Langevin dynamics of Rouse chains under flow

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Abstract
A systematic approach is developed for describing the hydrodynamics of flowing polymer solutions by using a microscopic Langevin model for which the inertial nonlinearities and solvent advection are ignored. The influence of polymer motion on the solution velocity field is evaluated by averaging over the polymer degrees of freedom at a time in the distant past in order to derive an effective hydrodynamic equation of motion for the averaged polymer solution. The polymer’s contribution to the fluid stress tensor is computed from the total solution stress tensor whose divergence appears in the averaged effective hydrodynamic equation. Introduction of the Rouse chain and long wavelength limits enables the analytical evaluation of this stress tensor for any time-dependent linear flows. All the material functions for the polymer solution are evaluated in a simplified fashion for these flows, recovering some known results and deriving several new ones.