Configuration-dependent friction coefficients and elastic dumbbell rheology |
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Authors: | Xi-Jun Fan R. Byron Bird Michael Renardy |
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Affiliation: | Chemical Engineering Department and Rheology Research Center, University of Wisconsin, Madison, WI 53706, U.S.A.;Department of Mathematics and Mathematics Research Center, University of Wisconsin, Madison, WI 53706 U.S.A. |
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Abstract: | The kinetic theory of nonlinear elastic dumbbells, with bead friction coefficients that depend linearly on the interbead distance, is used to obtain the elongational viscosity and the dumbbell stretching as a function of elongation rate. The results are obtained by solving numerically the “diffusion equation” for the configurational distribution function. No S-shaped curves were found for the elongational viscosity or for the mean-square end-to-end distance. Previous investigators did report S-shaped curves and related “hysteresis” effects. However, their results were based on using mathematical approximations that now appear to be inappropriate. |
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