Macromolecules in nonhomogeneous velocity gradient fields

Abstract

Some dilute solution kinetic theory results for bead‐spring‐type macromolecular models (linearly elastic dumbbell and Rouse) in nonuniform velocity gradient fields are obtained. It is shown that contrary to the homogeneous flow result, in general, a macromolecular solute does not move with the local center‐of‐mass solvent velocity in a nonhomogeneous flow. This results essentially from a unique coupling between segmental Brownian motion of the macromolecule in the flowfield and the center‐of‐mass translational diffusion possible only in nonhomogeneous flow. Poiseuille flow between parallel plates and circular Couette flow problems are solved for the dumbbell and some results are obtained for the Rouse model. Migration along streamlines occurs in the Poiseuille flow and migration across streamlines occurs in the Couette flow. Additional energy dissipation results for the Rouse model in Poiseuille flow relative to the simple shear flow case. Nonuniform concentration profiles are calculated in Couette flow by taking the appropriate average of the exact equation for the dumbbell configuration space distribution function.