Numerical solution of linear stability of micro and nanofilms of the electrolyte under an external electric field

Authors

  • Gorbacheva E.V. Kuban State University, Krasnodar, Russian Federation
  • Ganchenko G.S. Kuban State University, Krasnodar, Russian Federation
  • Demekhin E.A. Kuban State University, Krasnodar, Russian Federation
  • Kiriy V.A. Kuban State University, Krasnodar, Russian Federation

UDC

532.517.4 : 537.2

Abstract

Problems of electrokinetics have recently attracted a great deal of attention due to a rapid development of micro-, nano- and biotechnologies. Micro-nano scale phenomena with liquid/gas interface are of particular practical interest to move non-conductive liquids, creating a highly nonuniform velocity profile, mixing, etc. The article considers the effect of a thin film electrolyte under the influence of an external electric field. The presence of an inhomogeneous surface charge at the interface of gas/liquid leads to an instability and distortion of free surface. In this paper we obtain one-dimensional equilibrium and study the linear stability of this state. We find the critical values of the parameters after which a one-dimensional steady-state solution is no longer stable. Also we found long-wave instability and obtained four modes.

Keywords:

liquid film, mobile surface charge, free interface, instability, Galerkin method, electrolyte, Nernst-Planck-Poisson system, double ion layer

Funding information

Работа выполнена при частичной финансовой поддержке РФФИ (14-08-31260 мол-а, 14-08-00789-a, 14-08-01171-а, 13-08-96536-р_юг_а).

Author info

  • Ekaterina V. Gorbacheva

    магистрант кафедры математического моделирования Кубанского государственного университета

  • Georgiy S. Ganchenko

    аспирант кафедры вычислительной математики и информатики Кубанского государственного университета

  • Evgeniy A. Demekhin

    д-р физ.-мат. наук, профессор кафедры вычислительной математики и информатики Кубанского государственного университета

  • Vladimir A. Kiriy

    аспирант кафедры вычислительной математики и информатики Кубанского государственного университета

References

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Downloads

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Issue

Vol.  (2014) No. 4

Pages

29-37

Section

Article

Dates

Submitted

October 6, 2014

Accepted

October 17, 2014

Published

December 22, 2014

How to Cite

[1]
Gorbacheva, E.V., Ganchenko, G.S., Demekhin, E.A., Kiriy, V.A., Numerical solution of linear stability of micro and nanofilms of the electrolyte under an external electric field. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2014, № 4, pp. 29–37.

License

Copyright (c) 2014 Горбачёва Е.В., Ганченко Г.С., Демёхин Е.А., Кирий В.А.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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