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Journal of RheologyVolume 42, Issue 4 (July-August 1998) |
Contents
A Model for the Necking Phenomenon in High-Speed Fiber Spinning Based on Flow-Induced Crystallization Jaydeep A. Kulkarni and Antony N. Beris* AbstractIn this work we investigate the use of an inhomogeneous structural model which explicitly takes into account flow-induced crystallization for representing the necking phenomenon in high-speed fiber spinning. For simplicity, we have considered an one-dimensional (cross section averaged) approximation for an isothermal system with no surface tension and air drag, with or without inertia. Flory's approach (J. Chem. Phys. 15, 397-408 (1947)) is used to predict the onset of crystallization in the spinline. After the onset of crystallization, the fiber is modeled as an inhomogeneous medium with two separate (meso) phases, one semi-crystalline and the other amorphous. The amorphous phase, before and after the onset of crystallization, is modeled as a viscoelastic fluid, represented here by the Extended White-Metzner model. The semi-crystalline phase is modeled as an anelastic solid. We demonstrate neck formation for a variety of processing conditions and material property values consistent with those encountered in practice. In particular, the addition of inertial effects, which can also be important in high-speed fiber spinning, shifts but does not eliminate the window in parameter space over which the inertialess model predicts neck formation. Based on these results, we propose as a mechanism for the neck formation the structural changes within the material induced by the crystallization and the ability of the semi-crystalline phase to rapidly take up high stresses. Shear-Thinning Predictions from Particle Motion ModelingRobert R. Bilodeau and Douglas W. Bousfield AbstractA Stokesian dynamics model is presented to predict suspension viscosity and microstructure for concentrated suspensions. The influence of electrostatic repulsive forces, London-van der Waals attractive forces and boundary interactions on the degree of shear-thinning is reported. Three different mechanisms for shear-thinning are described and quantified. The degree of shear-thinning caused by Brownian motion is well predicted by using random and layered structures. Shear-thinning for repulsive forces between particles is caused by the "melting" or breakup of an ordered or semi-crystalline configuration as the shear rate increases. For suspensions flocculated into a secondary minimum, shear-thinning is produced by breakup of particle aggregates as the hydrodynamic forces dominate the interparticle forces. At high concentrations, the dispersed and flocculated suspensions can form slip planes that reduce suspension viscosity. Rough walls increase the viscosity predictions by an order of magnitude and cause the shear thinning prediction to compare well with experimental results from the literature. Frequency Response of a Shear Stress TransducerInstalled in a Sliding Plate RheometerJohn M. Dealy and Ranjit S. Jeyaseelan AbstractA number of laboratories are currently using sliding plate rheometers equipped with shear stress transducers to study the nonlinear viscoelasticity and slip of molten polymers. In making such measurements, it is sometimes essential to know to what degree the dynamic response of the shear stress transducer itself is influencing the output signal. Experiments should be designed to minimize this effect, but some attenuation and phase shift is inevitable because of the presence of polymer inside the transducer. We have measured the dynamic response of a shear stress transducer in situ in a sliding plate rheometer for two molten polyethylenes. We have also developed a model for the transducer response. In oscillatory shear experiments above a frequency of 1 Hz, the amplitude ratio and phase lead are significant for both materials studied. Comparative Study of Visco-elastic Properties Using Virgin YogurtGuy Dimonte, Don Nelson, Sam Weaver, and
Marilyn Schneider AbstractWe describe six different tests used to obtain a consistent set of visco-elastic properties for yogurt. Prior to yield, the shear modulus m and viscosity h are measured non-destructively using the speed and damping of elastic waves. Although new to foodstuffs, this technique has been applied to diverse materials from metals to the earth's crust. The resultant shear modulus agrees with m ~ E/3 for incompressible materials, where the Young's modulus E is obtained from a stress-strain curve in compression. The tensile yield stress to is measured in compression and tension, with good agreement. The conventional vane and cone/plate rheometers measure a shear stress yield tos ~ to/Ö 3, as expected theoretically, but the inferred "apparent" viscosity from the cone/plate rheometer is much larger than the wave measurement due to the finite yield (tos ¹ 0). Finally, we inverted an open container of yogurt for 106 sec >> h/m and observed no motion. This demonstrates unequivocally that yogurt possesses a finite yield stress rather than a large viscosity. We present a constitutive model with a pre-yield viscosity to describe the damping of the elastic waves and use a simulation code to describe yielding in complex geometry.Steady and Transient Rheological Behavior of Mesophase PitchesO. Fleurot and D. D. Edie AbstractThe steady and transient rheological behavior of three mesophase pitches (two of them obtained from catalytic polymerization of naphthalene and methyl-naphthalene, respectively, and one from supercritical extraction of petroleum pitch) was investigated. Steady shear flow curves were generated and showed that all pitches exhibited a shear thinning behavior at low rates of shear (region I flow). For higher shear rates, the viscosity became constant (region II flow). Similarly to observations on liquid crystal polymers (LCPs), this behavior was attributed to the polydomain structure that mesophase pitches exhibit. Reflective polarized light microscopy on quenched samples showed that the mesophase pitches domain size decreased with increasing rates of shear. This domain shrinkage was successfully predicted using a model developed for LCPs [Marrucci (1984)]. The transient rheological behavior associated with inception and cessation of steady shear flow also was studied for the three mesophase pitches. The results showed that, upon start-up of flow, the shear stress exhibited an overshoot, and its magnitude greatly depended on the shear history of the mesophase pitches. This behavior, already reported for LCPs, is probably a result of the polydomain structure of mesophase pitches. The Work of Adhesion of Polymer/Wall Interfaces and Its Association With the Onset of Wall Slip Spiros H. Anastasiadis1 and
Savvas G. Hatzikiriakos2* AbstractThe interfacial characteristics of a variety of polymer/wall interfaces were measured by using the sessile drop method in order to calculate the work of adhesion. Polymers included linear low-density as well high-density polyethylenes, while wall substrates included clean stainless steel and modified stainless steel by applying two different fluoropolymers in order to alter its surface energy. A linear correlation is found between the critical shear stress for the onset of slip and the work of adhesion of the corresponding polymer/wall interface, in agreement with earlier publications of Hill et al. (1991) and Hatzikiriakos et al. (1993). In the present work, the experimental results are interpreted in terms of parameters defined by these two theories. It is suggested that small deviations from the no-slip boundary condition in the case of polymer melt flow are due to a stress-induced chain detachment/desorption of polymer chains from the wall. Some General Properties of Solid Polymer Inelastic Deformation Behavior and Their Application to a Class of Clock ModelsErhard Krempl AbstractResults of macroscopic experiments on the inelastic deformation behavior of solid polymers are used to establish general properties believed to be valid below the glass transition temperature. They include nonlinear rate sensitivity in the inelastic range in monotonic loading and the transition from primary, to primary and secondary, and to primary and secondary and tertiary creep as the creep stress level increases beyond the quasi linear region. Consistent with the notion of a solid it is presumed that a nonzero stress can be sustained at rest. The rest stresses at which relaxation tests terminate form the relaxation boundary. It is suggested that this relaxation boundary has the appearance of a nonlinear stress-strain curve. These properties are used as criteria in evaluating some types of "clock" models where ordinary time in the kernels of linear viscoelastic integral representations is replaced by a transformed time. It is a function of either the invariants of strain or the invariants of stress. It is shown that these models cannot reproduce the change in the creep properties as stress level increases. Creep always terminates. For large times when asymptotic solutions hold linear rate sensitivity and a linear relaxation boundary are predicted. Nonlinear rate sensitivity can be modeled before the asymptotic solution is reached. Shear Thinning of Colloidal DispersionsR. A. Lionberger AbstractIn this paper we calculate numerically the shear induced distortion of the equilibrium microstructure in a dilute colloidal suspension. In the low density limit, our predictions both with and without hydrodynamic interactions follow the form of the Ree-Eyring equation for the shear rate dependence of the rheology. For low to intermediate shear rates, rescaling the low density solutions by appropriate volume fraction dependent scale factors captures many of the qualitative features observed in simulation and experiment on systems at high concentration, including shear thinning and normal stresses. At high shear rates, more detailed consideration of many-particle interactions are required to account for the observed phenomenology and the use of the mean-field approximation inherent in the rescalings fails. Comparison of systems with and without hydrodynamic interactions suggests that both hydrodynamic and thermodynamic forces act to increase the stress relaxation time in concentrated suspensions. Measurement of Foam Modulus via a Vane RheometerX. D. Zhang, D. W. Giles, V. H. Barocas1,
K. Yasunaga2, C. W. Macosko* AbstractA vane rheometer was used to measure the modulus of foam systems. Modulus development in a reactive polyurethane foam system was captured using a commercial stress controlled rheometer with a four-blade vane geometry test fixture. The results were compared to those from a temperature programmed flooded parallel plate method. The vane geometry method was shown to be a convenient and accurate way to measure the physical gelation time of the reactive foaming system, without the complexity of the temperature-program method. Shaving cream was used as a calibration material to show the validity of the vane method for foam modulus measurements. For open cell foams, the error in the vane method increases due to the additional compressibility of the foam. The nature and magnitude of this error was analyzed via numerical simulation. Viscosity Model for Polydisperse Polymer MeltsD. Nichetti and I. Manas-Zloczower AbstractA simple superposition model was used to define the relationship between molecular weight distribution and shear viscosity for linear polymeric systems. GPC data for molecular weight distributions were fitted using statistical distribution functions. A simple superposition model was then employed to calculate the shear viscosity for the systems investigated. The effect of polydispersity on the shape of the flow curves was calculated. The simplicity of the model makes feasible its use in numerical simulations of complex geometries as encountered in polymer processing equipment. The present study sheds also some light on the relationship between entanglement and disentanglement phenomena in polymeric systems. Toward a Rationalization of the Slump Test for Fresh Concrete: Comparisons of Calculations and ExperimentsW. R. Schowalter and G. Christensen* AbstractData are presented to confirm that a simple analysis based upon the Bingham model correlates slump data for a wide variety of materials, including concrete, silt, and mayonnaise. Viscoelastic Behavior of Bimodal SuspensionsToshiyuki Shikata*, Hirokazu Niwa, and
Yotaro Morishima AbstractThe dynamic viscoelastic behavior of suspensions with bimodal particle radius distributions was examined varying the ratio of the radii of large and small particles (rL/rS) up to 3.3. Monodisperse silica spherical particles with radii ranging from 65 to 215 nm were used. The medium was ethyleneglycol possessing a refractive index very close to that of the used silica particles. The medium reduced effectively interparticle potentials due to dispersion forces, and it provided bimodal suspensions with only the hard core interparticle potential. The total weight fraction of the suspended particles was kept at 52 wt%, while the weight composition of the small particles (Xs) to the total particulate mass was increased from 0 to 1 with a 0.2 interval. The bimodal suspensions showed viscoelastic behavior with a frequency dependence similar to that of a unimodal (monodisperse) suspension, which was attributed to the contribution of Brownian motion of suspended particles. The zero-shear viscosities ( h0) of the bimodal suspensions showed minima at Xs values dependent on rL/rS, whereas the high frequency limiting viscosities showed no obvious minima. A simple model is proposed to interpret these viscoelastic features in the bimodal suspensions. In the model, we assumed that in the suspension a Brownian motion of a hypothetical particle with an average radius governed the whole viscoelastic features. Values of h0 predicted by the model and experiments agreed fairly well.The Rheology of Aqueous Dispersions of Spindle-type Colloidal Hematite RodsM. J. Solomon* and D.V. Boger Department of Chemical Engineering and Advanced Mineral Products Research Centre University of Melbourne, Parkville, Victoria 3052 Australia *Current address: Department of Chemical Engineering University of Michigan, Ann Arbor, MI 48109 E-mail: mjsolo@umich.edu AbstractThe rheology of aqueous dispersions of colloidal hematite ( a-Fe2O3) rods with well-characterized shape and dimension was investigated. The effects of volume fraction (f), aspect ratio and Debye length (k0–1) on the rheology were studied in particular. The particles were spindle-type bodies with aspect ratios equal to 8.4 and 4.8. They were dispersed in aqueous solutions of known ionic strength at a z-potential which was characterized in the Smoluchowski limit. Their rheology was compared to that of spherical hematite prepared by the method of Matijevic (1985). Dilute solution viscometry indicated that the effects of k0–1 and aspect ratio on the O(f2) contribution to the low-shear effective viscosity were of comparable magnitude, and that the Huggins coefficient was a decreasing function of aspect ratio. For concentrated suspensions, the dimensionless shear thinning was adequately fit by a correlation involving a critical stress which was originally developed for spherical suspensions (Krieger and Dougherty, 1959). The volume fraction dependence of the zero-shear viscosity, h0, was found to be a strong function of both aspect ratio and k0–1. The aspect ratio affected both the volume fraction at which h0 diverged (fm), and the strength of the singular behavior (characterized by a in h0/m = (1 – f/fm)–a). In contrast, k0–1 affected fm, but not a. The effect of aspect ratio and volume fraction on the linear viscoelasticity of suspensions for f > fm was quantified. The results highlight the particular ways in which the colloidal suspension rheology of moderate aspect ratio rods differs from that of spheres.Particle-Phase Pressure in a Slow Shearing Flow Based on the Numerical Simulation of a Planar Suspension of Rough Contacting CylindersJ. J. Haan* and P. S. Steif AbstractPlanar Stokes flow of a concentrated planar suspension of rigid cylinders is simulated using the finite element method. A constraint condition, limiting cylinder approach to a specified distance, is applied to simulate inter-particle contacts. The results of these simulations reveal a stress response and ordering of the cylinders which is similar to experimental observations of suspensions of nominally spherical particles. These results include direct observations of anisotropic structure, as well as the development of a distinct particle-phase pressure resulting from the asymmetry of inter-particle contacts and the consequent developed anisotropy. A simple pair-wise interaction model is proposed for abinitio prediction of the particle-phase pressure for these planar suspensions of cylinders. The Rheology of the Rheotens Test M.H. Wagner and A. Bernnat AbstractIsothermal melt spinning is a prototypical example of many polymer processes: The polymer melt is first subjected to simple shear flow in the extrusion die, which is followed by uniaxial extension under constant force in the spinline. In a Rheotens test, the tensile force needed for elongation of an extruded filament is measured as a function of the draw ratio. In this way, a whole set of melt spinning conditions is probed during one test run. The analysis of this complicated deformation history is simplified by the existence of Rheotens Grandmastercurves. These allow a direct and straightforward description of material behaviour in the fiber spinning process, and a simplified determination of an apparent elongational viscosity under the action of a constant drawdown force. Interfacial Molecular Instability Mechanism for Sharkskin Phenomenon in Capillary Extrusion of Linear PolyethylenesJ.R. Barone, N. Plucktaveesak, and S. Q.
Wang* AbstractA comprehensive study of sharkskin behavior in linear polyethylene extrusion is carried out to explore its molecular origin. Experimental characteristics are analyzed as a function of temperature, applied stress, and die surface condition. The experimental data favor an interfacial molecular instability (IMI) mechanism for sharkskin formation over a non-interfacial continuum mechanical mechanism. The effect of a local cooling of the die exit is demonstrated to be predictable by the proposed IMI mechanism. The IMI mechanism states that sharkskin occurs because of a local conformational transition at the die exit wall where the adsorbed chains entrap a layer of interfacial chains. This layer oscillates between entanglement and disentanglement states due to a reversible coil «stretch transition. The corresponding oscillation of the exit wall boundary condition leads to cycles of local stress relaxation and growth and to periodic perturbation of the extrudate swell in the form of sharkskin-like surface roughening on the extrudate. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |