Thermoelectrokinetic instability and salt superconcentration near permselective electric membranes

E. N. Kalaydin, N. Yu. Ganchenko, G. S. Ganchenko, N. V. Nikitin, and E. A. Demekhin
Phys. Rev. Fluids 2, 114201 – Published 14 November 2017

Abstract

A sophisticated type of electrohydrodynamic instability, the thermoelectrokinetic instability, in an electrolyte solution near ion-selective surfaces in an external electric field was discovered and investigated theoretically. The investigation used parallel computing on the SKIF MSU Lomonosov supercomputer and it was based on the direct numerical simulation of the Nernst-Planck-Poisson-Navier-Stokes system, along with the energy equation and corresponding boundary conditions. Although the physical mechanism of the instability is connected with Joule heating, it dramatically differs from the well-known Raleigh-Bénard convection: The instability is caused by nonuniformity of the electric current and electric conductivity and, in contrast to the Raleigh-Bénard instability, it occurs when the heating is from above. The thermoelectrokinetic instability prevails in long microchannels and a good enough thermal insulation of the system and it can be an additional factor for the overlimiting current mode. Initial unstable small random disturbances of the unknowns evolve towards rather unusual coherent structures. For the cation-exchange membranes, the salt concentration was eventually localized in long narrow fingers that are similar to stalactites and that stretched from the anode in the direction of the cathode. Outside the stalactites, the salt concentration was practically zero, while inside the stalactites it could reach hundreds from the initial concentration. Consequently, it is possible to talk about its superconcentration. The electric current propagates in a narrow needle along the stalactite with maximal electric conductivity and this gives rise to Joule heating in this region. The space charge forms crownlike micropatterns near the cathode. Note that the regime of chaotic motion that is characteristic of the electrokinetic instability was not observed for the thermoelectrokinetic instability.

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  • Received 25 July 2017

DOI:https://doi.org/10.1103/PhysRevFluids.2.114201

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

E. N. Kalaydin1,2, N. Yu. Ganchenko2, G. S. Ganchenko3, N. V. Nikitin4, and E. A. Demekhin1,3,4,*

  • 1Department of Mathematics and Informatics, Financial University, Krasnodar 350051, Russian Federation
  • 2Department of Mathematical and Computer Methods, Kuban State University, Krasnodar 350040, Russian Federation
  • 3Laboratory of Micro- and Nanoscale Electro- and Hydrodynamics, Financial University, Krasnodar 350051, Russian Federation
  • 4Laboratory of General Aeromechanics, Institute of Mechanics, Moscow State University, Moscow 119192, Russian Federation

  • *edemekhi@gmail.com

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Issue

Vol. 2, Iss. 11 — November 2017

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