DIFFUSIOPHORESIS AND ELECTROPHORESIS OF COLLOIDAL CYLINDERS

This paper deals with the theories of diffusiophoresis and electrophoresis of a rigid insulating cylinder of infinite length in a uniform applied field oriented arbitrarily with respect to its axis. The range of the interaction between the solute species and the particle's surface is assumed small relative to the particle's radius, but the polarization of the diffuse species in the solute-particle interaction layer is allowed. To solve the conservative equations governing the system, a slip velocity of fluid and normal fluxes of solute species at the outer edge of the thin diffuse layer can be used as the boundary conditions for the fluid domain outside the diffuse layer. Expressions for the migration velocity of the particle are obtained in simple closed forms for the cases of diffusiophoresis in a nonelectrolyte gradient, diffusiophoresis in a gradient of symmetric electrolyte, and electrophoresis in an external electric field. A remarkable feature is found that the diffusiophoretic or electrophoretic velocity of the cylinder in a transverse imposed field, neglecting the end effects, is exactly the same as the corresponding velocity of a rigid sphere with an equal radius.