Electroconvection in a layer and in a loop

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