Macromolecules in nonhomogeneous flow fields: A general study for dumbbell model macromolecules

The hydrodynamics of bead-spring model macromolecules in nonhomogeneous flows has recently been worked out. By taking a non-infinite distance between the beads (relative to the bead size) into account a hydrodynamic driving force was found. In this paper we explore the kinetic theory consequence of that force and show that non-uniform (polymer) concentration profiles are to be expected in nonhomogeneous flows. The diffusion equation for a dilute polymer solution is derived from the continuity equation for the distribution function. Arguments, leading to a well-ordered pertubation expansion of the continuity equation are advanced and the zeroth order function of this hierarchy is studied for models with linear springs. Details for the channel flow system are worked out with special emphasis on the relation between the polymer concentration and the parameters of the system. Explicit results are presented for models with linear springs. It is shown that if the Oseen tensor is not preaveraged, inadmissible results emerge.