up experiment at constant shear rate, the shear stress and the first normal stress difference both go through a maximum at approximately γ=2. The material, a random copolyester of 73 mol % 4‐hydroxybenzoic acid and 27 mol % 6‐hydroxy‐2‐naphthoic acid (Vectra A900 of Hoechst–Celanese), was shown to be stable at the experimental temperature of 290 °C for at least 1 h if first preheated to 320 °C.

Time‐dependent behavior and wall slip in concentrated shear thickening dispersions

Abstract: The viscosity of concentrated shear thickening dispersions was measured as a function of shear rate, Couette cylinder size, and time. The level of the low shear rate viscosity, which was found to be independent of system size and time, could be predicted by the equation of Frankel and Acrivos. At shear rates above the critical shear rate for shear thickening in highly concentrated (φ≳0.57) dispersions of monodisperse particles strong viscosity instabilities were detected, together with a dependence on cylinder size. The instabilities are attributed to reversible order–disorder transitions, e.g., from strings to clusters. This dependence on cylinder size is due to wall slip, slipping planes in the dispersion, and even plug flow in the gap. With less concentrated or polydisperse dispersions the effects are much less severe but there is thixotropy, probably due to a reordering of the dispersion.

Yield stresses in magnetic suspensions

Abstract: Static yield stresses are measured on magnetic suspensions as a function of the applied magnetic field. Two differents systems are used: One is an aqueous suspension of polystyrene spheres containing iron oxide inclusions and the second one is of ordinary polystyrene spheres dispersed in a ferrofluid. The experimental results are analyzed with the help of a model based on the calculation of forces between two particles in an effective medium. This model is discussed and tested against experimental measurements of forces on centimetric iron spheres placed in a magnetic field.

Determination of the relaxation spectrum from oscillatory shear data

Abstract: In order to use either a linear or nonlinear model of viscoelasticity to calculate the stress response of a material to various deformations, it is usually necessary to have available an explicit equation for the linear relaxation modulus G(t). The most popular procedure is to use the data from a small‐amplitude oscillatory shear experiment to determine the parameters of a generalized Maxwell model. However, this is an ill‐posed problem and is not at all a straightforward curve‐fitting operation. We compare three procedures for determining a set of relaxation times and discrete moduli that can then be used as empirical fitting parameters in fluid mechanics computations. These are linear regression, with and without regularization, and nonlinear regression. Nonlinear regression is found to give a good fit of the data with a minimum number of parameters.

Rheo‐optical studies on aligned nematic solutions of a rodlike polymer

Abstract: Rheo‐optical studies on shear deformation of well‐aligned nematic solutions of the rodlike poly (1,4‐phenylene‐2,6‐benzobisthiazole), PBT, are reported. Conoscopic microscopy was used to follow the director during shear, and during relaxation on cessation of flow. The results show that the molecules are not homogeneously aligned in shearing flow. Rather, various complex director field distortions may occur, depending on the relative orientation of the initial director to the flow direction. The results are compared quantitatively with predictions based on the Ericksen–Leslie constitutive equation for nematic fluids.

A novel simulation method for the quasi‐static mechanics of granular assemblages

Abstract: The following is a description of a new computer‐simulation technique for the quasi‐static particle mechanics of granular media and its application to the dilatant simple shear of periodic 2D arrays of nearly rigid frictional disks. By means of supercomputer implementation, we have investigated the effects of (Coulomb) particle friction and polydispersity on Reynolds dilatancy and plasticity of a granular mass subject to a constant isotropic confining pressure. The simulation employs deforming periodic‐cell boundary conditions, with subcells arranged to reduce the contact‐search effort, together with a quasi‐static motion algorithm which converts an assumed global deformation to a local forcing of particle motion. Nearly identical shearing dilatancy s = deV/dγ is obtained for samples of 56, 132, and 306 polydisperse disks under identical conditions. Our computed dilatancy s=0.81 for the monodisperse assemblage obtained in this study is larger than the Reynolds‐type prediction of 0.5 for isotropic assembla...

Solutions of the constitutive equations for the flow of an electrorheological fluid in radial configurations

Abstract: Analyses are presented of the effect of radial electric field distribution on the performance on an ideal electrorheological fluid in annular film shear and flow rheometers. Influences of the assumed form of yield stress–electric field relationship are shown. For the parabolic case few problems are raised provided the film thickness to radius ratio is small, though some asymmetry is seen in the flow velocity profiles. When the prospect of a barrier or activation voltage threshold is introduced, significant plug flow formation can be encountered. For high field strengths, where the ER effect is most attractive, a relatively uniform shear rate profile is achieved in a Couette viscometer only at higher operating speeds. In both cases the field distribution is taken to be that of a perfect dielectric and the properties of the fluid as a Bingham plastic.

Hydrodynamic lubrication theory for the Bingham plastic flow model

Abstract: When the shear stress magnitude of a Bingham material exceeds the yield shear stress, quasi‐Newtonian flow results, otherwise the material is rigid. The Bingham model has been used in tribology to describe the behavior of greases, but may also be used for electrorheological fluids proposed as ‘‘smart’’ lubricants. For two‐dimensional flow, different modified Reynolds’ equations are obtained, depending on the possible local formation of a rigid core which may be attached to either surface, or float between the surfaces. From the modified Reynolds’ equation it is straightforward to predict bearing behavior, patching together the different core formation cases. Results are presented for two geometries: the squeeze film damper and the journal bearing.

Viscoelastic response of electrorheological fluids. I. Frequency dependence

Abstract: We calculate the linear frequency‐dependent modulus of a model electrorheological (ER) fluid at low and intermediate concentrations, assuming that particle strings are the dominant structures. At low concentrations hydrodynamic interactions along a single string act to reduce the dissipation of modes with low wave number (just as in the case of random‐coil polymers). At higher concentrations we expect hydrodynamic screening to be effective. This results in a dissipative part to the modulus. G ‘(ω) which has a broad plateau over a frequency bandwidth (L/a)2, where L is the characteristic string length and a of the order of the particle size. By contrast, the magnitude of G ‘(ω) is limited by the fraction of incomplete or broken strings. The real part of the dynamic modulus G ’(ω) is dominated by strings which span the electrodes, and shows very little structure with frequency when the majority of strings are complete.

The temperature dependence of the electrical properties and strength of electrorheological fluids

Abstract: Electrical and rheological properties were determined at 25–160 °C for an electrorheological fluid consisting of 20 vol % zeolite particles (containing 8 wt % water) in silicone oil. A model is proposed which explains the mechanical response in terms of the dielectric mismatch between the particles and the carrier fluid and a local concentration of the electric field. Thermal activation analysis of the data suggests that the temperature dependence of the electrical conductivity of the fluid reflects the diffusion of the Na+ ions in the zeolite particles. It is not clear whether the temperature dependence of the shear stress and the dielectric constant of the particles represents an equilibrium or kinetic process.

Transient and steady rheological behavior of the thermotropic liquid crystal copolymer 73/27 HBA/HNA

Abstract: Transient and steady rheological measurements of shear and normal stresses are reported for a liquid crystal copolymer of 73 hydroxybenzoic acid/27 hydroxynaphthoic acid. Dynamic time sweeps indicate a sensitiveness of the rheological parameters to thermal history, probably related to polymerization phenomena. In the shear rate range 0.1–1 s−1 at T=310 °C the normalized stress overshoots vs strain curves nearly superpose. The steady values of the viscosity seem to follow the three region scheme of Onogi and Asada. The steady values of the first normal stress difference are positive in all the shear rate range analyzed. Constant stress measurements are also reported to prove that the low shear rate data are not significantly affected by the polymerization phenomena. Moreover, the constant stress data show that a true yield stress cannot be detected in the LCP studied.

The influence of materials of construction on biconical rotor and capillary measurements of shear viscosity of rubber and its compounds and considerations of slippage

Abstract: An experimental study is presented of the flow of elastomers and their compounds in biconical and capillary geometries using rotors and capillaries produced from different materials including aluminum, brass, copper, steel, and stainless steel plus polytetrafluorethylene (PTFE). The rotational rheometer could be operated at various controlled pressure levels. A butadiene–styrene copolymer (SBR) was investigated as well as an SBR compound with 20 vol % carbon black and a second SBR compound with 7% zinc stearate added. It was found in the pressurized rheometer, when the pressure was greater than 0.2 MPa, that the data for SBR and SBR–carbon black was essentially the same for smooth and grooved rotors fabricated from different metals. However when the pressure was reduced the torques were substantially reduced and the data for the grooved rotors were higher than for the smooth rotors. Generally, the copper and brass gave rise to higher shear stresses than the steel or stainless steel. The PTFE yielded the l...

High frequency dynamic mechanical study of an aluminosilicate electrorheological material

Abstract: An electrorheological (ER) material composed of aluminosilicate particles in paraffin oil is studied for its response to sinusoidally oscillating shear strains of frequencies in the range of 300–400 rad/s. The response of the material is linear viscoelastic when subjected to electric fields in the range of 0.0–3.0 kV/mm. The linear viscoelastic parameters−shear loss modulus, shear storage modulus, and loss tangent−were calculated and related to the strength of the field applied to the material. The moduli were found to increase with increasing applied field and the loss tangent decreased with increasing applied field. Finally, a nonlinear data correlator program was used to simulate the ER material’s shear loss modulus as a function of frequency when modeling the ER material using the constitutive equations for a three‐parameter solid.

A constitutive equation for the viscosity of stored red cell suspensions: Effect of hematocrit, shear rate, and suspending phase

Abstract: Despite the extensive previous work on the viscosity of red blood cell suspensions, experimental data at very high cell concentrations are limited and scattered, and available constitutive equations for the steady‐state viscosity are unsuitable for numerical calculations that require accurate well‐behaved analytical expressions valid over a wide range of shear rates and which include these very high cell concentrations. The steady‐state viscosity of suspensions of stored red blood cells in both saline and plasma were measured in a coaxial cylinder viscometer at shear rates ranging from below 1–300 s−1 and at cell volume fractions up to 0.98. Emphasis was placed on the evaluation of viscosity at very high cell concentrations because of the lack of available data in this regime and its importance in understanding and modeling cross‐flow microfiltration of red cell suspensions, the application which motivated the current study. This data base was supplemented by additional measurements previously reported in...