FENE dumbbell model and its several linear and nonlinear closure approximations

We present some analytical and numerical studies on the finite extendible nonlinear elasticity (FENE) model of polymeric fluids and its several moment-closure approximations. The well-posedness of the FENE model is established under the influence of a steady flow field. We further infer existence of long-time and steady-state solutions for purely symmetric or antisymmetric velocity gradients. The stability of the steady-state solution for a general velocity gradient is illuminated by the analysis of the FENE-P closure approximation. We also propose a new linear closure approximation utilizing higher moments, which is shown to generate more accurate approximations than other existing closure models for moderate shear or extension rates. An instability phenomenon under a large strain is also investigated. This paper is a sequel to our earlier work [P. Yu, Q. Du, and C. Liu, Multiscale Model. Simul., 3 (2005), pp. 895-917].