Center of mass description of polymer flow: Friction approximation for the pressure tensor with antisymmetric stress

Abstract

A statistical mechanical derivation of the equations of continuity and motion appropriate for the fluid dynamical description of dilute polymeric liquids is presented. This provides a molecular interpretation for the fluid densities of mass and momentum and their corresponding fluxes, which is different from that obtained by Curtiss, Bird, and Hassager [Adv. Chem. Phys. 35, 31 (1976)]. Comparisons are made with that theory. In particular, the pressure tensor appropriate to the present description has an antisymmetric component. For a dilute solution of dumbbells the symmetric part of the polymer contribution to the pressure tensor is reduced (with two approximations standard in polymer theory) to the familiar Giesekus result. Within the context of the same approximations the antisymmetric part is evaluated and found to be of comparable size.