The spatial evolution of the ionic concentration of an electrolyte in an isothermal electrochemical cell with a porous separator between the electrodes was investigated for large values of Rayleigh number. The reaction kinetics were described by the Butler-Volmer equation. The full problem, involving the coupled partial differential equations describing the velocity field, the ionic concentration, and the electric potential, was reduced by means of regular and singular perturbation theory, to a simplified evolution equation, coupled with a transcendental function for the ionic concentration and electric potential; the solution was found to agree well with the numerical solution of the full problem. In the limit of large and small cell voltages, closed analytical solutions were secured for the concentration, potential, and overall current density.