Autophoresis of two adsorbing/desorbing particles in an electrolyte solution

Abstract

Classical diffusiophoresis describes the motion of particles in an electrolyte or non-electrolyte solution with an imposed concentration gradient. We investigate the autophoresis of two particles in an electrolyte solution where the concentration gradient is produced by either adsorption or desorption of ions at the particle surfaces. We find that when the sorption fluxes are large, the ion concentration near the particle surfaces, and consequently the Debye length, is strongly modified, resulting in a nonlinear dependence of the phoretic speed on the sorption flux. In particular, we show that the phoretic velocity saturates at a finite value for large desorption fluxes, but depends superlinearly on the flux for adsorption fluxes, where both conclusions are in contrast with previous results that predict a linear relationship between autophoretic velocity and sorption flux. Our theory can also be applied to precipitation/dissolution and other surface chemical processes.