The diffusion tensor for a flowing dilute solution of Hookean dumbbells: Anisotropy and flow rate dependence

For a dilute solution of Hookean dumbbells, the consistent averaging and Gaussian approximations for the hydrodynamic interaction have recently been shown to lead to an anisotropic translational diffusion tensor, which is shear rate dependent in steady shear flow. These properties of the diffusion tensor arise because of the nature of the average friction experienced by the dumbbell as it translates through the solvent. In this paper, the relationship between the average friction on the dumbbell and the spatial distribution of mass about the center of the dumbbell is examined. It is found that the anisotropic and flow rate dependent distribution of mass caused by the solvent flow field is responsible for the average friction having the same properties.