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–Benárd 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.

中文翻译：

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电膜间电解质中焦耳加热下的热重力对流和热电动不稳定模式

在外部电场中，离子选择性阳离子交换膜附近的焦耳加热会引起两种不稳定性，即热重力对流和热不稳定，这是一种众所周知的瑞利-贝纳德对流，还有一种新型的不稳定性，即热电不稳定性。在广泛的瑞利数范围内，研究了无穷小正弦扰动的静态一维稳态解的稳定性。已经发现，对于两种模式，极限电流和极限电流都发生不稳定性。因此，从限制制度的某个角度出发，可以绕过限制制度而发生向限制制度的过渡。请注意，Rubinstein–Zaltzman不稳定性仅发生在极限电流上。瑞利数 重新计算为经典对流，范围在500到1300之间，这与经典热对流对流结果一致。还已经表明，临界瑞利数太大，因此，膜之间的临界距离太小，以致于不可能在微通道中表现出热重力对流。这驳斥了热引力不稳定性产生微流体问题中过渡到极限电流的关键机制之一的观点。膜之间的临界距离太小，以至于不可能在微通道中表现出热重力对流。这驳斥了热引力不稳定性产生微流体问题中过渡到极限电流的关键机制之一的观点。膜之间的临界距离太小，以至于不可能在微通道中表现出热重力对流。这驳斥了热引力不稳定性产生微流体问题中过渡到极限电流的关键机制之一的观点。