Mathematical Modeling for Complex Fluids and Flows by Michel O. Deville & Thomas B. Gatski

Author:Michel O. Deville & Thomas B. Gatski
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(5.266)

Using appropriate averages of (5.262) with the second moments, one is led (after a few pages of algebra (sic)) to the equation

(5.267)

At equilibrium when there is no flow,

(5.268)

and the polymeric stress is then given by

(5.269)

where G e is the plateau modulus k B θ per displaced volume of an entanglement segment.

The Rolie-Poly model, aimed at an easier computational treatment, was designed by Likhtman and Graham (2003). The one-mode equation is a simplified version of the full model (5.267), and can be obtained through several routes. The simplest one is to drop the dependencies with respect to s in f(s,s′) to generate the polymeric stress in terms of G e units

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