# Transient Gel Diffusiophoresis of a Spherical Colloidal Particle

## TL;DR

This paper presents a theory for how a charged particle moves in a gel when an electrolyte concentration gradient is suddenly applied.

## Contribution

The paper derives a new relaxation function for transient diffusiophoresis in gels, showing independence from electrolyte type.

## Key findings

- The relaxation function depends on particle properties and fluid characteristics but not electrolyte type.
- The form of the relaxation function is the same for diffusiophoresis and electrophoresis in gels.
- The theory applies to weakly charged particles with thin electrical double layers.

## Abstract

A general theory is presented to analyze the time-dependent, transient diffusiophoresis of a charged spherical colloidal particle in an uncharged gel medium containing a symmetrical electrolyte when an electrolyte concentration gradient is suddenly applied. We derive the inverse Laplace transform of an approximate expression for the relaxation function R(t), which describes the time-course of the ratio of the diffusiophoretic mobility of a weakly charged spherical colloidal particle, possessing a thin electrical double layer, to its steady-state diffusiophoretic mobility. The relaxation function depends on the mass density ratio of the particle to the electrolyte solution, the particle radius, the Brinkman screening length, and the kinematic viscosity. However, it does not depend on the type of electrolyte (e.g., KCl or NaCl), which affects only the steady-state gel diffusiophoretic mobility. It is also found that the expression for the relaxation function in transient gel diffusiophoresis of a weakly charged spherical colloidal particle with a thin electrical double layer takes the same form as that for its transient gel electrophoresis.