Diffusiophoresis of a Colloidal Cylinder at Small Finite Péclet Numbers

The diffusiophoretic migration of a circular cylindrical particle in a nonelectrolyte solution with a solute concentration gradient normal to its axis is analytically studied for a small but finite Péclet number P e . The interfacial layer of interaction between the solute molecules and the particle is taken to be thin, but the polarization of its mobile molecules is allowed. Using a method of matched asymptotic expansions, we solve the governing equations of conservation of the system and obtain an explicit formula for the diffusiophoretic velocity of the cylinder correct to the order P e 2 . It is found that the perturbed solute concentration and fluid velocity distributions have the order P e , but the leading correction to the particle velocity has the higher order P e 2 ln P e . The correction to the particle velocity to the order P e 2 can be either positive or negative depending on the polarization parameter of the thin interfacial layer, establishing that the solute convection effect is complicated and can enhance or retard the diffusiophoretic motion. The particle velocity at P e = 0.6 can be about 17% smaller or 0.2% greater than that at P e = 0 . Under practical conditions, the solute convection effect on the diffusiophoretic velocity is much greater for a cylindrical particle than for a spherical particle, whose leading correction has the order P e 2 .