to the effective decrease in size (15). The attachment of An analytical study is presented for the quasisteady translation polymers to microporous membranes offers the possibility and steady rotation of a spherical particle covered by a layer of of manipulating the transport rate of solvent and solutes adsorbed polymers located at the center of a spherical cavity that and negating the adverse effects of pore-size distribution on may also have an adsorbed polymer layer on its inside wall. The membrane separations ( 16).
Reynolds number is assumed to be small, and the surface polymer
The structure of an adsorbed polymer layer depends on layers are assumed to be thin with respect to the particle radius the nature of the polymer, the solvent, and the interface. In and the spacing between solid surfaces. To solve the Stokes flow general, the adsorbed polymer chains consist of a collection equations within and outside the polymer layers a method of of ''trains,'' in which each polymer segment contacts the matched asymptotic expansions in small parameters l 1 and l 2 is used, where l 1 and l 2 are the ratios of the polymer-layer length interface, ''loops,'' in which only the initial and final segscale to the radius of curvature at the particle surface and at the ments attach to the interface, and ''tails,'' which begin at cavity wall, respectively. The results for the hydrodynamic force the interface but terminate in the solution (17, 18). Since and torque exerted on the particle are expressed as an effective the adsorbed polymer layer is diffuse, there is no unique hydrodynamic thickness (L) of the adsorbed polymer layer surmeasure of its thickness. One convenient definition, applicarounding the particle, which are accurate to O(l 2 1 ). The O(l 1 ) term ble to both colloidal particles and micropores, is the hydrofor L normalized by its value in the absence of the cavity is found dynamic thickness which is the distance the ''no-slip'' to be independent of the polymer segment distribution, the hydroboundary condition on the fluid velocity must be moved into dynamic interactions among the segments, and the volume fracthe fluid phase to produce the same hydrodynamic effect as tion of the segments. The O(l 2 1 ) term for L, however, is a sensitive the polymer layer. For the case of a polymer layer that is function of the polymer segment distribution and the volume fracthin relative to the radii of curvature of the solid surface, tion of the segments. In general, the boundary effects on the motion of a polymer-coated particle can be quite significant in appropriate previous theoretical analyses (19-21) predict the same value situations. แญง 1997 Academic Press of the hydrodynamic thickness for different external flows Key Words: particle translation; particle rotation; adsorbed polyand geometries, given the same local rheological model for mers; hydrodynamic thickness; boundary effects.
flow within the surface layer. It has been found both theoretically (19) and experimentally (22) that the hydrodynamic thickness is often much larger than the layer thickness deterenergy between particles (14). Another spectacular effect of calculations indicated that (i) the O(l 2 1 ) term is negative, such adsorption is the restriction of flow in capillaries due meaning the hydrodynamic thickness decreases as the particle radius decreases assuming all other conditions are con-1 To whom correspondence should be addressed. stant, (ii) the free-draining assumption for flow through the 411