Showing papers in "Journal of Rheology in 1988"
TL;DR: In this article, the authors present a new analysis of the Couette geometry that requires only two measurements rather than the three used by Mooney, and demonstrate the experimental data on a clay suspension and oil-in-water emulsion.
Abstract: Often for slurries, gels, emulsions, and foams inhomogeneous fluid properties at solid boundaries create “apparent wall slip.” The reduced fluid viscosity at the boundary creates a thin layer of fluid having a large velocity gradient that can be treated as a “slipping layer”. In measurements of fluid viscosity it is necessary to correct for wall slip to determine the true deformation experienced by the bulk of the sample and the true viscosity. The classic earlier techniques for capillaries and Couette geometries were first presented by Mooney. We present a new analysis of the Couette geometry that requires only two measurements rather than the three used by Mooney. We also present a new analysis for flow between rotating parallel disks. The parallel disk geometry has several experimental advantages for measuring fluid viscosities in the presence of wall slip. The analysis of experimental data on a clay suspension and oil‐in‐water emulsion are presented to demonstrate these new techniques.
494 citations
TL;DR: In this paper, a fundamental investigation of the influence of particulate and matrix properties on the shear viscosity, primary normal stress coefficient, dynamic viscosities, and storage modulus of composite systems was undertaken.
Abstract: A fundamental investigation of the influence of particulate and matrix properties on the shear viscosity, primary normal stress coefficient, dynamic viscosity, and storage modulus of composite systems was undertaken. As expected, all four rheological properties were observed to increase upon addition of solid particulates and some of the composite systems exhibited a yield stress. The present research showed that a new equation obtained by a phenomenological modification of the Tanaka and White model allowed the a priori prediction of suspensionviscosity for shear‐thinning systems as a function of matrix properties, volume fraction of particulates, and shear rate. It also provided the flexibility of describing suspensionviscosity of systems exhibiting an apparent yield stress. Investigation of the other rheological properties showed that a form of the Kitano et al. expression could describe the relative primary normal stress coefficient and the relative storage modulus; whereas, a form of the Chong et al. expression could describe the relative dynamic viscosity of the various composite systems.
238 citations
TL;DR: In this paper, a method is described for generating reproducible and stable foam capable of retaining its structure for prolonged times. But the experimental study of foam is complicated by its inherently unstable nature and the presence of a liquid film slip layer at the wall.
Abstract: The experimental study of foam is complicated by its inherently unstable nature and by the presence of a liquid film slip layer at the wall. A method is described for generating reproducible and stable foam capable of retaining its structure for prolonged times. An experimental technique has also been devised which eliminates problems associated with wall slippage and allows measurement of material functions without use of any empiricisms for the wall region. In a steady‐shear flow, foam behaves like a Bingham plastic with a viscosity inversely proportional to shear rate indicating the presence of a yield stress τ0. The value of the viscosity, which is significantly higher than the parent liquid viscosity, is an increasing function of gas volume fraction φ. Yield stress values obtained by extrapolating viscosity versus shear stress data agree with direct τ0 measurements obtained by using a stress relaxation technique. The yield stress is also found to increase with φ. Small amplitude oscillatory shearing ...
187 citations
TL;DR: In this article, the authors investigated the influence of a bimodal size distribution of particulates on the shear viscosity, primary normal stress coefficient, dynamic viscoity, and storage modulus of filled polymeric systems.
Abstract: An investigation was undertaken to study the influence of a bimodal size distribution of particulates on the shear viscosity, primary normal stress coefficient, dynamic viscosity, and storage modulus of filled polymeric systems. As expected, all four rheological properties of the composite systems with a bimodal size distribution of solids were reduced in comparison to the properties of the composite systems with a unimodal size distribution of particulates. In addition, the maximum packing fraction was increased when the modality of the solids mixtures was increased. The present research effort showed that a design equation given by Ouchiyama and Tanaka and used by Gupta and Seshadri allows the a priori prediction of the maximum packing parameter as a function of particle size and size distribution. Consequently, it was possible to calculate an optimum reduction of rheological properties due to a bimodal size distribution of particulates that was in agreement with experimental results.
127 citations
95 citations
TL;DR: In this paper, a numerical study is performed to resolve the impact of the fluid mechanics of mold filling on the molecular orientation of the final part, as reflected in available birefringence measurements.
Abstract: A complex molecular orientation distribution is observed in the injection molding of amorphous polymers. A major contribution is due to the flow‐induced deformation of the polymer molecules during mold filling and incomplete relaxation during cooling, after cessation of flow. In this work a numerical study is undertaken in an effort to resolve the impact of the fluid mechanics of mold filling on the molecular orientation of the final part, as reflected in available birefringence measurements. Viscoelasticity of the polymer melt is accounted for with the multimode Leonov model. A finite‐element solution of the fountain flow problem is obtained and the effect of the flow field on the deformation experienced by the fluid is elucidated. Frozen‐in stresses are calculated based only on material parameters and processing conditions. Predicted birefringence distributions agree well with published experimental results.
94 citations
TL;DR: The K•BKZ constitutive model is now 25 years old as mentioned in this paper and the connections of the model and its variants with continuum mechanics, molecular theory, and experiment are reviewed.
Abstract: The K‐BKZ constitutive model is now 25 years old. The article reviews the connections of the model and its variants with continuum mechanics, molecular theory, and experiment. An application of this type of model to computation is mentioned.
81 citations
TL;DR: In the presence of glissement, the viscosite apparente peut etre nettement inferieure a la viscosite reelle as mentioned in this paper, e.g.
Abstract: En presence de glissement la viscosite apparente peut etre nettement inferieure a la viscosite reelle. On essaie de determiner si un glissement a lieu d'apres les formes d'ondes de contrainte dans des mesures de cisaillement dynamique oscillatoire
67 citations
TL;DR: In this article, the authors present the results of a study of the mechanisms that account for the pseudoplastic behavior of a concentrated suspension of noncolloidal particles, which is correlated with the calculated Hamaker constant for interparticular van der Waals attraction.
Abstract: This article presents the results of a study of the mechanisms that account for the pseudoplastic behavior of a concentrated suspension of noncolloidal particles. Specifically, the measured flow behavior index of the suspension is correlated with the calculated Hamaker constant for interparticular van der Waals attraction. As the interparticular attraction increases, the number of aggregated particles increases. In turn, the number of aggregated particles decreases as the shear rate increases. As a result, unless the interparticular attraction is negligible, the concentrated suspension is pseudoplastic at low and moderate shear rates, but becomes Newtonian at high shear rates when the hydrodynamic force predominates. The measured viscosities both for high shear Newtonian limits of polystyrene suspensions and for the Newtonian suspensions of glass beads in silicone oil are in excellent agreement with the predicted values of the rigid sphere model for colloidal suspensions. In addition, we found that while ...
53 citations
TL;DR: In this paper, stress relaxation behavior of concentrated solutions of high molecular weight polystyrene following a step shear strain is studied using both mechanical and optical birefringence techniques. But the results do not conform to the Lodge-Meissner relationship, especially at long times, suggesting the formation of regions in which imposed strain is not homogeneously distributed.
Abstract: Stress relaxation behavior of concentrated solutions of high molecular weight polystyrene following a step shear strain is studied using both mechanical and optical birefringence techniques. Using the stress‐optic law, which we find to be valid for our solutions, we obtain time‐dependent shear stress and first normal stress difference values from birefringence measurement that are free of transducer compliance effects. Similar to the previously reported experimental observations of Fukuda, Osaki and Kurata, we obtain unusually low values for nonlinear shear moduli, much lower than the predictions of Doi‐Edwards model, for the sample with more than about 60 entanglements per molecule. Moreover, the shear stress and first normal stress difference data measured on this sample do not conform to the Lodge‐Meissner relationship, especially at long times, suggesting the formation of regions in which the imposed strain is not homogeneously distributed.
52 citations
TL;DR: In this paper, the authors used the simulation program of Kermode and Weaire to calculate stress-strain curves for a number of samples of two-dimensional foam under extensional shear (planar extension).
Abstract: Using the simulation program of Kermode and Weaire, we have calculated stress‐strain curves for a number of samples of two‐dimensional foam, under extensional shear (planar extension). The elastic constant takes a value close to that of the ideal hexagonal foam (with the same mean cell area) for all the samples studied. Similarly the plastic behavior shows only slight variation among reasonable disordered structures. Stress increases monotonically with strain, with an asymptotic yield stress of the same order as the values calculated by Kermode and Weaire for the hexagonal structure. The stress‐strain relationship is therefore roughly represented by a hyperbolic tangent function.
TL;DR: In this article, the reattachment length and eddy intensity in planar and axisymmetric abrupt expansions are correlated with Reynolds number and dimensionless yield stress for Bingham and Casson materials.
Abstract: Solutions are obtained for steady‐state low Reynolds number flow of viscoplastic materials in systems with recirculating eddies using the finite‐element method. The reattachment length and eddy intensity in planar and axisymmetric abrupt expansions are correlated with Reynolds number and dimensionless yield stress for Bingham and Casson materials. Flow in a stenosis is examined using Newtonian and Casson constitutive relationships. The separation zones in a 180 degree planar bifurcation with straight and bent inlets are compared for Bingham and Newtonian fluids. The results show that the size and strength of recirculation is reduced for viscoplastic materials.
TL;DR: In this paper, the extent of fiber generation and dissipation is related to the coating's dynamic uniaxial extensional viscosity (DUEV), and the extensional behavior of polymer solutions varying in segmental and conformational rigidity is examined as a means of delineating the complexities.
Abstract: Rib and web growth leading to fiber generation and dissipation—to spatter in waterborne latex coatings and to misting in water‐reducible coatings—in roll applications are discussed. The extent of growth and dissipation phenomena are related to the coating's dynamic uniaxial extensional viscosity (DUEV). Complexities in the analysis include limitations in DUEV determinations via the fiber‐suction technique, variations in maximum shear and extension rates in roll application, and the relative contribution of the shear viscosifying component to the magnitude of DUEV data. The extensional behavior of polymer solutions varying in segmental and conformational rigidity are examined as a means of delineating the complexities.
TL;DR: The importance of dynamic uniaxial extensional viscosities (DUEVs) relative to shear viscosity and viscoelastic parameters in the onset of ribbing, web growth, and fiber formation in roll application is illustrated with water-soluble polymer blends.
Abstract: The importance of dynamic uniaxial extensional viscosities (DUEVs) relative to shear viscosity and viscoelastic parameters in the onset of ribbing, web growth, and fiber formation in roll application is illustrated with water‐soluble polymer blends. The blends consist of variable component ratios of high‐molecular‐weight, water‐soluble polymers of different segmental rigidities. The blends provide non‐Newtonian aqueous solutions varying in dynamic uniaxial extensional viscosities, but with identical shear viscosities at a given shear rate over a 104 s−1 range. As the DUEV of these “same‐shear viscosity,” non‐Newtonian fluids is increased an earlier onset of ribbing is observed. After onset, a decrease in the number of ribs is observed with increasing DUEV of the fluid; the decrease is associated with growth in web size. Increasing the radius of the roll effects an earlier onset of ribbing, but the number of ribs formed at higher peripheral velocities and smaller nip spacings decreases relative to smaller ...
TL;DR: In this article, a dilute polymer solution is modeled by linear and nonlinear dumbbells suspended in a Newtonian solvent and the Langevin equations governing the motion of the dumbbell in the tube are solved with the help of Brownian dynamics simulations consistent with the momentum balance equation.
Abstract: A dilute polymer solution is modeled by linear and nonlinear dumbbells suspended in a Newtonian solvent. The Langevin equations governing the motion of the dumbbells in the tube are solved with the help of Brownian dynamics simulations consistent with the momentum balance equation. To this purpose a previously presented consistent numerical approach has to be specialized to tube flow. The models show typical features as the slip effect, the flow enhancement, and the reduction in viscosity with decreasing tube radius.
TL;DR: In this paper, exit pressure measurements were performed for three low-density polyethylene melts for a shear rate range of 1-350 reciprocal seconds, and the measured pressure profiles were fit by both linear and quadratic functions.
Abstract: Exit pressure experiments are performed for three low‐density polyethylene melts. Viscosity and exit pressure data are obtained for a shear rate range of 1–350 reciprocal seconds. The measured pressure profiles are fit by both linear and quadratic functions. Extrapolation of the linear pressure profiles yields negative exit pressures which increase in magnitude with shear rate or shear stress. Extrapolation of the quadratic pressure profiles yields small, positive values for the exit pressures. The curvature in the pressure profiles is attributed to the pressure dependence of viscosity. If the data from quadratic pressure profiles is analyzed using the exit pressure theory the estimation of first normal stress difference agrees with independent measurements for shear rates as high as 100 s−1.
TL;DR: In this paper, material functions of two engineering plastics were characterized, including the shear viscosity, first normal stress coefficient, storage and loss moduli, growth and relaxation of shear stress, and normal stress coefficients and relaxation moduli.
Abstract: Material functions of two engineering plastics [a poly(phenylene ether) and a poly(ether imide)] were characterized, including the shear viscosity, first normal stress coefficient, storage and loss moduli, growth and relaxation of shear stress, and first normal stress coefficient and relaxation moduli. The oscillatory shear and relaxation moduli data were employed to determine the temperature‐dependent parameters of Wagner model. Various material functions, which were determined on the basis of this model in conjunction with the fitted parameters agreed reasonably well with the experimental results. The reported data and parameters should facilitate a better understanding of the processability characteristics of these two engineering plastics.
TL;DR: In this article, the authors derived an exact asymptotic expression for the first normal stress coefficient for rigid dumbbells with Oseen-Burgers hydrodynamic interaction.
Abstract: Both Hinch and Leal and Stewart and Sorensen solved the diffusion equation for the configurational distribution function of rigid dumbbells at high shear rates by several different numerical methods and obtained asymptotic expressions for the viscometric functions. In this note we have considered only a contracted distribution function which, however, can be calculated analytically. This contracted distribution function not only contains interesting information about the behavior of rigid dumbbells at high shear rates but can also be used to find an exact asymptotic expression for the first normal‐stress coefficient. By introducing modified time constants, the results of the present paper, which have been derived for rigid dumb‐bells with Oseen‐Burgers hydrodynamic interaction, can easily be generalized to rigid multibead rods and Rotne‐Prager‐Yamakawa hydrodynamic interaction.
TL;DR: In this article, the CEF model was used for the constant-force squeezing of three highly viscous polymers, including polybutenes and low-density polyethylene melt (IUPAC sample X).
Abstract: Experimental results are reported for the constant‐force squeezing of three highly viscous polymers. Profiles for the plate separation versus time were measured with the use of a modified materials testing system. Two polybutenes were tested at 25 °C, and a low‐density polyethylene melt (IUPAC sample X) was studied at 150 °C. Measured half‐times show that the polybutenes behave as inelastic fluids with viscosities that decrease slightly with shear rate. In slow squeezes the experimental results agree with the predictions of Newtonian fluid theory corresponding to the available viscosity measurements. The behavior of LDPE X is described by the CEF model in both slow and fast squeezes. Although shear rates are as high as 1000 s−1, the elastic effects for LDPE X are small compared to viscous effects.
TL;DR: In this article, the authors used tractions as primitive variables in the calculations to avoid the need to add separately the pressure and extra stress tensors as is usually the case in other numerical methods.
Abstract: Some new (boundary‐element) computations of the flow over a slot are reported. By studying the Maxwell model, we find the hole pressure effect is −0.24N1 for this case, which is close to the −0.25N1 result for a second‐order fluid. We believe this accurate result at low Weissenberg numbers is due to the use of tractions as primitive variables in the calculations; this avoids the need to add separately the pressure and extra stress tensors as is usually the case in other numerical methods. Using a modified Phan‐Thien‐Tanner model we were able to perform computations which are a very good fit to the experimental data of Pike and Baird for polystyrene. Various parameters were changed in the MPTT model, and we confirm the approximate validity of the Higashitani‐Pritchard analysis.
TL;DR: In this article, the anomalous behavior associated with polymer adsorption gel formation on a surface was investigated for the flow at low shear of aqueous Polyox coagulant and WSR•301 solutions, containing 0-100 ppm of the polymer, in beds of monosized spheres.
Abstract: The anomalous behavior associated with polymer adsorption‐gel formation on a surface was investigated for the flow at low shear of aqueous Polyox coagulant and WSR‐301 solutions, containing 0–100 ppm of the polymer, in beds of monosized spheres. The flow measurements were conducted using stainless steel and Jaytron spheres and three sizes in the radius range 0.0796–0.2000 and 0.1187–0.1988 cm, respectively. The effective hydrodynamic thickness of the surface layer was evaluated from the negative effective velocity at the packing surface as an effective increase in the radius of the spheres. For the two Polyox homologs, the surface layer thickness increased with an increase in sphere radius and macromolecular size and exhibited a pseudo‐Langmuir‐type polymer concentration dependence, with a peak at the 30 ppm polymer concentration level. The present evaluations are in qualitative agreement with predictions based on the equation Δ=4AR2n found for low shear tubular flow of the same solutions. The deviations ...
TL;DR: In this paper, the constitutive equation for the elastic flexible reptating rope model is derived and the analytical expressions for the relative extension and the one-and two-segment distribution functions are derived.
Abstract: The constitutive equation for the “elastic flexible reptating rope” model is derived. In this model the macromolecule is represented by a continuous flexible elastic rope, confined in a tube along its contour and performing a reptation motion. The analytical expressions for the relative extension and the one‐ and two‐segment distribution functions are derived. This enables the determination of the explicit form of the constitutive equation. Due to the elasticity of the rope, fast internal relaxation modes appear in the theory as well as long reptation times. It is expected that fast deformation processes can therefore be described accurately by this constitutive equation.
Abstract: A flow visualization technique based on photochromic dyes has been used for the study of polymeric fluids in a number of flow configurations. The technique is based on the activation of the dye by ultraviolet light. This photoactivation results in the apparition of dark marker lines in the midst of the fluid. High‐speed movies can then be digitized and allow us to compute velocities anywhere inside the flow field. The results presented here address more particularly the case of the tubeless siphon. We have measured the velocity profile inside its fluid column for a number of flow conditions, and observed unexpectedly large velocity gradients. Indeed, the axial velocity at the centerline was found to be much greater than the velocity of the free surface at the same axial location. An interesting feature of this flow field is that the velocity profile appears to be a linear function of the radial location over most of the cross‐section of the column.
TL;DR: In this paper, a 0.15 weight fraction solution of polystyrene (Mw=410,000) in either tritolylphosphate (TCP) or 1,2-di(2−ethyl hexyl)phthalate (DOP) solvents was used for dispersions.
Abstract: Rheological data are reported for dispersions of crosslinked polystyrene beads (170 nm diameter) in a 0.15 weight fraction solution of polystyrene (Mw=410,000) in either of two solvents: tritolylphosphate (TCP) or 1,2‐di(2‐ethyl hexyl)phthalate (DOP). With these solvents, for fixed polymer concentration, the osmotic pressure is larger in solutions in TCP. Experiments include creep, recovery, stress‐growth at constant strain rate, and strain sinusoidal in time. Dispersions were studied, with 0.05, 0.10, 0.15, and 0.20 weight fraction wB of the beads. The dispersions exhibited solidlike behavior provided the strain did not exceed about 0.02, with an equilibrium modulus proportional to the square of the bead concentration. For larger strain, the behavior with slow deformation rates can be described by a pseudolinear constitutive equation, with a viscosity that decreases with increasing shear rate κ. The yield stress, as obtained from creep measurements, marking the transition from solidlike to fluidlike beha...
TL;DR: In this paper, the orientation distribution of rigid macromolecules dissolved at low concentration in a dielectric Newtonian fluid is solved for the case in which simultaneous hydrodynamic and electric fields are applied.
Abstract: The orientation distribution of rigid macromolecules dissolved at low concentration in a dielectric Newtonian fluid is solved for the case in which simultaneous hydrodynamic and electric fields are applied. Macromolecules are taken to be Brownian rigid spheroids of arbitrary aspect ratio and both permanent and induced dipole moments are included. To solve the problem with arbitrary strength of fields, the Galerkin method based on spherical harmonics is adopted. The converged solutions are used in the prediction of the steady state birefringence and extinction angle over very wide ranges of field strengths. Due to the coupled effects of flow and external field, somewhat complicated responses are predicted and saturation features are revealed at the strong flow limit. External field dependence due to the induced dipole is similar to that of the permanent case for most field conditions. Finally, it is shown, taking poly‐γ‐benzyl‐L‐glutamate solutions with various molecular weights as an example, how results in this article are applicable to an analysis of a real system.
TL;DR: In this article, the axisymmetric boundary layer with swirl equations, Galerkin finite-element discretization with free surface parameterization, and Newton iteration are analyzed by means of the axismmetric thin film flows on a rotating cone of Newtonian and non-Newtonian liquids.
Abstract: Steady axisymmetric thin film flows on a rotating cone of Newtonian and non‐Newtonian liquids are analyzed by means of the axisymmetric boundary layer with swirl equations, Galerkin finite‐element discretization with free surface parameterization, and Newton iteration, which permits the simultaneous evaluation of the boundary layer thickness with the primary unknowns which are the three velocity components. The significance of the inlet boundary conditions on the accuracy of the finite‐element predictions is discussed in detail. It is shown that natural inlet boundary conditions compatible with the local dynamics are superior to essential boundary conditions which may give rise to artificial finite‐element solutions. The analysis accounts for inertia, viscous, and surface tension effects. Both centrifugal and Coriolis accelerations are included. Results are presented and compared for Newtonian, shear‐thinning and shear‐thickening, Bingham plastic, and second‐order viscoelastic liquids at different operating conditions. In the limiting case of a rotating disk, in spin coating, the effects of the Coriolis acceleration, which have been omitted in earlier analyses are investigated. Closed form asymptotic solutions agree with the finite‐element predictions at high rotation. At low rotation, the asymptotic solution breaks down and so the finite‐element solution becomes essential.
TL;DR: In this article, a rheological theory is developed for a planar fluid surface which supercedes previous dynamic theories by explicitly acknowledging the nonlocal nature of the three-dimensional interfacial transition zone.
Abstract: The intrinsic rheology of a fluid‐fluid interface has been found significant to multiphase flows for which surfactant material is present and the surface‐to‐volume ratio is large, such as in emulsification and demulsification, foam and emulsion stability, foam rheology, the dynamics of small bubbles or droplets, and interfacial mass transfer. An understanding of surface rheology therefore has practical relevance to engineering technologies wherein such phenomena occur: examples include the enhanced recovery of oil and the processing of food materials. Herein, a rheological theory is developed for a planar fluid surface which supercedes previous dynamic theories by explicitly acknowledging the nonlocal nature of the three‐dimensional interfacial transition zone. Beyond providing insight into the nature of the surface excess pressure tensor without the complicating features accompanying surface curvature, the treatment will provide a foundation for subsequent articles which will examine the rheology of curved surfaces possessing curvature as large as occurs in microemulsion systems. In the equilibrium state, the surface excess pressure tensor is shown to result from the highly inhomogeneous nature of the phase interface, whereas in the dynamic state a linear constitutive assumption results in the classical surface properties of surface viscosity and surface tension.
TL;DR: In this article, a stress equation of motion with polymer is presented, where the solvent velocity at a place of position vector r (relative to an origin 0 fixed in space) at time t and the velocity gradient tensor K is independent of r. This is the state of the art.
Abstract: can be imposed, for instance, by moving apparatus walls. v(r, t) denotes the solvent velocity at a place of position vector r (relative to an origin 0 fixed in space) at time t; the velocity gradient tensor K is independent of r. v, denotes the solvent velocity at 0. If, as is usually assumed, inertial forces in the stress equation of motion can be neglected, addition of polymer results in addition of extra terms to (11, yielding an equation of the form
TL;DR: In this paper, the penalty-Galerkin finite element method is used to simulate the flow of a polystyrene melt over a rectangular slot placed perpendicular to the flow direction, and good agreement is still found between predicted values of stress using the coarse mesh and those measured by means of flow birefringence.
Abstract: The penalty‐Galerkin finite‐element method is used to simulate the flow of a polystyrene melt over a rectangular slot placed perpendicular to the flow direction. The White‐Metzner constitutive equation is used with a Carreau model viscosity function and a shear rate‐dependent relaxation time defined so that the primary normal stress difference is exactly reproduced by the model in simple shear flow. Values of the stress field predicted by the simulation are compared with those obtained experimentally by means of flow birefringence. As observed by others, the limiting elasticity value as determined by the Weissenberg number (We) for convergence of the algorithm decreased with increased refinement of the mesh. However, good agreement is still found between predicted values of stress using the coarse mesh and those measured by means of flow birefringence. This work suggests that there may be an optimum mesh for a given flow and constitutive equation which will still give physically realistic results. The Wei...
TL;DR: In this paper, steady-shear and transient experiments are used to discriminate between three classes of integral constitutive equations: the K-BKZ, the LeRoy-Pierrard, and the Carreau equations.
Abstract: Rheological tests based on steady‐shear and transient experiments are used to discriminate between three classes of integral constitutive equations: the K‐BKZ, the LeRoy‐Pierrard, and the Carreau equations. The tests derived from the given equations require no prior evaluation of model parameters. Reliable data obtained for steady‐shear, stress growth, and stress‐relaxation experiments conducted with various polystyrene solutions are used. The Carreau and K‐BKZ equations appear to be the most flexible, but none of the equations is capable of describing the whole spectrum of behavior observed in relaxation. The strains at which the maximum values of the shear and normal stresses are observed for the polystyrene solutions increase with the applied shear rate. This behavior can be described by the Carreau equation. This contrasts with results reported in the literature on low density polyethylene for which the strains were found to be constant.