Determination of critical Rayleigh number for binary solutions in a nonlinear theory of convective stability

Abstract

The Rayleigh–Benard convective instability in a cell with horizontal copper electrodes is considered. The space between the electrodes is filled with a CuSO4 solution. The dependence of the variation in the limiting current of copper deposition, ΔI, which is caused by the formation of convective dissipative structures in the system, on the solution concentration \(c_{{\text{CuSO}}_{\text{4}} } \) is determined experimentally. The results agree satisfactorily with a nonlinear theory of convective stability that accounts for the electrical forces generated by the formation of a space charge near the electrode, along with the buoyancy forces. This enables one to determine the critical Rayleigh number for the system by extrapolating the linear dependence of ΔI on \(\sqrt c \). The critical Rayleigh number thus obtained agrees satisfactorily with the theoretical value calculated within the linear theory of stability.