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/kappa a is derived, where kappa is the Debye-Huckel parameter. It is found that the approximate expression correct to order unity can be applied for kappa a >= 50 with negligible errors, while the approximate expression correct to order 1/kappa a can be applied for kappa a >= 20 with negligible errors.

Automated summary

The general expression for the diffusiophoretic velocity of a spherical colloidal particle in a concentration gradient of symmetrical electrolyte is derived, from which simple approximate analytic expressions correcting up to the order of 1/kappa a are obtained. It is found that the approximate expressions correcting up to the unity order can be applied for kappa a >= 50 with negligible errors, while the expressions correcting up to the 1/kappa a order can be applied for kappa a >= 20 with negligible errors.