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Volume 46, Issue 3, May 2002

Shear and elongation flow properties of kaolin suspensions
View Description Hide DescriptionThe elongation viscosity of kaolin pigment suspensions (71 wt %–49 vol %) was measured with a technique developed in our laboratory. Elongation thickening became apparent at rates of while shear thickening occurred at a shear rate an order of magnitude larger. It is not entirely clear if elongation thickening was in fact due to shear within the elongation flow geometry, however, possible parasitic effects have been considered and it is believed the observed elongation thickening is close to a true material property. Torsional rheometer stress measurements at lower shear rates allowed the total stress to be deconvoluted into the viscous(hydrodynamic) and elastic (thermodynamic or structural) components using the stress jump technique. The total stress was equal to that obtained with the capillary rheometer lending some confidence in the experimental technique. Furthermore, it was found that the stress (or viscosity) at higher shear rates was dominated by the viscous component. Thus, particle hydrodynamics play a key role in shear thickening as well as in elongation thickening (should it be present). The ratio of the elongation to shear viscosity (Trouton ratio) was found to be a function of the particle size and quite remarkably had values of the order of 50–100, in line with those values frequently quoted for some polymer solutions and melts.

Viscosity bifurcation in thixotropic, yielding fluids
View Description Hide DescriptionMost concentrated colloidalsuspensions such as cement, drilling fluids, paints, muds, etc., have been considered until now thixotropic fluids with a flow curve of an ideal yield stress fluid. We start by showing from inclined plane tests, intended to determine the yield stress, that these systems in fact exhibit peculiar properties. Unlike ideal yield stress fluids, they stop flowing abruptly below a critical stress, and start flowing at a high velocity beyond a critical stress, which in addition increases with the time of preliminary rest. In order to clarify these features we carried out a complete set of rheometrical tests with a model fluid, a bentonite suspension. Our results show that under controlled stress, in some cases after significant flow, there is bifurcation of the behavior towards either stoppage or rapid shear, depending on the relative values of the imposed and critical stresses. As an immediate consequence, we find that no (homogeneous) steady state flows at a shear rate below a critical value can be obtained. These results can be qualitatively predicted by a simple theoretical model that assumes that the viscosity of the material results from the competition between aging and shear rejuvenation, associated to, respectively, the organization or disorganization of the network of particle interactions. This shows that the flow curve in the steady state of concentrated colloidalsuspensions and, more generally, of structured fluids, is strongly affected by their thixotropy.

NonFickian mass transport in polymers
View Description Hide DescriptionThe model of isothermal diffusion in a polymeric medium derived by El Afil et al. [A. El Afif, M. Grmela, and G. Lebon, J. NonNewtonian Fluid Mech. 86, 253 (1999)] is investigated in the absence of an overall flow and in mechanical equilibrium. First, we derive its more macroscopic reduced versions and compare them with the models introduced previously in the literature. Next, we investigate the wave propagation of disturbances in the solvent concentration. Subsequently, we specify the free energy and kinetic coefficients that appear in the general governing equations and solve (using both qualitative and numerical methods) the governing equations expressed in the material coordinates. In this way we obtain the time evolution of the solvent concentration, the diffusion flux, the swelling, the internal deformations and stresses, and the internal viscosity associated with the solvent penetration and the swelling. The governing equations involve three parameters that express the individual nature of the mixture: the relaxation time of the polymericstructure, the relaxation time of the diffusion flux, and one parameter that expresses coupling of the polymericstructure and the solvent concentration in free energy. As an illustration, we show that with these three characteristic parameters we can reproduce results of observations that we have selected from the literature [N. L. Thomas and A. H. Windle, Polymer19, 255 (1978)]. In particular, we reproduce the case II type diffusion observed in the absence of a glass–rubber transition.

Diffusion of plasticizer in elastomer probed by rheological analysis
View Description Hide DescriptionA free volume approach of the diffusion of organic molecules in polymers above their glass transition temperature is addressed in this work. The idea that molecular transport is regulated by free volume was first introduced by Cohen and Turnbull [M. H. Cohen and D. Turnbull, J. Chem. Phys. 31, 1164 (1959)]. Our hypothesis is that the diffusion of small molecules, like plasticizers, in a polymer, here the copolymer of ethylene and vinyl acetate (EVA) above can be described by Fick’s classical law. The experiments were carried out on a parallel plate geometry rheometer. We studied the diffusion of the diethyl 2hexyl phtalate (DOP) into the melted EVA at four different temperatures. Using Fick’s law, the concentration of the plasticizer was established for any given point of the thickness of the swelling elastomer at any time. Using a onedimensional grid to solve continuous equations that describe the different rheological contributions of each abscissa, we determined the linear viscoelastic response of the whole sample. By comparing the experimental loss modulus to the values calculated from the rheological model, we found the values of the three parameters of the free volume expression of the diffusion coefficient. A simple relation which describes the mutual diffusion coefficient of DOP into melt EVA and depends exponentially on and on the weight fraction of solvent was established to be

Numerical analysis of flow mark surface defects in injection molding flow
View Description Hide DescriptionIn order to elucidate the mechanism of flow mark surface defects, the stability of injection moldingflow is investigated numerically using a transient finite element method. Experiments performed by Schepens and Bulters [Bulters, M., and A. Schepens, “The origin of the surface defect ‘slipstick’ on injection moulded products,” Paper IL32, in Proceedings of the 16th Annual Meeting of the Polymer Processing Society, Shenghai, China, 2000a, pp. 144–145] using a novel two color injection molding technique are summarized and they indicate that surface defects are caused by a flow instability near the free surface during filling of the mold. Steady finite element calculations of a model injection moldingflow using a single mode, exponential PhanThien–Tanner constitutive equation supply information about the base state streamlines and polymer stresses. By varying the parameters of the model, the degree of strain hardening in the extensional viscosity can be controlled. Then a linear stability analysis is used to determine the most unstable eigenmode of the flow and the dependence on the extensional properties of the polymer. For strain softening materials, the injection moldingflow is predicted to be stable up to a Weissenberg number of five. However, the most unstable disturbance is consistent with the swirling flow near the interface observed experimentally. For strain hardening rheologies, an instability is observed in the channel flow far from the interface, in agreement with calculations performed by Grillet et al. [Grillet, A. M., A. C. B. Bogaerds, G. W. M. Peters, and F. P. T. Baaijens, “Stability analysis of constitutive equations for polymer melts in viscometric flows,” J. NonNewt. Fluid Mech. (accepted, 2001)] on planar Poiseuille flow of a PhanThien–Tanner fluid.

Linear rheology of binary melts from a phenomenological tube model of entangled polymers
View Description Hide DescriptionWe develop a simple phenomenological theory to describe linear viscoelasticity in bidisperse linear polymer melts. We describe the singlechain relaxation spectrum using a local description of relaxation times along the chain, which includes contourlength fluctuations as well as reptative motion. The complex modulus is calculated by summing the contributions from all the segments along the chain, and weighting the contributions by the entangled volume fraction remaining at each time. We find that the resulting predictions for the modulus fit data of binary blends of polybutadiene better than those of the widely used double reptation model.

Viscoelastic properties of aggrecan aggregate solutions: Dependence on aggrecan concentration and ionic strength
View Description Hide DescriptionAggrecan is the selfassembling proteoglycan complex whose physiological function is to provide a hydrated gel in cartilage that stabilizes the spatial distribution of the collagen fibers, and absorbs and resists compressive loads. The linear and nonlinear viscoelastic behavior of aggrecan solutions was studied as a function of aggrecan concentration and ionic strength. At physiological ionic strength, a soltogel transition occurs at an aggrecan concentration just above the overlap value. Concentrated solutions exhibit a reversible yield point similar to that predicted and observed for closepacked dispersions of soft spheres. In contrast to the behavior of linear polyelectrolytesolutions, the storage modulus increases with ionic strength, until above which the modulus decreases. In light of the dense polyelectrolyte brush structure of aggrecan, we suggest that this behavior is a manifestation of the crossover from “osmotic brush” to “salted brush” conditions.

Direct determination by nuclear magnetic resonance of the thixotropic and yielding behavior of suspensions
View Description Hide DescriptionWe carried out coupled, controlled velocity, magnetic resonance imaging (MRI)rheometry experiments with colloidalsuspensions. For not too high relative velocity of the tools the velocity profiles between coaxial cylinders are composed of two parts: close to the inner cylinder the fluid is sheared at a rate larger than a critical, finite value (in contrast with the behavior of an ideal yield stress fluid) while the fluid is not sheared at all close to the outer cylinder. Even in the steady state the position (critical radius) of the interface between these two regions depends on previous flow history. In particular it decreases with the time of preliminary rest, while the critical shear rate and shear stress along the interface increase because of fluid restructuring in the static region. Using a new MRI procedure the velocity profiles have also been recorded during transient tests. We thus could observe the displacement of the critical radius in time after sudden changes of the imposed rotation velocity. In that case the rheological analysis of the velocity profiles show that the effective behavior in the sheared region does not change significantly with velocity, time, or flow history: as a first approximation it can be represented by a simple powerlaw model with constant parameters. This means that the apparent rheological behavior, i.e., as deduced from usual rheometrical tests without taking into account this discontinuity in shear rate, does not represent the effective behavior of the material. Furthermore, the apparent thixotropy of these fluids might be basically dictated by the displacement of the interface between the sheared and unsheared regions.

Effect of fluid relaxation time of dilute polymer solutions on jet breakup due to a forced disturbance
View Description Hide DescriptionIn inertiadominated breakup of a lowviscosity liquid jet, complex disintegration mechanisms lead to a polydisperse distribution of the sizes of droplets formed. Macromolecules in solution increase the extensional viscosity and suppress the formation of satellite drops. Large extensional stresses lead to, and prevent, viscoelastic filaments from breaking up (beadsonstring structure). The drainage rate of fluid from the filaments into the beads is constant and can be used to estimate the relaxation time of the fluid. The nature of capillary breakup due to an imposed disturbance is investigated as a function of disturbance wavelengthtodiameter ratio and initial disturbance amplitude. We identify the key dynamics of the process and its relation to the fluid relaxation time; this allows us to control satellite drop formation. There is a minimum fluid relaxation time for suppression of satellite drops. Above this relaxation time, suppression of satellite drops is a function of the disturbance parameters. The results identify the fluid relaxation time and the time scale of the disturbance growth as the relevant time scales in capillary breakup of viscoelastic fluids. Through this study, we demonstrate that the drop size distribution from capillary breakup of polymer solutions can be controlled through choice of molecular weight of the polymer.

Sedimentation of a sphere in a suspension of neutrally buoyant fibers
View Description Hide DescriptionThe sedimentation of a dense sphere in a suspension of neutrally buoyant nonBrownian fibers is investigated experimentally. We consider in particular the effect of the ratio of the sphere diameter D to the fiber length L on the extra drag force experienced by the sphere in a broader range than in previous studies reported in the literature. For a given fiber concentration, the drag coefficient is found to be a strong function of the sphere diameter to the fiber length ratio, particularly when the ball diameter is on the order of the fiber length. When the ball diameter is increased, the drag coefficient rises, passes through a maximum for and then decreases to a steady state value for large spheres. Our experimental results are in qualitative agreement with the numerical simulations of Harlen et al. (O. G. Harlen et al., J. Fluid. Mech. 388, 355 (1999)].