Nonlocal Hydrodynamic Theory of Flow in Polymer Layers

Abstract

We present a nonlocal hydrodynamic theory for flow through an adsorbed layer of homopolymer. Our theory is based upon a multiple-scattering treatment in which the polymer is decomposed into loops, each attached to the surface at a point and obeying Zimm dynamics. The multiple scattering series is converted into an integral equation which we solve numerically. The dependence of our results on the truncation procedure in the sum over Zimm modes is discussed. Unlike previous models, which rely on a local porosity description, our theory explicitly incorporates polymer dynamics and is hence applicable to finite frequencies and (in principle) nonlinear responses. For an isolated layer, we present results for weak oscillatory and steady shear flows at ϑ conditions. We also give results for steady flow between a pair of parallel plates coated with homopolymer, which may be relevant to the dynamics of polymer-coated colloids undergoing hydrodynamic collisions.