Thick Double Layers: From Energy Storage to~Diffusiophoresis

We~study two distinct out-of-equilibrium processes relating to thick double layers:~(a) charging dynamics of electrical double layers in a nanopore, and (b) diffusiophoretic~mobility of colloidal particles in a~time-dependent concentration field. \newline \newline The~charging dynamics of electrical double layers inside a cylindrical pore has~been widely studied for the thin double layer limit. However, a model for the~thick double layer limit is not readily available.~Here, we demonstrate that the~charging dynamics in the limit of thick double layers can be represented through~an effective circuit model, much like the thin double layer limit. However, the~physical~meaning of the effective circuit elements, i.e., resistors and~capacitors, is different between the two limits.~~~ \newline \newline Diffusiophoresis~refers to the movement of colloidal particles in a concentration gradient of~an electrolyte. It is typically assumed that the diffusiophoretic mobility does~not vary with electrolyte~concentration. Here, we show that the~diffusiophoretic mobility is coupled with electrolyte concentration, especially~in a time-dependent concentration field where the regions of thick double layer~may be~more prevalent. We demonstrate that the diffusiophoretic mobility possesses~a maximum with electrolyte concentration.~