Potentiostatic electroconvection in a layer and in a loop

Abstract

This paper concerns electroconvectional stability of a conduction state in an electrolyte layer flanked by cation-permselective walls (electrodialysis membranes, electrodes) under potentiostatic conditions. It is shown through a numerical finite difference solution of the linear stability problem that above a certain voltage threshold the basic conduction state becomes electroconvectionally unstable. Marginal stability curves in the voltage/wave number plane are calculated and the dependence of the critical threshold characteristics on the system’s parameters (ionic diffusivities ratio, electroconventional Péclet number) studied. Electroconvectional instability is shown to occur for an arbitrary ionic diffusivities ratio. A model problem of electroconvection in a loop under potentiostatic conditions is solved explicitly for a steady state. It is shown that above a certain voltage threshold, the quiescent conduction in the loop bifurcates into a pair of electroconvectional steady state circulations.