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Journal of RheologyVolume 46, Issue 3 (May-June 2002) |
Contents
Numerical analysis of flow mark surface defects in injection molding flowAnne M. Grillet a,c), Arjen C. B. Bogaerds a), Gerrit W. M. Peters a), Markus Bulters b), and Frank P. T. Baaijens a,d) a) Dutch Polymer Institute, Department of
Mechanical Engineering, Eindhoven University of Technology b) DSM Research, P. O. Box 18, 6160 MD Geleen,
The Netherlands AbstractIn order to elucidate the mechanism of flow mark surface defects, the stability of injection molding flow is investigated numerically using a transient finite element method. Experiments performed by Schepens & Bulters (2000a) using a novel two color injection molding technique are summarized which indicate that the surface defects are caused by a flow instability near the free surface during mold filling. Steady finite element calculations on a model injection molding flow using a single mode, exponential Phan-Thien 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 molding flow is predicted to be stable up to Weissenberg number of five. However, the most unstable disturbance is consistent with the swirling flow near the interface observed experimentally. However 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. (in press) on planar Poiseuille flow of a Phan-Thien-Tanner fluid. c) Current address:
Sandia National Laboratories, P. O. Box 5800 MS 0834, Albuquerque, NM
87185, U. S. A. Linear rheology of binary melts from a phenomenological tube model of entangled polymersAmalie L. Frischknecht
a,b) and Scott T. Milner AbstractWe develop a simple phenomenological theory to describe linear viscoelasticity in bidisperse linear polymer melts. We describe the single-chain relaxation spectrum using a local description of relaxation times along the chain, which includes contour-length 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 on binary blends of polybutadiene better than the widely used double reptation model. a) Author to whom correspondence should be
addressed; electronic mail:
alfrisc@sandia.gov Shear and elongation flow properties of kaolin suspensionsVincent T. O'Brien and Michael E. Mackay a) Materials Characterisation and Processing Centre AbstractThe elongation viscosity of kaolin pigment suspensions (71wt% ~ 49vo1%) was measured with a technique developed in our laboratory. Elongation thickening became apparent at rates of 103 s-1 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 experimental technique. Futhermore, 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 elongation thickening (should it be present). The ratio of the elongation to shear viscosity (Trouton ratio) was found to be a function of particle size and quite remarkably had values of order 50-100, in line with those values frequently quoted for some polymer solutions and melts. a) Corresponding author; present address - Department of Chemical Engineering and Materials Science; Michigan State University; East Lansing, MI 48824, USA. E-mail: mackay@msu.edu; URL: www.memackay.com Viscosity bifurcation in thixotropic, yielding fluidsP. Coussot a,d), Q. D. Nguyen b), H. T. Huynh a), and D. Bonn c) a) Laboratoire des Materiaux et des Structures du Génie Civil, Champs sur Marne, France b) University of Adelaide, Department of Chemical Engineering, Australia c) Laboratoire de Physique Statistique, Ecole Normale Supérieure, France AbstractMost concentrated colloidal suspensions such as cement, drilling
fluids, paints, muds, etc, have been considered until now as 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 a significant flow, there is a
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 assuming that the
viscosity of the material results from the competition between aging and
shear rejuvenation, associated respectively to the organization or
disorganisation of the network of particle interactions. This shows that
the flow curve in steady state of concentrated colloidal suspensions and,
more generally, of structured fluids, is strongly affected by their
thixotropy. d) To whom correspondence should be sent. E-mail: philippe.coussot@lcpc.fr Sedimentation of a sphere in a suspension of neutrally buoyant fibersDavid Antonio and Mohend Chaouche a) Laboratoire de Mécanique
et Technologie AbstractThe sedimentation of a dense sphere in a suspension of neutrally buoyant non-Brownian 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 the 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, in particular 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 D = O(L), 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. (J. Fluid. Mech., 388, 355-388 (1999)). a) Corresponding author. Electronic mail: chaouche@lmt.ens-cachan.fr Effect of fluid relaxation time of dilute polymer solutions on jet break up due to a forced disturbanceYenny Christanti and Lynn M. Walker a) Center for Complex Fluids Engineering AbstractIn inertia-dominated break up of a low-viscosity 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 (beads-onstring 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 break up due to an imposed disturbance is investigated as a function of disturbance wavelength-to-diameter 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 break up of viscoelastic fluids. Through this study, we demonstrate that the drop size distribution from capillary break up of polymer solutions can be controlled through choice of molecular weight of the polymer. a) Corresponding author (lwalker@andrew.cmu.edu) Viscoelastic properties of aggrecan aggregate solutions: Dependence on aggrecan concentration and ionic strengthNispa Meechai a), Alexander M. Jamieson a,d), John Blackwell a), David A. Carrino b), and Rekha Bansal c) a) Department of Macromolecular Science and
Engineering b) Department of Biology c) Gliatech Corporation, Beachwood, OH, U. S.
A. AbstractAggrecan is the self-assembling 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 non-linear viscoelastic behavior of aggrecan solutions was studied as a function of aggrecan concentration and ionic strength. At physiological ionic strength, I = 0.15, a sol-to-gel 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 close-packed dispersions of soft spheres. In contrast to the behavior of linear polyelectrolyte solutions, the storage modulus increases with ionic strength, until I = 0.75, 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. a) Corresponding author. Phone: 216-368-4172; Fax: 216-368-4202; E-mail: amj@po.cwru.edu Direct determination by NMR of the thixotropic and yielding behavior of suspensionsJ. S. Raynaud a), P. Moucheront a), J. C. Baudez b), F. Bertrand a), J. P. Guilbaud a), and P. Coussot a,c) a) Laboratoire des Materiaux et des Structures
du Genie Civil b) Cemagref, Domaine des Palaquins, 03150 Montoldre, France AbstractWe carried out coupled, controlled velocity, MRI-rheometry experiments with colloidal suspensions. For not too high relative velocity of the tools (< 70 rpm), 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 power-law 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. c) To whom correspondence should be sent. Non-Fickian mass transport in polymersA. El Afif and M. Grmela a) Ecole
Polytechnique, Universite de Montreal AbstractThe new model of isothermal diffusion in a polymeric medium derived in [ A. El Afif, M. Grmela, and G. Lebon, J. Non-Newtonian 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 appearing in the general governing equations and solve (by 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 expressing the individual nature of the mixture: a relaxation time of the polymeric structure, a relaxation time of the diffusion flux, and. one parameter expressing the coupling of the polymeric structure and the solvent concentration in the free energy. As an illustration, we show that with these three characteristic parameters we reproduce results of observations that we have selected from the literature [N. L. Thomas and A. H. Windle, Polymer, 19, 255 (1978)]. In particular, we reproduce the observed Case II type diffusion in the absence of the glass-rubber transition. a) Corresponding author: miroslav.grmela@polymtl.ca Diffusion of plasticizer in elastomer probed by rheological analysisC. Joubert a,b), P. Cassagnau a,c), L. Choplin b), and A. Michel a) a) Laboratoire des Matériaux
Plastiques et Biomatériaux b) GEMICO, ENSIC AbstractA free volume approach of the diffusion of organic molecules in polymers above their glass transition temperature (Tg) is addressed in the present work. The idea that molecular transport is regulated by free volume was first introduced by Cohen and Turnbull (Cohen M. H., Turnbull D., 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 Tg, 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 one-dimensional grid to solve continuous equations that describe the different rheological contributions of each abscissa, we determined the linear viscoelastic response of the whole sample. 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. Lastly, a simple relation, which describes the mutual diffusion coefficient of DOP into melt EVA and depends exponentially on 1/T and on the weight fraction of solvent (w1), was established as: D1 = 0.157 exp (-90.3×103/RT) exp (15.8 w1) c) To whom all correspondence should be addressed. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |