Diffusiophoresis of a colloidal sphere in nonelectrolyte gradients perpendicular to two plane walls

The problem of the diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute situated at an arbitrary position between two infinite parallel plane walls is studied theoretically in the quasisteady limit of negligible Peclet and Reynolds numbers. The applied solute concentration gradient is uniform and perpendicular to the plane walls. The particle–solute interaction layer at the particle surface is assumed to be thin relative to the particle radius and to the particle–wall gap widths, but the polarization effect of the diffuse solute in the thin interfacial layer caused by the strong adsorption of the solute is incorporated. The presence of the walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is altered by the walls, thereby speeding up or slowing down the moving particle; second, the walls enhance the viscous retardation of the particle. A boundary-collocation method is used to semianalytically solve the solutal and hydrodynamic governing equations of the system. Numerical results for the diffusiophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various cases. The collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The net effect of the confining walls is always to reduce the particle velocity, irrespective of the surface properties of the particle or the relative particle–wall separation distances. The boundary effect on diffusiophoresis of a particle normal to two plane walls is found to be quite significant and generally stronger than that parallel to the walls.