Diffusiophoresis of a charged particle in a microtube

The diffusiophoresis of a charged sphere along the axis of a circular microtube filled with an electrolyte solution is studied theoretically. The tube wall may be either nonconductive and impermeable or prescribed with a linear electrolyte concentration distribution. The electric double layers at the solid surfaces are thin, but the diffuse-layer polarization effect over the particle surface is considered. The general solutions to the electrokinetic differential equations are expressed in spherical and cylindrical coordinates, whereas the boundary conditions at the particle surface are satisfied by a collocation technique. The collocation solutions for the diffusiophoretic velocity of the particle, which are in good agreement with the asymptotic formula derived from a reflection method, are obtained for various values of the radius ratio and zeta potential ratio between the particle and the microtube and of other relevant parameters. The contributions from the diffusioosmotic flow along the tube wall and wall-corrected diffusiophoretic driving force to the particle velocity can be superimposed due to the linearity. Although the diffusiophoretic velocity in an uncharged microtube is in general a decreasing function of the particle-to-tube radius ratio and can reverse its direction, it can increase with increases in this ratio due to the competition of the wall effects of possible electrochemical enhancement and hydrodynamic retardation to the particle motion. When the zeta potentials associated with the tube and particle are equivalent, the diffusioosmotic flow induced by the tube wall dominates the diffusiophoretic motion.