Diffusioosmosis of electrolyte solutions in uniformly charged channels

Abstract

When the concentration of electrolyte solution varies along the channel the forces arise that drag the fluid toward the higher or lower concentration region inducing a flow termed diffusio-osmotic. This article investigates a flow that emerges in channels with constant density of surface charge {\sigma} and thin compared to their thickness electrostatic diffuse layers. An equation for the fluid flow rate Q is derived and used to describe analytically the flux of ions, and local potentials and concentrations. This equation, which allows to treat the diffusio-osmotic problems without tedious and time consuming computations, clarifies that the global flow rate is controlled only by the surface charge and concentration drop between the channel ends, and indicates that there always exist two different values of {\sigma} that correspond to a particular Q. Our theory provides a simple explanation of the directions of the fluid flow rate and ionic flux depending on the surface charge and diffusivity of ions, predicts a non-linear concentration distribution along the channel caused by convection, and relates it to the local potential changes by a compact formula. We also present and interpret the variations of the diffusio-osmotic velocity profiles and the apparent slip velocity along the channel and show that the latter is highly non-uniform and could even becomes alternating. The relevance of our results for diffusio-osmotic experiments and for some electrochemistry and membrane science issues is discussed briefly.