Electroconvection at an electrically inhomogeneous permselective interface

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Abstract
This paper concerns electroconvection—a nongravitational free convection in macroscopic domains of electrolyte solution. Electroconvection results from the interaction of the electric field in the system with the respective space charge within the limits of validity of local electroneutrality approximation. It follows from the dimensional analysis that the electroconvectional Péclet number, evaluated near the equilibrium in a macroscopic ionic system, characterized by a single length scale, is universally of order unity, independently of the size of the system and of the typical electrolyte concentration. An electroconvectional flow in a two-dimensional diffusion layer adjacent to a periodic electrically inhomogeneous permselective interface is calculated by an integral method to leading order in small electroconvectional Péclet number, occurring in the considered large aspect ratio case due to the presence of two separate macroscopic length scales. Explicit expressions for the flow characteristics are worked out through an asymptotic procedure valid in the vicinity of electrodiffusional limiting current.