Skip to main content
SpringerLink
Log in

On Some Peculiarities of Implementation of Instability of Flat Charged Surface of Electroconductive Liquid

  • Published:
Surface Engineering and Applied Electrochemistry Aims and scope Submit manuscript

Abstract

The characteristic sizes and charges of droplets formed during the realization of the electrostatic instability of a uniformly charged, charge-induced flat surface of an electrically conductive liquid are calculated on the base of the principle of the least energy dissipation in the Onsager nonequilibrium processes. It was found that the droplets of the same size and charges are emitted when the electrostatic instability of a flat liquid surface is realized. The surface should be infinitely extended along both axes of the Cartesian coordinate system of the liquid, and the axes should be perpendicular to the direction of gravity. If to compare the same characteristics of the charged droplet disintegration, unstable to its own charge, then there will be a number of differences, i.e., in the number of emitted progeny droplets, in their sizes and charges, and in the tendency of all parameters to change with an increase in the ordinal number of the progeny droplet. The paper considers the progeny droplets to be initially unstable to the electric charge which is located on them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Tonks, L.A., Theory of liquid surface rupture by uniform electric field, Phys. Rev., 1935, vol. 48, p. 562.

    Article  Google Scholar 

  2. Frenkel, Ya.I., To the theory of Tonks on the rupture of the surface of a liquid by a constant electric field in a vacuum, Zh. Exp. Teor. Fiz., 1936, vol. 6, no. 4, p. 348.

    MATH  Google Scholar 

  3. Taylor, G.I. and McEwan, A.D., The stability of horizontal fluid interface in a vertical electric field, J. Fluid Mech., 1965, vol. 22, no. 1, p. 1.

    Article  MATH  Google Scholar 

  4. Alexandrov, M.L., Gall, L.N., Ivanov, V.Ia., Nikolaev, V.I., et al., Calculation of the free surface of the conductive fluid in a strong electric field, Akad. Nauk SSSR, Izv., Mekh. Zhidk. Gaza, 1983, no. 6, p. 165.

  5. Allen, J.E., A note on the Taylor cone, J. Phys. D: Appl. Phys., 1985, vol. 18, p. 59.

    Article  Google Scholar 

  6. Suvorov, V.G. and Zubarev, N.M., Formation of the Taylor cone on the surface of liquid metal in the presence of an electric field, J. Phys. D: Appl. Phys., 2004, vol. 37, p. 289.

    Article  Google Scholar 

  7. Grigor’ev, A.I., Shiryaeva, S.O., Belonozhko, D.F., and Klimov, A.V., On the Taylor cone and characteristic growth time, Surf. Eng. Appl. Electrochem., 2004, no. 4, p. 34.

  8. Gabovich, M.D., Liquid-metal ion emitters, Sov. Phys. Usp., 1983, vol. 26, no 5, p. 447. https://doi.org/10.1070/PU1983v026n05ABEH004407

    Article  Google Scholar 

  9. Landau, L.D. and Lifshits, E.M., Elektrodinamika sploshnykh sred (Electrodynamics of Continuous Media), Moscow: Nauka, 1992.

  10. Lord Rayleigh F.R.S., XX. On the equilibrium of liquid conducting masses charged with electricity, Lond. Edinb. Dublin Philos. Mag. J. Sci., 1882, vol. 14, no. 87, p. 184. https://doi.org/10.1080/14786448208628425

    Article  MathSciNet  Google Scholar 

  11. Taylor, G., Electrically driven jets, Proc. Roy. Soc., Lond., 1969, vol. A313, no. 1515, p. 453. https://doi.org/10.1098/rspa.1969.0205

    Article  Google Scholar 

  12. Saville, D., Stability of electrically charged viscous cylinders, Phys. Fluids, 1971, vol. 14, no. 6, p. 1095.

    Article  Google Scholar 

  13. Grigor’ev, A.I. and Shiryaeva, S.O., The theoretical consideration of physical regularities of the electrostatic dispersion of liquids as aerosols, J. Aerosol Sci., 1994, vol. 25, no. 6, p. 1079.

    Article  Google Scholar 

  14. Cloupeau, M. and Prunet Foch, B., Electrohydrodynamic spraying functioning modes: A critical review, J. Aerosol Sci., 1994, vol. 25, no. 6, p. 1021.

    Article  Google Scholar 

  15. Verdoold, S., Agostinho, L.L.F., Yurteri, C.U., and Marijennisen, J.S.W., A generic electrospray classification, J. Aerosol Sci., 2014, vol. 67, p. 87.

    Article  Google Scholar 

  16. Fong Chee Sheng, Black, N.D., Kiefer, P.A., and Shaw, R.A., An experiment on the Rayleigh instability of charged liquid drops, Am. J. Phys., 2007, vol. 75, no. 6, p. 499.

    Article  Google Scholar 

  17. Hunter, H.C. and Ray Asit, K., On progeny droplets emitted during Coulombic fission of charged microdrops, Phys. Chem. Chem. Phys., 2009, vol. 11, no. 29, p. 6156.

    Article  Google Scholar 

  18. Drozin, V.G., The electrical dispersion of liquids as aerosols, J. Coll. Sci., 1955, vol. 10, no. 2, p. 158.

    Article  Google Scholar 

  19. Doyle, A., Moffet, D.R., and Vonnegut, B., Behavior of evaporating electrically charged droplets, J. Coll. Sci., 1964, vol. 19, p. 136.

    Article  Google Scholar 

  20. Roth, D.S. and Kelly, A.J., Analysis of the disruption of evaporating charged droplets, IEEE Trans. Ind. Appl., 1983, vol. IA-19, no. 5, p. 771.

    Article  Google Scholar 

  21. Elghazaly, H.M.A. and Castle, G.S.P., Analysis of the multysiblig instability of charged liquid drops, IEEE Trans. Ind. Appl., 1987, vol. IA-23, no. 1, p. 108.

    Article  Google Scholar 

  22. Grigor’ev, A.I. and Shiryaeva, S.O., Mechanism of electrostatic polidispersion of liquid, J. Phys. D.: Appl. Phys., 1990, vol. 23, no. 11, p. 1361. https://doi.org/10.1088/0022-3727/23/11/004

    Article  Google Scholar 

  23. Grigor’ev, A.I., Shiryaeva, S.O., and Verbitskii, S.S., Theory of production of monodisperse particles by electrostatic spraying of liquids, J. Coll. Int. Sci., 1991, vol. 146, no. 1, p. 137.

    Article  Google Scholar 

  24. Grigor’ev, A.I. and Shiryaeva, S.O., Parameters of electrostatic disintegration of charged drops suspended in a superposition of electrostatic, gravitational, and aerodynamic fields, Surf. Eng. Appl. Electrochem., 2021, vol. 57, no. 3, p. 294. https://doi.org/10.3103/S1068375521030078

    Article  Google Scholar 

  25. Grigor’ev, A.I., Shiryaeva, S.O., and Belavina, E.I., The equilibrium form of a charged drop in electric and gravitational fields, Zh. Tekh. Fiz., 1989, vol. 59, no. 6, p. 27.

    Google Scholar 

  26. Taylor, G.I., Disintegration of water drops in an electric field, Proc. Roy. Soc., London, 1964, vol. A280, p. 383.

    MATH  Google Scholar 

  27. Grigor’ev, A.I. and Shiryaeva, S.O., On realization peculiarities of electrostatic instability of a fluid’s charged surface in different geometries, Surf. Eng. Appl. Electrochem., 2022, vol. 58, no. 3, p. 231. https://doi.org/10.3103/S1068375522030097

    Article  Google Scholar 

  28. Grigor’ev, A.I. and Shiryaeva, S.O., Electrostatic instability of high azimuthal modes of a charged jet, Akad. Nauk SSSR, Izv., Mekh. Zhidk. Gaza, 2021, no. 3, p. 48.

  29. Grigor’ev, A.I. and Shiryaeva, S.O., On the influence of physicochemical characteristics of liquids on the regularities of their electrodispersion, Colloid J., 2021, vol. 83, no. 5, p. 566. https://doi.org/10.1134/S1061933X21050057

    Article  Google Scholar 

  30. Shutov, A.A., Generation of electrohydrodynymic waves at the liquid–vacuum interface, Zh. Tekh. Fiz., 2002, vol. 72, no. 8, p. 126.

    Google Scholar 

  31. Stretton, J.A., Electromagnetism Theory, New York: McGraw-Hill, 1941.

    Google Scholar 

  32. Yang, Ch.T. and Song, Ch.S., Encyclopedia of Fluid Mechanics, vol. 1: Flow Phenomena and Measurement, Houston: Gulf Publishing Company, 1986.

    Google Scholar 

  33. Grigor’ev, A.I., On some regularities of the realization of instability of a highly charged viscous drop, Zh. Tekh. Fiz., 2001, vol. 71, no. 10, p. 1.

    Google Scholar 

Download references

Funding

The work was performed within the framework of the State Assignment (Contract no. AAAA-A20-120011690131-7.

Author information

Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    A. I. Grigor’ev

Authors
  1. A. I. Grigor’ev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Grigor’ev.

Ethics declarations

The author declares that he has no conflicts of interest.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grigor’ev, A.I. On Some Peculiarities of Implementation of Instability of Flat Charged Surface of Electroconductive Liquid. Surf. Engin. Appl.Electrochem. 59, 618–627 (2023). https://doi.org/10.3103/S1068375523050083

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068375523050083

Keywords:

Search

Navigation