Effect of uniform magnetic field on the stability of the Rayleigh-Benard convection in a binary electrolyte: A theoretical analysis

The Rayleigh-Benard stability in an electrochemical cell with a binary electrolyte in a uniform magnetic field is studied theoretically. The mathematical model is based on equations describing the motion of incompressible viscous liquid in the Boussinesq approximation, which account for the Archimedean buoyancy force and the Lorentz force, and equations of material balance with the electroneutrality condition. The set of equations for perturbation amplitudes is solved analytically by the Galerkin method and numerically, by the Runge-Kutta method. Dependences of the critical value of the Rayleigh number on the Hartmann number, which expresses the ratio between magnetic and viscous forces, are obtained for monotonic instability of limiting current at liquid and solid electrodes. The effect the variations in the electrolyte's electroconductance, which are caused by concentration variations, exert on the instability emergence is analyzed.