Improvement of relation for electroosmotic slip velocity

Authors

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

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

Acknowledgement

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

Author Infos

Elizaveta A. Frants

магистрант кафедры математического моделирования Кубанского государственного университета

e-mail: gandizel@mail.ru

Vladimir A. Kiriy

аспирант кафедры вычислительной математики и информатики Кубанского государственного университета

e-mail: vladimir@kiriy.ru

Vladimir S. Shelistov

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

e-mail: shelistov_v@mail.ru

Aleksandr S. Kutsepalov

аспирант кафедры вычислительной математики и информатики Кубанского государственного университета

e-mail: alex.kuzepalov@gmail.com

Evgeniy A. Demekhin

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

e-mail: edemekhi@gmail.com

References

  1. Rubinstein I., Zaltzman B. Electro-osmotically induced convection at a permselective membrane. Physical Review E. 2000, vol. 62, pp. 2238-2251. doi: 10.1103/PhysRevE.62.2238
  2. 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. 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. 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

Issue

Pages

79-83

Submitted

2015-06-20

Published

2015-09-30

How to Cite

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, no. 3, pp. 79-83. (In Russian)