Abstract
The authors use experimental and theoretical results to study ionic transport through a charge-selective membrane system and show the nonequilibrium, short-wave, nature of electro-convective instability.
Highlights
INTRODUCTIONOne-dimensional steady-state passage of the direct electric current from an aqueous binary electrolyte solution into a charge-selective (perm-selective) solid is a fundamental electrochemical transport situation and a cornerstone of numerous
This makes it impossible to determine whether the observed growth of the emerging electroconvective vortices is due to the nonlinear evolution typical of the nonequilibrium mechanism, or is just an outcome of the thickening of the diffusion layer in accordance with the equilibrium mechanism
The only way to resolve this ambiguity is to wait for about one hour below the instability threshold until the limiting current decreases to its steady state, and only cross the threshold to see if the emerging vortices are small compared to the diffusion layer thickness
Summary
One-dimensional steady-state passage of the direct electric current from an aqueous binary electrolyte solution into a charge-selective (perm-selective) solid is a fundamental electrochemical transport situation and a cornerstone of numerous. The increase of the vortex size reduces the stabilizing effect of heat diffusion, which alludes to the possibility of long-wave instability This stands in contrast with the Rayleigh-Bénard instability where the initial temperature perturbation induced by the test vortex is dissolved by heat diffusion in the vortex plane. In this limit, keeping the leading-order term in the power expansion of the interface electrolyte concentration and replacing the tangential variation of the concentration logarithm by that of its normal derivative, one arrives at the expression for the nonequilibrium electro-osmosis slip velocity We apply this expression to estimate the test vortex lifetime and find that it is proportional to the third power of the perturbation wavelength, that is, the vortex size. Some experimental and theoretical details are diverted to the Appendixes
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