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Journal of RheologyVolume 43, Issue 1 (January-February 1999) |
Contents
"Volume Preserving" Rheological Models For Polymer Melts and Solutions Using the GENERIC Formalism Abdellatif Ait-Kadi* and Ahmad Ramazani Chemical Engineering Department and CERSIM Laval University, Ste-Foy (Quebec) Canada - G1K 7P4 Miroslav Grmela Chixing Zhou *Corresponding author AbstractA constrained rheological model for polymer solutions and melts is developed using the GENERIC formulation. The constraint, det c = constant, where c is a conformation tensor, is introduced in the general formulation using a modified mobility tensor, L1, and a Helmholtz free energy function expressed in terms of the scaled invariants of the conformation tensor. The predictions of this family of "volume-preserving" models are illustrated for a modified Hookean energy function and several expressions of the modified mobility tensor. The predictions are compared to experimental data taken from the literature for polymer melts and polymer solutions. The sensitivity of the predictions to model parameters (a maximum of four for this particular case) shows that in steady and transient shear flows, it is possible to cover a wide range of rheological behaviours generally observed for polymer melts and solutions. Comparison with experimental results for polymer melts and solutions shows that the model predicts very well the steady shear viscosity and first normal stress coefficient behaviour for an extended range of shear rates. Model predictions for material functions in shear start-up experiments compare fairly well with the experimental data. The modified Hookean energy function proposed to illustrate the approach is found to give larger overshoots than those observed experimentally in shear start-up experiments. Predictions for shear stress relaxation failed to compare with the set of experimental data for which this property is available. It is believed that these drawbacks with this particular choice of the Helmholtz free energy function can be overcome using multiple conformation variables. This can be easily done in this formulation.Uniaxial Extensional Characterization Of A Shear Thinning Fluid Using Axisymmetric Flow BirefringenceWesley R. Burghardt* and Ji-Ming LiDepartment of Chemical Engineering Northwestern University, Evanston, IL 60208 USA Bamin Khomami and Bin Yang *Corresponding Author: w-burghardt@nwu.edu AbstractComputations are reported for a shear thinning, elastic fluid in axisymmetric stagnation flows, in an attempt to predict flow birefringence data on a 5 wt% high molecular weight polystyrene solution. For multimode Phan-Thien Tanner (PTT) and Giesekus models, several parameter sets are chosen in which the degree of elongational hardening is systematically adjusted. The primary objective is to see whether the extensional properties of the fluid can be inferred from comparisons between these computations with normal stress measurements in flows dominated by uniaxial extension. Using the PTT model it is possible to vary extensional predictions while maintaining a good fit of shear viscosity data. Up to moderate Weissenberg number, these comparisons suggest a modest degree of extension hardening. Computations in rear stagnation flow using the PTT model fail at intermediate Weissenberg number. A multimode Giesekus model with parameters determined only by fitting shear data performs exceptionally well in forward stagnation flow at all Weissenberg numbers, but is deficient in rear stagnation flow at the two highest experimental Weissenberg number. Attempts to selectively enhance extensional hardening at high rates do improve normal stress predictions in the rear stagnation region, but only at the expense of degraded predictions of shear stress in rear stagnation flow, and all stresses in forward stagnation flow.A Mesoscopic Theory of Liquid Crystalline Polymers Mark N. Kawaguchi* and Morton M. Denn Materials Sciences Division, Lawrence Berkeley National Laboratory and Department of Chemical Engineering University of California, Berkeley, CA 94720-1462 USA *Present address: Chemical Integration and Technology AbstractA kinetic equation for polydomains is used to develop a formal structure for a mesoscopic constitutive theory of textured liquid crystalline polymers. The lowest-order approximation for the texture terms leads to the Larson and Doi (1991) theory, but with a different meaning for the model parameters. Predicted macroscopic order parameters are in the range observed experimentally.Rheology of Transient Colloidal Gels by Brownian Dynamics: Computer Simulation J. F. M. Lodge* and D. M. Heyes Department of Chemistry, University of Surrey Guildford, GU2 5XH, United Kingdom *Present address: Van't Hoff Laboratory for Physical and Colloid
Chemistry AbstractBrownian Dynamics, BD, simulation has been used to model the dynamics and rheology of transient particle colloidal gels during formation, by quenching monodisperse attractive spherical colloidal particles from a supercritical state point into the vapor-liquid or vapor-solid parts of the phase diagram. Calculations were performed with particles interacting via 12:6, 24:12 and 36:18 Lennard-Jones type interaction laws at subcritical temperatures (kT/e > 0.3, where e is the depth of the potential well) and low volume fractions (j £ 0.2). These systems developed a gel-like morphology during the simulation with the aggregate morphology and rheology being sensitive to the range of the attractive part of the potential and its underlying phase diagram. The long range 12:6 systems rapidly formed compact structures, whereas the systems generated using the shorter-ranged 24:12 and 36:18 potentials persisted in a more diffuse network for the duration of the simulations and evolved much more slowly with time, although none showed any indication of coming to a structural or rheological arrest. The rheology of these systems was characterized principally using linear stress relaxation functions computed using the Green-Kubo fluctuation formula. An approximate direct method for computing the dynamic moduli that does not rely on a Fourier Transformation of the stress relaxation function was also tested. The rheology of many of the systems evolved with time from the initial uniform distribution of particles, to a gel-like viscoelastic material, especially for the long-range attractive interaction potentials. Despite being the most short-lived, the 12:6 potential systems give the most pronounced gel-like rheological features.Viscoelastic Behavior of Cubic Phases in Block Copolymer Melts M. B. Kossuth, D. C. Morse*, and F. S. Bates* Department of Chemical Engineering and Materials Science University of Minnesota, Minneapolis, MN 55455 *Corresponding Authors AbstractThe viscoelastic behavior of block copolymer melts that exhibit a cubic phase has been examined by oscillatory shear experiments. A low frequency plateau in the measured storage modulus that is absent in the disordered phase is found for both gyroid and body-centered cubic sphere phases of diblock and triblock copolymer melts. The magnitude of the apparent plateau modulus is found to be insensitive to strain amplitude for strains of 0.05-5%, and so is believed to be characteristic of the true linear response. The value of the apparent terminal relaxation frequency, beneath which G"(w) > G'(w), is, however, sensitive to strain amplitude in the same range of strains and decreases steadily with decreasing strain, indicating that the terminal regime is highly sensitive to nonlinear effects. The presence of one or more entangled blocks is found to decrease the terminal frequency, and thus extend the range of linear behavior. Experimental results for the dependence of the plateau modulus and the unit cell size upon molecular volume yield effective power law exponents that are close, but not identical, to those predicted by self-consistent field theory.Comparison of Dumbbell-Based Theory and Experiment for A Dilute Polymer Solution in A Co-Rotating Two-Roll Mill Graham M. Harrison, Johan Remmelgas, and L. Gary Leal Department of Chemical Engineering University of California, Santa Barbara, CA 93106 USA AbstractThe Chilcott-Rallison FENE dumbbell model is used to solve for the polymer and flowfield response in transient startup flow of a dilute solution in a co-rotating two-roll mill. These predictions are then compared to experimental results obtained in an identical geometry using a high molecular weight dilute (c/c* ~ 0.1) polystyrene solution. As predicted by the dumbbell model, the experiments indicate a substantial coupling between the polymer deformation and changes to the Newtonian flowfield. As the polymer stretches, the experimentally measured shear rate decreases, as does the flow-type parameter. However, dumbbell model parameters based upon an isolated chain do not result in FENE model predictions quantitatively similar to the experimental results. Based upon steady-state birefringence values for the same dilute solution in an extension dominated flow at large strain-rates, it appears that chain-chain interactions restrict the maximum attainable polymer deformation. Further calculations incorporating this concept, via a reduced value of the extensibility parameter L, result in much better agreement with experimental results.The Effect of Temperature and Concentration on N1 and Tumbling in A Liquid Crystal Polymer C.-M. Huang and J. J. Magda* Departments of Materials Science Engineering and Chemical Fuels Engineering University of Utah, Salt Lake City, UT 84112 USA R. G. Larson *Corresponding Author AbstractThe shear rate gmin at the relative minimum in the N1 flow curve is studied as a function of temperature and concentration for liquid crystalline (hydroxypropyl)cellulose (HPC). For lyotropes, at least, gmin is the shear rate necessary to halt director "tumbling" and align the molecules. HPC is a convenient polymer for studying the relationship between lyotropic and thermotropic liquid crystalline polymers, because it exhibits a pure thermotropic phase at elevated temperatures, and room temperature lyotropic phases at moderate concentrations in m-cresol. At the highest possible polymer concentration at which reliable rheology data can be obtained (around 70 wt.% polymer), indirect evidence for director tumbling is observed, in that N1 retains a local minimum versus shear rate. For the highest concentrations this minimum N1 value is positive, rather than negative, as is the case at lower concentrations and as is predicted by the Doi theory. Empirical time-temperature and time-concentration shifting can be used to estimate gmin from measured values of the shear viscosity. A Continuum Model For Flow-Induced Crystallization Of Polymer Melts Antonios K. Doufas, Issam S. Dairanieh, and Anthony J. McHugh* *Corresponding Author AbstractA macroscopic, continuum model based on the Hamiltonian/Poisson Bracket formalism, combined with the Avrami equation, is developed to simulate flow-induced crystallization (FIC) of polymer melts in homogeneous flow fields under isothermal conditions. The model predicts crystallization kinetics as well as rheological and rheo-optical behavior of semi-crystalline systems. The amorphous phase is modeled as a modified Giesekus fluid and the crystalline phase is approximated as a collection of multi-bead rigid rods that grow and orient in the flow field. The two phases are coupled with crystallinity via the dissipative Poisson brackets. The input parameters of the model can be obtained from experiments. Orders of magnitude reduction in induction times and enhancements in crystallization rates are predicted to occur under flow. Critical deformation rates are captured above which induction times sharply decrease. Calculations show increases in stiffness and strain-hardening of the semi-crystalline system via dramatic increases in the system stresses during crystallization. Moreover, for the temperature range studied, hydrodynamic forces dominate the undercooling effect in the regime of high deformation rates. The simulations also predict more rapid induction of crystallization following cessation of flow relative to quiescent crystallization.Electrorheological Properties of a Type-I Immiscible Polymer Blend: Scaling and Structural Changes Hiroshi Orihara, Yasunari Hosoi, Kozo Tajiri, Yoshihiro Ishibashi, Masao
Doi Akio Inoue AbstractWe studied the electrorheological properties of a type-I immiscible polymer blend, in which droplets of liquid crystalline polymers are dispersed in a polydimethylsiloxane under no electric field. We measured flow curves of the blend at various applied electric fields under various temperatures, and made optical observations of the structure. Two anomalies were found in the flow curve, indicating that there should be three different structures, which are designated as N, A, and B in the order of increasing the shear rate. A is much higher than B and N in viscosity. By optical observations it was clarified that A and B coexist in a certain range of shear rate and there is a sharp boundary between them. In A we found a scaling relation in the flow curve and a dimensionless number Mn', which is the only one parameter characterizing the state of A.Transient Response of Electrorheological Effect to A Step Field in an Immiscible Polymer Blend: Second Mode in Type I Blend Kozo Tajiri, Hiroshi Orihara, Yoshihiro Ishibashi, Masao Doi Akio Inoue AbstractWe have investigated the transient response of an immiscible polymer blend electrorheological fluid to a step electric field. The response of shear stress consists of a slow rise following a fast one. The electric field and the shear rate dependences of the slow rise, called the second mode, were measured. It was found that the second mode is considerably different from the first mode (the fast rise) in the field and the shear rate dependences of the transient response. We made an optical observation of the structural change together with the measurement of shear stress in the second mode. It was observed that the blend separated into two phases with high and low viscosities, which is responsible for the second mode. The microscopic structures of these phases and the phase separation process will be discussed. Pointwise Observations For Rheological Characterization Using NMRI† Darren F. Arola* and Robert L. Powell** Geoffrey A. Barrall Michael J. McCarthy † Portions of this work were originally presented at the 68th Annual Society of Rheology Meeting, Galveston, Texas, February 16-20, 1997 and the Frontiers in Industrial Process Tomography-II Conference, Delft, The Netherlands, April 9-12, 1997.*Present Address: MBA Polymers, Inc., 500 West Ohio Avenue **Corresponding Author: rlpowell@ucdavis.edu AbstractThis study focuses on development of an NMRI-based viscometric technique using pulsed gradient NMR for characterizing fluid materials under steady tube flow conditions. By simultaneously measuring velocity profiles and pressure gradients it is possible to characterize complex fluids locally. Shear viscosity-shear rate data, ranging from one to over two decades of shear rate from one combined velocity profile/pressure drop per unit tube length measurement, are provided for five fluids that exhibit both Newtonian and shear thinning characteristics. The resolution of the velocity data controls the accuracy of the measured shear viscosity whereas the radial resolution prescribes the number of shear viscosity-shear rate data points and the minimum shear rate. Velocity profile measurements with a velocity resolution of 1 mm/s and radial resolutions which provided from 22 to 110 spatially resolved velocity data points accurately characterized fluids for shear rates greater than 0.1 s-1. Dynamic yield values measured from velocity data for a microfibrous cellulose solution were within 2% of those measured with a conventional rheometer using the controlled shear rate method and a vane attachment.Impact Of Viscoelasticity on Gage Variation in Film Casting Dilip Rajagopalan AbstractMathematical modeling of the melt draw step in film casting is used to understand the impact of viscoelasticity on gage variations. The thin film approximation is used to simplify the governing equations to a set of two-dimensional partial differential equations which are solved using the finite element method. Simulations using the Giesekus constitutive model show that the magnitude of thickness variations increases with increasing flow elasticity or Deborah number.Pressure Drop Created by A Sphere Settling In A Tube Containing A Fibre Suspension N. Phan-Thien and X.-J. Fan AbstractIn this work we report some numerical data on the pressure drop/drag force relation for the flow of a fibre suspension past a sphere in a tube, to test an analytical result due to Brenner (1962), which was derived for a creeping Newtonian flow. The numerical data are generated by a robust method based on the CONNFFESSIT idea of Öttinger (1996) and the DAVSS of Sun et al. (1998), which does not rely on any closure approximation. The numerical data support Brenner's relation very well. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |