Fluid dynamical effects of polymers adsorbed to spherical particles

The effects of adsorbed macromolecules (polymers) on certain transport coefficients of spherical particles are determined using methods of matched asymptotic expansions to solve the Stokes flow equations within and outside the polymer layer. The main advantage of this analysis is that it allows direct substitution of a linear, viscous model for flow through the polymer segments to obtain the desired transport coefficient without solving the entire set of fluid dynamics equations. The results, expressed as an effective ‘‘hydrodynamic thickness’’ (Lh) of the adsorbed polymer, are accurate to O(λ) where λ is the ratio of the polymer-layer length scale to the particle radius. Three flow configurations are considered: steady translation and steady rotation of a single particle, and pure straining flow around a single particle that produces stresses leading to enhanced viscosity of a suspension (intrinsic viscosity). The Reynolds number is assumed to be small in all cases. The O(λ0) term for Lh is the same for all three flows, but the O(λ) corrections differ. Sample calculations show that (1) the O(λ) correction is negative, meaning Lh increases as particle radius increases assuming all other conditions are constant; (2) a free-draining model for flow through the polymer chains is a very good approximation for calculating Lh if the Stokes radius of the polymer segments is much smaller than the length scale of the polymer scale; and (3) the presence of only a small amount of adsorbed polymer ‘‘tails’’ can make a significant contribution to Lh if the length scale of the extended tails exceeds the length scale of the ‘‘loops’’ by a factor of 2 or more. Finally, we derive the hydrodynamic response of a particle having polymer nonuniformly adsorbed to its surface and demonstrate through a sample calculation how an ‘‘adsorption dipole’’ can lead to strong orientational bias of the particle as it moves in response to an applied force.