Hydrodynamic Effects of Surface Layers on Colloidal Particles

Abstract

General solutions to the Stokes equations [or a sphere held fixed in a general quadratic flow are used todevelop the hydrodynamic effects of a thin layer of material at the surface which has different rheological properties than the solution. These surface-layer effects are developed as an expansion to O().') where Ais the ratio of the length scale of the surface layer (b) 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 rheological model for the surface layer into an analysis based on unidirectional flow; thus, the hydrodynamic effects to O(A') can be determined without solving the Stokes equations outside the layer. The O(A)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 flow types. However, the O(A') effects depend both on the properties of the surface layer and the type of flow about the particle. Examples are presented as models for particles in solutions of nonadsorbing and adsorbing polymers. In the case of an adsorbing polymer whose layer is modeled by the Brinkman equation, the O(A') 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 particles and between a particle and a solid boundary are developed by a method of reflections accounting for the presence of the surface layers on the particles.

Hydrodynamic radius approximation for spherical particles suspended in a viscous fluid: Influence of particle internal structure and boundary

“…[4]. In the last reference, ǫ (called there λ) was used as the expansion parameter, and the O(ǫ 2 ) corrections had to be evaluated, because they were not small.…”

“…Anderson et al analyzed theoretically hydrodynamic thickness of thin polymer layers at solid-liquid surfaces [3], and determined the effect of polymer layers adsorbed to colloidal particles on their basic hydrodynamic properties [4].…”

A study of an arbitrary Stokes flow past a fluid coated sphere in a fluid of a different viscosity

“…For instance, Anderson and Solomentsev [2] considered a general quadratic flow past a sphere and studied the hydrodynamic effects of a thin layer of material on the surface of the sphere, where the fluid in the thin layer has a lower effective viscosity than the bulk solution. This is considered as a model for the surface of colloidal particles suspended in a liquid containing polymer molecules which do not hold on to the surface of the particles resulting in a "depletion layer" whose thickness is small compared to the radius of the spherical particles.…”

Effects of dissolved polymer on the transport of colloidal particles through a microcapillary

“…More clearly, the increase in the PS particle diameter resulting from the adsorbed PEO layer was indicated by an increase in H TP with the average fluid velocity. If the PEO-adsorbed particles are pictured as composite spheres comprised of a rigid PS particle core surrounded by a permeable adsorbed PEO shell layer, then the diffusivity of the composite sphere D cs is given as [39] (7)…”