Effects of Adsorbed Polymers on the Axisymmetric Motion of Two Colloidal Spheres

Abstract

The effects of adsorbed polymer on the slow motion of two spherical particles along the line of their centers are examined semianalytically. The particles may have unequal radii, and their surface polymer layers are allowed to differ in characteristics. The surface polymer layer on each particle is assumed to be thin relative to the radius of the particle and to the surface-to-surface distance between the particles. A method of matched asymptotic expansions in small parameters λi(wherei= 1 and 2) combined with a boundary collocation technique is used to find the solution for the creeping flow field within and outside the adsorbed polymer layers, where λiis the ratio of the polymer-layer length scale to the radius of particlei. The results for the hydrodynamic forces exerted on the particles in a resistance problem and for the particle velocities in a mobility problem are expressed in terms of the effective hydrodynamic thicknesses (Li) of the polymer layers, which are accurate toO(λi2). TheO(λi) term forLinormalized by its value in the absence of the other particle is found to be independent of the polymer segment distribution, the hydrodynamic interactions among the segments, and the volume fraction of the segments. TheO(λi2) term forLi, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the effects of particle interactions on the motion of polymer-coated particles can be quite significant, especially when the particles are moving in the opposite directions.