Effect of adsorbed polymers on the slow motion of an assemblage of spherical particles relative to a fluid

Abstract

The effects of adsorbed polymers on the sedimentation of a homogeneous distribution of colloidal spheres and on the fluid flow through a bed of particles are investigated theoretically. The Reynolds number is assumed to be small, and the surface polymer layers are assumed to be thin with respect to the radius of particles and to the surface-to-surface spacing between neighboring particles. The effects of interaction of the individual particles are taken into explicit account by employing a fundamental cell-model representation which is known to provide good predictions for the motion of a swarm of spheres within a fluid in the absence of adsorbed polymers. To solve the Stokes flow equations within and outside the polymer layer a method of matched asymptotic expansions in a small parameter λ is used, where λ is the ratio of the length scale of the polymer layer to the particle radius. The results for the sedimentation rate and the pressure drop are expressed in terms of an effective hydrodynamic thickness (L) of the polymer layer, which are accurate to O(λ2). When the concentration of particles in a suspension or a bed is increased, L becomes larger, meaning the settling velocity decreases or the pressure drop increases. The O(λ) term for L normalized by its value in the limit λ → 0 is found to be independent of the polymer segment distribution, the hydrodynamic interactions among the segments, and the volume fraction of the segments. The O(λ2) term for L, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the particle-interaction effects on the motion of polymer-coated particles relative to a fluid can be quite significant.