Approximate analytic expressions for the diffusiophoretic velocity of a spherical colloidal particle.

The general expression is derived for the diffusiophoretic velocity of a spherical colloidal particle of radius a in a concentration gradient of symmetrical electrolyte. On the basis of this expression, simple approximate analytic expressions for the diffusiophoretic velocity correct up to the order of 1/κa is derived, where κ is the Debye-Hückel parameter. It is found that the approximate expression correct to order unity can be applied for κa ≥ 50 with negligible errors, while the approximate expression correct to order 1/κa can be applied for κa ≥ 20 with negligible errors.