Equilibrium electro-convective instability in concentration polarization: The effect of non-equal ionic diffusivities and longitudinal flow

For a long time, based on the analysis pertaining to a perfectly charge selective interface, electro-convective instability in concentration polarization was attributed to a nonequilibrium mechanism related to the extended space charge which forms next to that of the electric double layer near the limiting current. More recently, it was shown that imperfect charge selectivity of the interface makes equilibrium instability possible, driven by either equilibrium electro-osmosis or bulk electro-convection, or both. In that study, addressing stability of a quiescent binary electrolyte, equal ionic diffusivities were assumed. Here we study the effect of non-equal ionic diffusivities and imposed longitudinal flow upon the onset and further nonlinear development of the equilibrium electro-convective instability at a non-perfectly permselective interface. It is observed through a suitable analytical and numerical study that the imposed flow along the perm-selective interface does not affect fundamentally the equilibrium electro-convective instability in concentration polarization either in terms of the temporal instability threshold or the resulting nonlinear flow. For the former, the critical voltage is practically identical with that in quiescent concentration polarization. For the latter, with non-slip interface conditions, the resulting nonlinear flow, with high accuracy, may be represented as a superposition of the imposed Poiseuille flow and the vortices of the quiescent instability. Differing ionic diffusivities may have a considerable effect upon the onset of the electro-convective instability. In particular, co-ionic diffusivity appreciably lower than the counter-ionic one may yield an appreciable increase of the critical voltage. This is explained by the stabilizing effect of the diffusion potential’s contribution to the electric potential fluctuations.