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, Российская Федерация
  • Ganchenko G.S. Kuban State University, Krasnodar, Российская Федерация
  • Demekhin E.A. Kuban State University, Krasnodar, Российская Федерация
  • Kiriy V.A. Kuban State University, Krasnodar, Российская Федерация

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

Acknowledgement

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 Infos

Ekaterina V. Gorbacheva

магистрант кафедры математического моделирования Кубанского государственного университета

e-mail: katya1911@list.ru

Georgiy S. Ganchenko

аспирант кафедры вычислительной математики и информатики Кубанского государственного университета

e-mail: ganchenko.ru@gmail.com

Evgeniy A. Demekhin

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

e-mail: edemekhi@gmail.com

Vladimir A. Kiriy

аспирант кафедры вычислительной математики и информатики Кубанского государственного университета

e-mail: vladimir@kiriy.ru

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Issue

2014. No. 4

Pages

29-37

Submitted

2014-10-06

Published

2014-12-22

How to Cite

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, no. 4, pp. 29-37. (In Russian)

Copyright (c) 2014 Gorbacheva E.V., Ganchenko G.S., Demekhin E.A., Kiriy V.A.

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