Numerical Simulation of Rayleigh–Bènard Instability in Solutions Containing Ions of Three Types

Abstract

The conditions for appearance of a Rayleigh–Benard instability (RBI) induced by a constant current between two horizontal electrodes in solution containing electroactive ions and indifferent electrolyte (system with three kinds of ions) are analyzed. It is taken into account that all the components take part in the formation of buoyant forces. The problem is solved for a stationary case (as an expansion to a series by a small parameter), and then equations for low perturbations are solved by the Galerkin method. The calculation is performed with a program that accounts for any number of members in a Galerkin expansion. A diagram is obtained, which determines conditions for the RBI emergence in terms of ratios of partial Raleigh numbers. The ratio of diffusion coefficients for supporting cations and anions significantly affects position of the boundary dividing ranges of convective stability and RBI in a diagram of nonequilibrium phase transitions.