Renormalization-group calculation of viscometric functions based on conventional polymer kinetic theory

Hans Christian Öttinger, Yitzhak Rabin

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37 Scopus citations

Abstract

In order to obtain useful information from a perturbation expansion of hydrodynamic-interaction effects for long Rouse chains the basic equations of polymer kinetic theory are generalized to d-dimensional space. After solving the Kirkwood diffusion equation to first order in the strength of the hydrodynamic interactions, the Kramers expression for the stress tensor is used to calculate the corresponding first-order expansions of the zero-shear-rate viscometric functions for arbitrary d. Singularities occurring in these expansions near four dimensions indicate that local hydrodynamic interactions are not described in a proper way and, therefore, a renormalization of one of the model parameters, the bead friction coefficient, is necessary. With the renomalized perturbation expansions, various ratios of experimentally accessible quantities are calculated; in particular, ratios involving normal-stress coefficients are calculated for the first time by renormalization-group methods.

Original languageEnglish
Pages (from-to)53-93
Number of pages41
JournalJournal of Non-Newtonian Fluid Mechanics
Volume33
Issue number1 C
DOIs
StatePublished - 1989
Externally publishedYes

Bibliographical note

Funding Information:
We wish to thank Professors R.B. Bird and A. Silberberg for numerous helpful comments on the first draft of this article. Also, we would like to thank the Batsheva de Rothschild Foundation and the Deutsche For-schungsgemeinschaftf or their financial support for H.C.O.‘s visits to the Weizmann Institute of Science during which the work presented in this paper was begun. This work was also supported by the U.S.-Israel Binational Science Foundation grant No. 87-00134a nd by DARPA (through the La Jolla Institute, CA).

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