Rayleigh-Benard instability in a flat electrolyte solution layer between two horizontal ion-selective membranes

The convective stability of a flat layer of a binary electrolyte solution (an electrolyte containing cations of one type and anions of one type) between two horizontal ion-selective membranes under electric current flow conditions was studied theoretically. Membranes only permeable to anions were considered. Apart from changes in solution density resulting from solution concentration changes under the action of current, the effect of electroosmotic slip (violation of the adherence condition) at the interface between the membrane and electrolyte solution was taken into account. This effect was included in boundary conditions on hydrodynamic velocity. The critical Rayleigh and critical wave numbers were determined. It was shown that, in the electrochemical system under consideration, the critical Rayleigh number was significantly different from that for the problem of heat transfer in a horizontal liquid layer.