Electrophoresis and diffusiophoresis of a colloidal sphere with double-layer polarization in a concentric charged cavity

The electrophoretic and diffusiophoretic motions of a dielectric spherical particle situated at the center of a spherical cavity filled with an electrolyte solution are studied analytically. The applied electric field and electrolyte concentration gradient are uniform; the electric double layers at the particle surface and cavity wall are thin relative to the radius of the particle and distance between the solid surfaces, but the diffuse-layer polarization effect over the particle surface is considered. After solving the equations of conservation governing the systems, explicit formulas for the electrophoretic and diffusiophoretic velocities of the confined particle are obtained and their results relative to those of a particle under identical conditions in an unbounded solution are presented for various values of the radius ratio and zeta potential ratio between the particle and the cavity and of other parameters in the systems. The contributions from the electroosmotic and diffusioosmotic flows occurring along the cavity wall and from the wall-corrected electrophoretic and diffusiophoretic driving forces to the particle velocities are equivalently important and can be superimposed due to the linearity of the problems. The normalized migration velocities of the particle in general decrease with an increase in the particle-to-cavity radius ratio and increase with an increase in the cavity-to-particle zeta potential ratio. The effects of the charged cavity wall on the electrokinetic migrations of the particle are significant and can reverse their directions.