Kinetic theory of polyelectrolyte adsorption in shear flow

Abstract

The effect of hydrodynamic interactions on the adsorption of a polyelectrolyte molecule onto a wall in shear flow is investigated using a bead-spring dumbbell model. Bead-bead and bead-wall electrostatic interactions are taken into account using screened Coulombic interactions, and the hydrodynamic interactions are incorporated using the approach proposed by Ma and Graham [Phys. Fluids 17, 083103 (2005)]. An analytical expression for the concentration profile of the polyelectrolyte is derived which predicts a competition between bead-wall hydrodynamic interactions and bead-wall electrostatic attraction. The behavior of the concentration profile is explored as a function of the Weissenberg number, surface (wall) charge density, charge on the beads, and screening length. The charge on the beads assists migration of the dumbbell away from an uncharged wall, whereas for an oppositely charged wall it increases the probability of finding the dumbbell close to the wall. In some cases, the concentration profile shows a very sharp peak near the wall whose distance from the wall increases with dumbbell size, indicating the possibility of size-based separation.