Diffusiophoresis of a colloidal sphere in nonelectrolyte gradients in a circular cylindrical pore

The problem of the diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute along the centerline of a circular cylindrical pore is studied theoretically in the quasisteady limit of negligible Reynolds and Peclet numbers. The imposed solute concentration gradient is uniform and parallel to the pore wall, 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 width, 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 pore wall causes two basic effects on the particle velocity: first, the local solute concentration gradients on the particle surface are altered by the wall, thereby speeding up or slowing down the particle; secondly, the wall increases viscous retardation of the moving particle. To solve the equations of conservation of mass and momentum, the general solutions are constructed from the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the pore wall 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 distance between the particle and the pore wall. The collocation results agree well with the approximate analytical solution obtained by using a method of reflections. The wall-corrected particle velocity depends on the surface properties of the particle, the ratio of particle-to-pore radii, and the solutal boundary condition at the wall. In general, the boundary effect on diffusiophoresis is quite significant and complicated.