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ORIGINAL ARTICLE

Thermodiffusion in Electrolyte Between Electric Membranes Under External Electric Field Nataly Ganchenko1

· Maria Repina2 · Georgy Ganchenko3,4 · Evgeny Demekhin4

Received: 30 April 2020 / Accepted: 6 October 2020 / Published online: 2 November 2020 © Springer Nature B.V. 2020

Abstract Thermodiffusion of a binary electrolyte situated in the microgap between two ion-selective surfaces under external electric field is theoretically studied. It is assumed that temperature gradient occurs only by Joule heating of the electrolyte; and the concentration gradient may trigger an inner gravitational instability. There are three types of instability in such setup: electrokinetic, thermoelectrokinetic and internal gravitational instability. The direct numerical simulation of the problem shows that for the typical salts solutions such as NaCl or KCl the termodiffusion effect is negligible, while for some salts with bigger values of the reduced Soret coefficients of ions (for example, for tetra-n-butylammonium fluoride) the thermodiffusion may significantly affect the voltage-current characteristic. It is also obtained, that the negative thermodiffusion leads to the destabilization of the one-dimensional steady state regime and shifts the critical values of governing parameters for each aforementioned type of instability. The thermodiffusion mostly influences the classical electrokinetic instability and less — the internal gravitational instability. Under effect of both types of thermodiffusion (normal and negative), the thermoelectrokinetic instability manifests at smaller values of Rayleigh numbers. Keywords Ion-exchange membrane · Soret effect · Electrokinetic instability · Electroconvection · Microchannel

 Nataly Ganchenko

[email protected] Maria Repina [email protected] Georgy Ganchenko [email protected] Evgeny Demekhin [email protected] 1

Department of Mathematics and Computer Science, Kuban State University, Krasnodar 350040, Russian Federation

2

Institute of Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don, 344006, Russian Federation

3

Laboratory of Micro- and Nanoscale Electroand Hydrodynamics, Financial University under the Government of Russian Federation, Krasnodar 350051, Russian Federation

4

Laboratory of General Aeromechanics, Institute of Mechanics, Moscow State University, Moscow 119192, Russian Federation

Introduction C. Soret discovered in 1879 that a salt solution contained in a tube with the differently heated butt-ends did not remain uniform in composition: the salt concentration was higher near the cold end (Soret 1979). He concluded that the salt flux was generated by a temperature gradient leading, under stationary conditions, to a concentration gradient. Also, he formulated the first simple equations to describe the phenomenon (Soret 1979, 1881a, b) Since that time, it is common to indicate the transport mechanism, in which temperature gradient causes mass transfer in mixture, as thermodiffusion, or “Soret effect”. The