Boundary Effects on Diffusiophoresis and Electrophoresis: Motion of a Colloidal Sphere Normal to a Plane Wall

A combined analytical-numerical study of the diffusiophoresis and electrophoresis of a rigid sphere in a uniform applied field perpendicular to a plane wall is presented. The range of the interaction between the solute species and the solid surfaces is assumed to be small relative to the particle's radius and to the spacing between the particle and the wall, but the polarization of the diffuse species in the thin particle-solute interaction layer is allowed. A slip velocity of fluid and normal fluxes of solute species at the outer edge of the thin diffuse layer are used as the boundary conditions for the fluid domain outside the diffuse layer. Through the use of a collocation method along with these boundary conditions, a set of conservative equations governing the system is solved in the quasisteady state situation and the effects of a plane wall on diffusiophoresis and electrophoresis are calculated for various cases. For the cases of diffusiophoresis in a nonelectrolyte gradient and of electrophoresis, the particle velocity decreases monotonically with the decrease of the distance of the particle center from the wall. For the case of diffusiophoresis in an electrolyte gradient, however, the boundary effect is a complicated function of the properties of the particle and ions, and it no longer varies monotonically with the separation distance for some situations.