Linear viscoelastic behavior of the Hookean dumbbell with internal viscosity |
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Authors: | Chi C. Hua Prof. Jay D. Schieber Charles W. Manke |
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Affiliation: | (1) Department of Chemical Engineering, University of Houston, 77204-4792 Houston, Texas, USA;(2) Department of Chemical Engineering, Illinois Institute of Technology, 60616 Chicago, Illinois, USA;(3) Department of Chemical Engineering and Materials Science, Wayne State University, 5050 Anthony Wayne Dr., 48202 Detroit, Michigan, USA |
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Abstract: | The linear viscoelastic modulus G(t) predicted by the analytical formulations of Schieber (1993), Wedgewood (1993), Dasbach et al. (1992), and Booij and van Wiechen (1970) for the free-draining Hookean dumbbell with internal viscosity (IV) are compared with exact analytical results and exact numerical results obtained from Brownian dynamics simulations. All of these analytical formulations employ the Booij and van Wiechen expression for the IV force, thereby eliminating errors associated with linearization of the deformational velocity, however the theories differ in the approximations employed to solve configuration moment equations. Comparison with the exact G(t) results provides a means of testing these approximations. The approximate theories all correctly predict the singular part of G(t) at t = 0, providing correct predictions of , however deviations from the exact G(t) are seen in all cases for t > 0. |
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Keywords: | Internal viscosity linear viscoelasticity relaxation modulus Brownian dynamics closure approximations |
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