Motion of a Colloidal Particle Coated with a Layer of Adsorbed Polymers in a Spherical Cavity

Motion of a Colloidal Sphere Covered by a Layer of Adsorbed Polymers Normal to a Plane Surface

A combined analytical-numerical study is presented for the slow motion of a spherical particle coated with a layer of adsorbed polymers perpendicular to an infinite plane, which can be either a solid wall or a free surface. The Reynolds number is assumed to be vanishingly small, and the thickness of the surface polymer layer is assumed to be much smaller than the particle radius and the spacing between the particle and the plane boundary. A method of matched asymptotic expansions in a small parameter lambda incorporated with a boundary collocation technique is used to solve the creeping flow equations inside and outside the adsorbed polymer layer, where lambda is the ratio of the characteristic thickness of the polymer layer to the particle radius. The results for the hydrodynamic force exerted on the particle in a resistance problem and for the particle velocity in a mobility problem are expressed in terms of the effective hydrodynamic thickness (L) of the polymer layer, which is accurate to O(lambda2). The O(lambda) term for L normalized by its value in the absence of the plane boundary is found to be independent of the polymer segment distribution and the volume fraction of the segments. The O(lambda2) term for L, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the boundary effects on the motion of a polymer-coated particle can be quite significant. Copyright 1999 Academic Press.

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

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 lambdai (where i = 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 lambdai is the ratio of the polymer-layer length scale to the radius of particle i. 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 to O(lambdai2). The O(lambdai) term for Li normalized 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. The O(lambdai2) term for Li, 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. Copyright 1997 Academic Press. Copyright 1997Academic Press