Improvement of relation for electroosmotic slip velocity

Authors

  • Frants E.A. Kuban State University, Krasnodar, Russian Federation
  • Kiriy V.A. Kuban State University, Krasnodar, Russian Federation
  • Shelistov V.S. Krasnodar Branch of the Financial University under the Government of the Russian Federation, Krasnodar, Russian Federation
  • Kutsepalov A.S. Kuban State University, Krasnodar, Russian Federation
  • Demekhin E.A. Krasnodar branch of Financial University under the Government of the Russian Federation, Krasnodar, Russian Federation

UDC

532.516; 544.6

Abstract

On any surface, under the action of an external electric field, there is a space charge region of small thickness, in which occurs the accumulation of charge. On the outer edge of the area due to the tangential component of the electric field, the slip of fluid takes place. This phenomenon is theoretically investigated in a number of works of the 2000. Rubinstein and Salzman were obtained the estimated formula for the speed of electroosmotic-slip of liquid, which, however, is not without a flaw, and therefore needs to be refined. In this article we obtain refined formula of Rubinstein-Saltzman, and is a fairly detailed derivation of this formula in the space charge region on the basis of asymptotic expansions.

Keywords:

slip velocity, asymptotic method, stretching of variables, space charge region

Funding information

Работа выполнена при поддержке РФФИ (проекты №13-08-96536 А, 15-08-02483 А).

Author info

  • Elizaveta A. Frants

    магистрант кафедры математического моделирования Кубанского государственного университета

  • Vladimir A. Kiriy

    аспирант кафедры вычислительной математики и информатики Кубанского государственного университета

  • Vladimir S. Shelistov

    канд. физ.-мат. наук, ведущий научный сотрудник лаборатории электро- и гидродинамики микро- и наномасштабов Краснодарского филиала Финансового университета при Правительстве РФ

  • Aleksandr S. Kutsepalov

    аспирант кафедры вычислительной математики и информатики Кубанского государственного университета

  • Evgeniy A. Demekhin

    д-р физ.-мат. наук, профессор кафедры "Математика и информатика" Финансового университета при Правительстве Российской Федерации

References

  1. Rubinstein I., Zaltzman B. Electro-osmotically induced convection at a permselective membrane // Physical Review E. 2000. Vol. 62. P. 2238-2251. doi: 10.1103/PhysRevE.62.2238
  2. Уртенов М.Х. Краевые задачи для систем уравнений Нернста-Планка-Пуассона (факторизация, декомпозиция, модели, численный анализ). Краснодар: Кубанский государственный университет. 1998. 125 c. [Urtenov M.Kh. Kraevye zadachi dlya sistem uravneniy Nernsta-Planka-Puassona (faktorizatsiya, dekompozitsiya, modeli, chislennyy analiz) [Boundary value problems for systems of equations Nernst-Planck-Poisson (factorization, decomposition, models, numerical analysis)]. Krasnodar, Kubanskiy gosudarstvennyy universitet Publ., 1998, 125 p. (In Russian)]
  3. Уртенов М.Х. Краевые задачи для систем уравнений Нернста-Планка-Пуассона (асимптотические разложения и смежные вопросы). Краснодар: Кубанский государственный университет. 1999. 124 c. [Urtenov M.Kh. Kraevye zadachi dlya sistem uravneniy Nernsta-Planka-Puassona (asimptoticheskie razlozheniya i smezhnye voprosy) [Boundary value problems for systems of equations Nernst-Planck-Poisson (asymptotic expansions and related issues)]. Krasnodar, Kubanskiy gosudarstvennyy universitet Publ., 1999, 124 p. (In Russian)]
  4. Бабешко В.А., Заболоцкий В.И., Кириллова Е.В., Уртенов М.Х. Декомпозиция систем уравнений Нернста-Планка-Пуассона // ДАН. 1995. Т. 344. № 3. С. 485-486. [Babeshko V.A., Zabolotskij V.I., Kirillova E.V., Urtenov M.K. Dekompozitsiya sistem uravneniy Nernsta-Planka-Puassona [Decomposition of Nernst-Planck-Poisson equation]. Doklady RAN [Rep. of Russian Academy of Sciences], 1995, vol. 344, no. 3, pp. 485-486. (In Russian)]
  5. Demekhin E.A., Shelistov V.S., Polyanskikh S.V. Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability // Physical Review E. 2011. Vol. 84. 036318. doi: 10.1103/PhysRevE.84.036318

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Issue

No. 3 (2015)

Pages

79-83

Section

Article

Dates

Submitted

June 20, 2015

Accepted

June 25, 2015

Published

September 30, 2015

How to Cite

[1]
Frants, E.A., Kiriy, V.A., Shelistov, V.S., Kutsepalov, A.S., Demekhin, E.A., Improvement of relation for electroosmotic slip velocity. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2015, № 3, pp. 79–83.

License

Copyright (c) 2015 Франц Е.А., Кирий В.А., Шелистов В.С., Куцепалов А.С., Демёхин Е.А.

Creative Commons License

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

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