A Gaussian closure of the second-moment equation for a Hookean dumbbell with hydrodynamic interaction (Q1116821)

Most bead-spring models of dilute solutions of polymers with hydrodynamic interaction have relied on an averaging of the hydrodynamic interaction tensor, which removes the configuration dependence, but also leads to a solvable diffusion equation. In this paper, we attempt to retain the effects of the configuration dependence by postulating a Gaussian closure of the exact second moment equation for the Hookean dumbbell where the Oseen-Burgers tensor has been used to model the hydrodynamic interaction. The second-moment obtained from the closed set of equations is directly related to the stress tensor. For very low and very high shear rates in steady shear flow, the material properties calculated using the Gaussian closure compare well with those calculated from a Galerkin solution of the diffusion equation. Results for elongational flow and small-amplitude oscillatory shear flow are also included.