Gaussian approximation for Rouse chains with hydrodynamic interaction

A new approximate method for treating hydrodynamic interactions in a bead–spring model for dilute polymer solutions is developed. This method, which is based on the assumption that the configurational distribution function is Gaussian, accounts for fluctuations in the hydrodynamic interaction. In this Gaussian approximation, we construct a rheological equation of state and a codeformational memory-integral expansion for chains of arbitrary length. As a straightforward application of these general results, we discuss small-amplitude oscillatory and steady shear flows. For dumbbells, the rheological equation of state in the Gaussian approximation is obtained by a slight modification of the corresponding equation for the consistent averaging method.