HYDRODYNAMIC EFFECTS OF SURFACE-LAYERS ON COLLOIDAL PARTICLES

General solutions to the Stokes equations for a sphere held fixed in a general quadratic flow are used to develop the hydrodynamic effects o f a thin layer of material at the surface which has different rheologi cal properties than the solution. These surface-layer effects are deve loped as an expansion to O (lambda(2)) where lambda is the ratio of th e length scale of the surface layer (delta) to the particle radius (R) . The formalism is developed such that the force, couple and stresslet on the coated sphere are calculated directly by substituting a rheolo gical model for the surface layer into an analysis based on unidirecti onal how; thus, the hydrodynamic effects to O(lambda(2)) can be determ ined without solving the Stokes equations outside the layer. The O(lam bda) effect is independent of the type of flow (translation, rotation, extension) in the sense that a single parameter A, which depends only on the properties of the surface layer, applies to all how types. How ever, the O (lambda(2)) effects depend both on the properties of the s urface layer and the type of flow about the particle. Examples are pre sented as models for particles in solutions of nonadsorbing and adsorb ing polymers. In the case of an adsorbing polymer whose layer is model ed by the Brinkman equation, the O(lambda(2)) effects can be computed from the lowest order description of velocity field, that is, viscous flow past a flat surface. The hydrodynamic interactions between two pa rticles and between a particle and a solid boundary are developed by a method of reflections accounting for the presence of the surface laye rs on the particles.