Instability of thermodinamically non-equilibrium surface of a liquid metal in electric field
The mathematical theory of stability requires the analysis of the time evolution of an arbitrary initial perturbation of the system. However, arbitrary perturbations in real systems are possible only in thermodynamically non-equilibrium states. In this paper, this issue is considered on the example of the stability of the surface of a liquid metal in an electric field. The corresponding theory, which differs from the well-known Larmor - Tonks - Frenkel (LTF) theory, and experimentally confirmed by Serkov et al. It was also shown that account for the dependence of the surface tension on the radius of curvature of the surface in the LTF theory changes the critical electric field strength within 5%. It was found that the dependence of the critical intensity on the temperature T of the liquid metal in the theory is (1 - T / T 0)1/3, whereas for the theory considered in this paper, it practically does not depend on temperature.
Keywords
жидкие металлы,
электрогидродинамика,
неустойчивость Лармора - Тонкса - Френкеля,
liquid metals,
electrohydrodynamics,
Larmor - Tonks - Frenkel instabilityAuthors
Zon B.A. | Voronezh State University | zon@niif.vsu.ru |
Всего: 1
References
Ono S. and Kondo S. // Structure of Liquids / Struktur der Flüssigkeiten. Encyclopedia of Physics / Handbuch der Physik. - Berlin; Göttingen; Heidelberg: Springer, 1960. - V. 3/10.
Графутин В.И., Прокопьев Е.П. // УФН. - 2002. - Т. 172. - № 1. - С. 67-83.
Tolman R.C. // J. Chem. Phys. - 1949. - V. 17. - P. 333-337.
Dolgikh A.V., Dorofeev D.L., and Zon B.A. // Phys. Rev. E. - 2003. - V. 67. - P. 056311; Долгих А.В., Дорофеев Д.Л., Зон Б.А. // Изв. РАН МЖГ. - 2007. - № 2. - С. 148-153.
Ganán-Calvo A.M., López-Herrera J.M., Herrada M.A., et al. // J. Aerosol Sci. - 2018. - V. 125. - P. 32-56.
Стретт Дж.В. (лорд Рэлей). Теория звука. - M.: ГИТТЛ, 1955.
Martin T.P. // Phys. Rep. - 1996. - V. 273. - P. 199-241.
Белоножко Д.Ф., Ширяева С.О., Григорьев А.И. Нелинейные волны на заряженной поверхности жидкости. - Ярославль: ЯрГУ, 2006.
Melcher J.R. // Theoretical and Applied Mechanics. - Berlin; Heidelberg: Springer, 1973. - P. 240-263.
Зон Б.А., Ледовский С.Б., Лихолет А.Н. // ЖТФ. - 1998. - Т. 68. - Вып. 4. - С. 75-82; 2000. - Т. 70. - Вып. 4. - С. 38-41.
Nánai L., Hevesi I., Bunkin N.F., et al. // Appl. Phys. A. - 1990. - V. 50. - P. 27-34.
Alexiades V. and Solomon A.D. Mathematical Modeling of Melting and Freezing Processes. - Washington DC: Hemisphere Publ. Corp., 1993.
Френкель Я.И. // ЖЭТФ. - 1936. - Т. 6. - Вып. 4. - С. 348-350.
Larmor J. // Proc. Camb. Phil. Soc. - 1890. - V. 7. - P. 69-72.
Serkov A.A., Barmina E.V., Shafeev G.A., and Voronov V.V. // Appl. Surf. Sci. - 2015. - V. 348. - P. 16-21.
Ландау Л.Д., Лифшиц Е.М. Электродинамика сплошных сред. - М.: Наука, 1982.
Tonks L.A. // Phys. Rev. - 1935. - V. 48. - P. 562-568.
Zon B.A. // Phys. Lett. A. - 2001. - V. 292. - P. 203-206.
Forbes R.J., Graeme L., and Mair R. Liquid Metal Ion Sources: Handbook of Charged Particle Optics. - Boca Raton: CRC Press, 2017.
Eggers J. // Rev. Mod. Phys. - 1997. - V. 69. - P. 865.
Габович М.Д. // УФН. - 1983. - Т. 140. - Вып. 5. - С. 137-151.
Goldberger M.L. and Watson K.M. // Phys. Rev. - 1964. - V. 134. - P. B919.
Lakshmikantham V., Leela S., and Martynyuk A.A. Stability Analysis of Nonlinear Systems. - N.Y.: M. Dekker, 1989. - P. 249-275.
Заславский Г.М., Сагдеев Р.З. Введение в нелинейную физику. - М.: Наука, 1988.