Modes of Thermogravitational Convection and Thermoelectrokinetic Instability Under Joule Heating in Electrolyte Between Electric Membranes

Abstract

Joule heating near ion-selective cation-exchange membranes in an external electric field can cause two modes of instability, namely, the thermogravitational convection, which reminds a well-known Rayleigh–Benard convection, and a novel type of instability, the thermoelectrokinetic instability. Stability of a quiescent one-dimensional steady-state solution to infinite small sinusoidal perturbations has been investigated in a wide range of the Rayleigh numbers. It has been found that, for the both modes, instability occurs for the limiting as well as for the underlimiting currents. Hence, a transition to the overlimiting regimes can happen bypassing the limiting regime, from some point of the underlimiting regime. Note that the Rubinstein–Zaltzman instability takes place only for the limiting currents. The Rayleigh numbers, recalculated to the classical ones, vary in a range from 500 to 1300, which is consistent with the classical thermogravitational convection results. It has been also shown, that the critical Rayleigh numbers are too large and, hence, critical distances between the membranes are too small to make the thermogravitational convection possible to manifest in the microchannels. This refutes the opinion that the thermogravitational instability produces one of the key mechanisms of transition to overlimiting currents in the problems of microfluidics.