Mathematical Modeling of Autwave Process in a Thin Layer of Magnetic Colloid

Authors

  • Chekanov V.S. North Caucasian Federal University, Stavropol, Russian Federation
  • Kovalenko A.V. Kuban State University, Krasnodar, Russian Federation
  • Diskaeva E.N. MIREA - Russian Technological University branch in Stavropol, Stavropol, Russian Federation
  • Kirillova E.V. RheinMain University of Applied Sciences in Wiesbaden, Wiesbaden, Germany

UDC

538.97:539.216:539.23

EDN

DPHKCR

DOI:

10.31429/vestnik-17-4-57-67

Abstract

At present, quite complex models of autowave processes have been developed that are suitable for their quantitative description. They are boundary value problems for systems of nonlinear partial differential equations, however, their solution and interpretation of the results are rather difficult. Therefore, it is relevant to construct simplified models of autowaves, which make it possible to study and analyze their basic properties.

The scientific novelty of the work is the developed new adequate mathematical 1D models of the autowave process. This process has been experimentally recorded in a thin layer of a magnetic colloid (magnetic fluid). In addition, the scientific novelty of this study lies in the fact that the authors obtained solutions in the environment of computer modeling of physical processes COMSOL Multiphysics 5.5. The predictive value of this model is the determination of the critical value of the potential jump, the determination of the time to establish the oscillation period and other characteristics of the process.

Keywords:

autowaves, magnetic fluid, computer modeling, mathematical modeling, nonlinear processes, 1D model of an autowave process, particle recharge, COMSOL

Funding information

Исследование выполнено в рамках работы Международной лаборатории компьютерного и математического моделирования нелинейных процессов "Computer and mathematical modeling of nonlinear processes".

Authors info

  • Vladimir S. Chekanov

    канд. техн. наук, доцент, доцент кафедры информационных систем и технологий Северо-Кавказского федерального университета, доцент кафедры информационных технологий филиала МИРЭА - Российского технологического университета в г. Ставрополь

  • Anna V. Kovalenko

    канд. экон. наук, доцент, заведующая кафедрой интелектуальных информационных систем Кубанского государственного университета

  • Elena N. Diskaeva

    доцент кафедры промышленных технологий филиала МИРЭА - Российского технологического университета в г. Ставрополь

  • Evgenia V. Kirillova

    канд. физ.-мат. наук, профессор Университета прикладных наук Рейн Майн в г. Висбаден

References

  1. Диканский Ю.И., Нечаева О.А., Закинян А.Р. Деформация микрокапель магниточувствительной эмульсии в магнитном и электрическом полях // Коллоидный журнал. 2006. Т. 68. № 2. С. 161–165. [Dikansky, Yu.I., Nechaeva, O.A., Zakinyan, A.R. Deformatsiya mikrokapel' magnitochuvstvitel'noy emul'sii v magnitnom i elektricheskom polyakh [Deformation of the microcapsule of the magnetic emulsion in the magnetic and electric poles]. Kolloidnyy zhurnal [Colloidal Journal], 2006, vol. 68, no. 2, pp. 161–165. (In Russian)]
  2. Бутенко А.А., Ларионов Ю.А., Никитин Л.В., Тулинов A.A., Чеканов В.В.Оптическая и магнитная интерференция в тонком прозрачном электроде, граничащем с магнитной жидкостью // Изв. АН СССР. Серия физ. 1991. Т. 55. №6. С. 1141–1145. [Butenko, A.A., Larionov, Yu.A., Nikitin, L.V. et al. Opticheskaya i magnitnaya interferentsiya v tonkom prozrachnom elektrode, granichashchem s magnitnoy zhidkost'yu [Optical and magnetic interference in a thin transparent electrode bordering a magnetic fluid]. Izvestiya AN SSSR. Seriya fizicheskaya [Izvestiya USSR Academy of Sciences. Series of physical]. 1991, vol. 55, no. 6, pp. 1141–1145. (In Russian)]
  3. Chekanov V.V. Kandaurova N.V. Chekanov V.S. Phase autowaves in the near-electrode layer in the electrochemical cell with a magnetic fluid // Journal of Magnetism and Magnetic Materials. 2017. Vol. 431. P. 38–41.
  4. Чеканов В.В., Кандаурова Н.В., Чеканов В.С. Экспериментальное наблюдение изменения коэффициента отражения света от поверхности раздела сред "вода– магнитная жидкость" в электрическом поле, волновое движение и неустойчивость поверхности // Журнал технической физики. 2014. Вып. 9. Т. 84. С. 26–31. [Chekanov, V.V., Kandaurova, N.V., Chekanov, V.S. Eksperimental'noe nablyudenie izmeneniya koeffitsienta otrazheniya sveta ot poverkhnosti razdela sred "voda–magnitnaya zhidkost'" v elektricheskom pole, volnovoe dvizhenie i neustoychivost' poverkhnosti [Experimental observation of the change in the reflection coefficient of light from the interface between the "water-magnetic fluid" media in an electric field, wave motion, instability of the surface]. Zhurnal tekhnicheskoy fiziki [Journal of technical physics], 2014, vol. 84, iss. 9, pp. 26–31. (In Russian)]
  5. Electrohydrodynamics. CISM Courses and Lectures. No. 380. Undine. Italy, 1998. 363 p.
  6. Zhakin A.I. Electrohydrodynamics: Basic Concepts, Problems and Applications. Kursk: University press, 1998. 132 с.
  7. Жакин А.И. Ионная электропроводность и комплексообразование в жидких диэлектриках // УФН. 2003. Т. 173. № 1. С. 51–68. [Zhakin, A.I. Ionnaya elektroprovodnost' i kompleksoobrazovanie v zhidkikh dielektrikakh [Ionic conductivity and complexation in liquid dielectrics]. Uspekhi fizicheskikh nauk [Advances in Physical Sciences], 2003, vol. 173, no. 1, pp. 51–68. (In Russian)]
  8. Жакин А.И. Приэлектродные и переходные процессы в жидких диэлектриках // УФН. 2006. Т. 176. № 3. С. 289–310. [Zhakin, A.I. Near-electrode and transient processes in liquid dielectrics. Uspekhi fizicheskikh nauk [Advances in Physical Sciences], 2006, vol. 176, no. 3, pp. 289–310. (In Russian)]
  9. Жакин А.И. Электрогидродинамика // УФН. 2012. Т. 182. № 5. С. 495–520. [Zhakin, A.I. Electrohydrodynamics. Uspekhi fizicheskikh nauk [Advances in Physical Sciences], 2012, vol. 182, no. 5, pp. 495–520. (In Russian)]
  10. Диканский, Ю.И., Нечаева, О.А. Структурные превращения в магнитной жидкости в электрическом и магнитных полях // Коллоидный журнал. 2003. Т. 65. № 3. С. 338–342. [Dikansky, Yu.I., Nechaeva, O.A. Strukturnye prevrashcheniya v magnitnoy zhidkosti v elektricheskom i magnitnykh polyakh [Structural transformations in a magnetic fluid in electric and magnetic fields]. Colloid journal [Kolloidnyy zhurnal], 2003, vol. 65, no. 3, pp. 338–342. (In Russian)]
  11. Остроумов Г.А. Межэлектродная осцилляция частиц дисперсной фазы. Взаимодействие электрических и гидродинамических полей. М.: Наука, 1979. 319 с. [Ostroumov, G.A. Mezhelektrodnaya ostsillyatsiya chastits dispersnoy fazy. Vzaimodeystvie elektricheskikh i gidrodinamicheskikh poley [Interelectrode oscillation of dispersed phase particles. Interaction of electric and hydrodynamic fields]. Nauka, Moscow, 1979. (In Russian)]
  12. Шилов В.Н., Дейнега Ю.Ф. К теории эффектов межэлектродной циркуляции, межэлектродного сжатия дисперсной фазы в неводных дисперсных системах // Коллоидный журнал. 1969. Т. 31. С. 908–912. [Shilov, V.N., Deynega, Yu.F. K teorii effektov mezhelektrodnoy tsirkulyatsii, mezhelektrodnogo szhatiya dispersnoy fazy v nevodnykh dispersnykh sistemakh [On the theory of the effects of interelectrode circulation, interelectrode compression of the dispersed phase in non-aqueous dispersed systems]. Colloid journal [Kolloidnyy zhurnal], 1969, vol. 31, pp. 908–912. (In Russian)]
  13. Chekanov V.V., Kandaurova N.V., Chekanov V.S. Calculation of the membrane thickness of magnetite nanoparticles on the surface of the transparent conductive electrode in the electric field // Journal of Nano- and Electronic Physics. 2015. Vol. 7. Iss. 4, Part 1. P. 04041–04043.
  14. Chekanov V.V., Kandaurova N.V., Chekanov V.S. Thickness Calculation of thin transparent conductive membrane on the border with a magnetic fluid // Journal of Nano- and Electronic Physics. 2016. Vol. 8. Iss. 4. P. 04045–04048.
  15. Ньюмен Дж. Электрохимические системы. М.: Мир, 1977. 463 с. [Newman, J. Elektrokhimicheskie sistemy [Electrochemical systems]. Mir, Moscow, 1977. (In Russian)]

Downloads

Download data is not yet available.

Downloads

Issue

Vol. 17 (2020) No. 4

Pages

57-67

Section

Physics

Dates

Submitted

December 13, 2020

Accepted

December 18, 2020

Published

December 27, 2020

How to Cite

[1]
Chekanov, V.S., Kovalenko, A.V., Diskaeva, E.N., Kirillova, E.V., Mathematical Modeling of Autwave Process in a Thin Layer of Magnetic Colloid. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, т. 17, № 4, pp. 57–67. DOI: 10.31429/vestnik-17-4-57-67

License

Copyright (c) 2020 Чеканов В.С., Коваленко А.В., Дискаева Е.Н., Кириллова Е.В.

Creative Commons License

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

Similar Articles

1-10 of 329

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)

1 2 > >>