Diffusiophoresis of a colloidal sphere in nonelectrolyte gradients parallel to one or two plane walls

Abstract

The quasisteady diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute located between two infinite parallel plane walls is studied theoretically in the absence of fluid inertia and solute convection. The imposed solute concentration gradient is constant and parallel to the two plane walls, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. 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 neighboring walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is enhanced or reduced by the walls, thereby speeding up or slowing down the particle; secondly, the walls increase viscous retardation of the moving particle. To solve the continuity and momentum equations, the general solutions are constructed from the fundamental solutions in both the rectangular and the spherical coordinate systems. The boundary conditions are enforced first at the plane walls by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the diffusiophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various values of the relaxation parameter of the particle as well as the relative separation distances between the particle and the two plates. For the special case of diffusiophoretic motions of a spherical particle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the particle velocity, depending on the surface properties of the particle, the relative particle–wall separation distances, and the solutal boundary condition at the walls. In general, the boundary effect on diffusiophoresis is quite complicated and relatively weak in comparison with that on sedimentation.