Diffusiophoresis of a charge-regulated sphere along the axis of an uncharged cylindrical pore

The diffusiophoresis of a charge-regulated spherical particle along the axis of a cylindrical pore is modeled. The problem considered allows us to examine simultaneously the effects of the presence of a boundary, the charge conditions on the particle surface, the thickness of the double layer, and the nature of a dispersion medium including its pH value and the diffusivities of the ionic species with respect to the diffusiophoretic behavior of a particle. We show that, in addition to the factors of double-layer polarization, electrophoresis, and the osmotic flow of solvent, the diffusiophoretic behavior of the particle can also be affected significantly by the electrical repulsive interaction between the particle and the co-ions immediately outside the double layer as they diffuse through the gap between the double layer and the pore. The last effect, which can influence the diffusiophoretic behavior of a particle both quantitatively and qualitatively, is absent in the diffusiophresis of a sphere in a spherical cavity. The competition of those effects yields many interesting results that are of practical significance in the design of a diffusiophoretic apparatus and/or the interpretation of experimental data.