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Journal of RheologyVolume 42, Issue 2 (March-April 1998) |
Contents
A Thin-Filament Melt Spinning Model with Radial Resolution of Temperature and StressG. M. Henson, D. Cao,* S. E. Bechtel M. G. Forest *Present address: Department of Biomedical
Engineering AbstractExisting non-isothermal thin-filament melt spinning models treat temperature as a one-dimensional (1-D) quantity, varying only with axial distance. Such models accurately simulate processes in which the melt has high thermal conductivity relative to the surface heat loss (i.e. small Biot number), or the ambient air temperature is near the melt temperature. However, in industrial melt spinning processes, where neither of these characteristics is true, a leading-order transverse temperature variation exists, no matter how slender the filament. Alternative models implement a hybrid 1-D mass and momentum, 2-D energy computation. Here we extend existing 1-D models to include radial as well as axial resolution of temperature, thereby also providing a 2-D resolution of stress, while retaining the computational advantages of 1-D models. The model's predictions depend on the thermal conductivity of the melt, a property absent from existing 1-D models. In addition to demonstrating the 2-D resolution afforded by the new model, we also demonstrate significant differences between the new model and existing 1-D models in predictions of fundamentally 1-D quantities such as average axial stress, the quantity from which performance properties of the spun fiber are typically inferred. X-Ray Scattering Investigation of Highly Concentrated Poly(benzyl glutamate) Solutions Under Shear FlowV. M. Ugaz, D. K. Cinader, Jr., and W. R.
Burghardt* *Corresponding Author: w-burghardt@nwu.edu AbstractIn-situ x-ray scattering techniques are used to measure molecular orientation and investigate the coexistence of hexagonal and nematic phases in highly concentrated PBG/cresol solutions under shear flow. Beyond a threshold concentration, the diffuse nematic lobe in x-ray scattering patterns is accompanied by sharp reflections indicating lateral packing of molecules in a hexagonal arrangement. The threshold concentration for formation of this hexagonal phase depends on molecular weight, but occurs near 35 wt% PBG and corresponds directly to the onset of Region I shear thinning. Applied shear acts to reduce the amount of hexagonal phase and ultimately, at high enough shear rates, return the solution to a fully nematic state. Relaxation experiments at high shear rates indicate that the final state of the solution is highly sensitive to the continued presence of the hexagonal phase during shear. Specifically, a much higher final orientation results if the hexagonal phase—even a very small amount—persists during the preceding shear. We postulate a nucleation mechanism to explain this behavior, in which re-growth of the hexagonal phase during relaxation is promoted in such a way that molecular orientation is favored in a direction parallel to the residual hexagonal phase in the sample at the onset of relaxation. This results in increased molecular orientation in both the hexagonal and nematic phases. Finally, we show examples of erratic relaxation behavior observed in PBG/cresol at concentrations immediately below the threshold of hexagonal phase formation. The degree of this erratic behavior appears to depend on the amount of strain applied before flow cessation. A Shear Device for the Microscopic Observations of Suspensions and EmulsionsM. Fermigier, C. L'Héveder, and P. Jenffer J. H. E. Promislow AbstractWe describe a shear device designed to allow the visualization of suspensions or emulsions under an optical microscope. The optical axis of the microscope is perpendicular to the plane of shear. The detailed flow profile is determined by numerical simulation with two different aspect ratios of the flow cell . We use this shear device to investigate the structure of dilute suspensions of colloidal magnetic particles submitted to a magnetic field and to a flow. Three Dimensional Shape of a Drop under Simple Shear FlowStefano Guido* and Marco Villone *Corresponding Author: steguido@unina.it AbstractThe three dimensional deformation of an isolated drop in an immiscible liquid phase undergoing simple shear flow was investigated by using a parallel plate apparatus. The drop was observed by video-enhanced contrast optical microscopy, either along the vorticity direction or along the velocity gradient direction of the shear flow. An experimental methodology based on image analysis was especially developed to study in a quantitative way the three dimensional shape of the deformed drop, both under steady state flow and during transients. Up to moderate deformations, the steady state drop shape was well described within experimental error by an ellipsoid having three different axes. The deviation of drop shape from an ellipsoid at higher deformations was also characterized in a quantitative way. Good agreement was found between the experimental results of this work and numerical simulations reported in the literature. Particle Migration in a Couette Apparatus: Experiment and ModelingNicholas Tetlow, Alan L. Graham Marc S. Ingber Samuel R. Subia, Lisa A. Mondy Steve A. Altobelli AbstractSuspensions comprised of neutrally buoyant spheres in Newtonian fluids undergoing creeping flow in the annular region between two rotating, coaxial cylinders (a wide-gap Couette) display a bulk migration of particles towards regions of lower shear rate. A series of experiments are performed to characterize this particle migration, including the influence of particle size, surface roughness, and volume fraction. Little, if any, effect of particle surface roughness is observed. An existing continuum diffusive-flux model (Phillips et al., 1992) for predicting particle concentration profiles in monomodal suspensions is evaluated using the current series of experimental data. This model predicts a dependence of the migration rate on the square of the suspended particles' radius, a2; whereas the present experiments indicate that systems with average particle volume fractions of 50% display a rate that scales with a3. Previous use of the diffusive-flux model has assumed constant values for diffusion coefficients which serve as tuning parameters in the phenomenological equation. Here the experimental data are used to investigate variations of the model in which the diffusion coefficients depend upon either the local or global particle volume fraction. For initially uniform suspensions, the coefficients are found to be best modeled as functions of the local particle volume fraction. Rheological Behavior of a Lamellar Lyotropic Phase as a Function of the Substrate NatureN. Jager-Lézer1 *, J.F. Tranchant2, V. Alard2, J. Doucet3, and J.L. Grossiord1 1 Laboratoire de Physique
Pharmaceutique, Centre de Châtenay-Malabry 2 Laboratoire de Physico-Chimie,
Perfums Christian Dior 3 Laboratoire pour l'Utilisation
du Rayonnement Electromagnétique (L.U.R.E.) *Corresponding Author: jager@phypha.u-psud.fr AbstractVarious rheological experiments were carried out on a lamellar phase system in order to analyse its structural organization, using different geometries. The results showed a rheological behavior which depended on the chemical nature of the geometry. For stainless steel substrates, the rheological profile presented a liquid plastic behavior with a predominantly elastic character for low stresses. ln the case of quartz, the rheological behavior was different, displaying a predominantly viscous and shear-thinning character. A detailed rheological analysis allowed us to conclude on the existence of an inhomogeneous shear effect of the sample on quartz, probably induced by a local alignment effect of the lamellar layers in the vicinity of the quartz plates. X-ray analysis of the lamellar sample placed on either stainless steel or quartz showed a parallel alignment of the lamellar layers. However, on quartz substrates, this orientation was almost perfect in the vicinity of the plates and more marked than that observed on stainless steel substrates. Conformational and Rheological Dynamics of Semi-Flexible Macromolecules Undergoing Shear Flow: A Non-Equilibrium Brownian Dynamics StudyN. C. Andrews1, A. J. McHugh1, and J. D. Schieber2 1Department of Chemical
Engineering, 2Department of Chemical
Engineering, AbstractNon-Equilibrium Brownian Dynamics Simulations (NEBD) are used to model the dynamics of semi-flexible macromolecules undergoing shear flow. The mathematical model utilizes a discretized version of the Kratky-Porod wormlike (or persistent) chain as the building block, generalized to include flow. The Fokker-Planck equation resulting from such an analysis is converted to a Stochastic Differential Equation (SDE) from which the simulation algorithm for the NEBD is obtained. Various conformational and rheological quantities are monitored, under both steady-state and transient conditions, with the primary independent variable being the flexibility parameter b, the bending constant of the chain. The model qualitatively describes many of the experimentally-observed effects in such systems, most notably birefringence overshoots, cessation effects, and various steady-state effects. In addition, many of the qualitative rheological features of both rigid rod (or flexible) polymers are captured as b is made very large or small). The advantage of the NEBD over an analytical treatment is its ability to incorporate (analytically intractable) effects such as Hydrodynamic Interactions and its (natural) ability to obtain transient information, a facet useful in comprehending the differing dynamics of rigid and less rigid macromolecules. Textures During Recoil of Anisotropic Hydroxypropylcellulose SolutionsJean-Bernard Riti and Patrick Navard* *Corresponding Author AbstractThe recoil of anisotropic hydroxypropylcellulose solutions was studied by optical microscopy and light scattering. Different stresses were applied before stopping the flow and observing the recoil. At low stress levels, the scaling of the recoverable strain versus scaled relaxation time applies. A change of texture is noticeable only after most of the strain has been recovered. At high stress level, a band texture appears during recoil. The appearance of this band texture stops the recovery process until the band texture disappears, and the recovery process then continues. The presence of a band texture during recoil is shown to promote a larger recoil. High Frequency Shear Modulus of Polymerically Stabilized ColloidsS. L. Elliott and W. B. Russel AbstractRheological measurements on concentrated colloidal dispersions at high frequencies probe interactions at small separations and provide the most direct link between the shear modulus and the pair potential. For colloids stabilized with a grafted polymer layer, others have extracted the pair potential from measurements of the high frequency shear modulus via a molecular theory, which does not account for hydrodynamic interactions. Here we apply a nonequilibrium theory that includes the repulsion between polymer layers and its effect on the equilibrium structure, while accounting for flow of the suspending fluid within the layer in evaluation of the hydrodynamics. Predictions with a simple approximation for the hydrodynamic interactions, which interpolates between the lubrication and far field limits, are compared with the molecular theory. We also demonstrate qualitative agreement with experimental data and assess over what range of effective volume fractions neglect of hydrodynamic interactions permits data to be inverted to obtain an interaction potential. Rheological Analysis of Highly Pigmented Inks: Flocculation at High TemperaturesM. Fernández, M. E. Muñoz, and A.
Santamaría R. Azaldegui, R. Díez, and M. Peláez AbstractContinuous flow and oscillatory measurement results of a series of highly pigmented inks, containing a bimodal distribution of solid particles and dissolved polymer in the ink vehicle, are presented. Viscosity versus shear rate data are adjusted to a"Bingham Exponential Decrease" model, showing that the viscosity at high shear rates decreases with temperature following an Arrhenius-like equation. However, yield stress, viscosity taken at a shear stress of 250 Pa and thixotropy, increase with temperature, displaying an unusual behavior. It is assumed that a reinforcement of the cohesive interactions between components takes place on heating. Time, temperature and frequency effects on dynamic viscoelastic functions are analyzed, confirming the existence of flocculation due to interparticle attractions. The results are characterized by the following features: i) On the contrary to what is usually observed in liquids, both storage and loss moduli increase with temperature. ii) Both viscoelastic functions increase in a convex way with time, following an adapted Cheng-Evans model. iii) The increase of the viscoelastic functions is not altered by periods of resting time. The experimental results indicate that at rest the dispersions flocculate to a greater extent at high temperatures (typically at 40 and 60°C) than at 20°C. To explain these results we assume that heteroflocculation, through bridging of small particles, is promoted by phase separation of polymer solution forming the ink vehicle, which takes place at 36°C. Investigation of the Nonlinear Mixing Rule for Its Adequacy in Viscosity-to-MWD TransformsYongming Liu and Montgomery T. Shaw AbstractWhile the MWD model of Bersted and Slee, and later Malkin and Teishev, has been widely used in viscosity-to-MWD transformation, a fundamental assumption in the model — the empirical nonlinear mixing rule for homologous blends h1/a = S wi hi1/a — has not examined as a function of deformation rate and MWD. In this study of the nonlinear mixing rule, we evaluated the influence of deformation rate and MWD, both experimentally by using real polymers and theoretically. Direct experimental results indicate that the nonlinear mixing rule exponent can be a function of deformation rate. According to the theory-based quadratic mixing rule, the exponent a depends on both the deformation rate and the MWD of blends, suggesting that the nonlinear mixing rule is fundamentally invalid. However, for moderately wide distributions (Mw/Mn < 2), the nonlinear mixing rule with a constant a of 3.4 for all shear rates and MWDs, is almost equivalent to the quadratic mixing rule. Thus the simplified mixing-rule assumption of Bersted and Slee should be valid for many practical applications. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |