Skip to main content
Log in

The effect of the density of the medium on the stability of a dielectric liquid jet moving collinearly to a uniform electrostatic field

  • Electrical Processes in Engineering and Chemistry
  • Published:
Surface Engineering and Applied Electrochemistry Aims and scope Submit manuscript

Abstract

The analysis of the dispersion equation for capillary waves of arbitrary symmetry on the surface of a jet that moves collinearly to an external uniform electrostatic field in an ideal incompressible dielectric medium has been performed. It is shown that an increase in the relative density of the medium is a destabilizing factor for waves on the jet’s surface regardless of their symmetry. The instability of the nonaxially symmetric waves is associated with a threshold for the jet’s velocity with regard to the medium.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Grigor’ev, A.I., Shiryaeva, S.O., and Egorova, E.V., On Some Specifics of Nonlinear Resonance Interaction of the Modes of a Charged Jet, Electronic Processing of Mater., 2005, vol. 41, no. 1, p. 42–50.

    Google Scholar 

  2. Grigor’ev, A.I., Shiryaeva, S.O., Voronina, N.V., and Egorova, E.V., About Oscillations and Spontaneous Disintegration of Charged Liquid Jets, Electronic Processing of Mater., 2006, vol. 42, no. 6, p. 23–34.

    Google Scholar 

  3. Shutov, A.A., Formation and Stability of a Charged Viscous Jet in a Strong Electric Field, Izv. RAN. Mekh. Zhidk. i Gaza, 2006, no. 6, p. 52–67.

  4. Shiryaeva, S.O., Grigor’ev, A.I., and Volkova, M.V., Spontannyi kapillyarnyi raspad zaryazhennykh strui (Spontaneous Capillary Disintegration of Charged Jets), Yaroslavl’: Yaroslavl’ State Univ., 2007.

    Google Scholar 

  5. Eggers, J. and Willermaux, E., Physics of Liquid Jets, Rep. Prog. Phys., 2008, vol. 71, no. 036601, pp. 1–79.

    Google Scholar 

  6. Shiryaeva, S.O. and Grigor’ev, A.I., On Stabilization of Capillary Instability of Dielectric Liquid Jet by Volume Electric Charge, Surface Engineering and Applied Electrochemistry, 2009, vol. 45, no. 5, pp. 357–363.

    Article  Google Scholar 

  7. Grigor’ev, A.I. and Shiryaeva, S.O., On Electrostatic Instability of a Space-Charged Jet of Dielectric Liquid, Surface Engineering and Applied Electrochemistry, 2009, vol. 45, no. 6, pp. 465–470.

    Article  MATH  Google Scholar 

  8. Glonti, G.A., Towards the Instability Theory of Liquid Jets in an Electric Field Zh. Exper. Theor. Phyz., 1958, vol. 34, no. 5, pp. 1328–1330.

    Google Scholar 

  9. Nayyar, N.K. and Murty, G.S., The Stability of a Dielectric Jet in a Presence of a Longitudinal Electric Field, Proc. Phys. Soc., 1960, vol. 75, Pt. 3., pp. 369–373.

    Article  Google Scholar 

  10. Saville, D.A., Elecrohydrodynamic Stability: Fluid Cylinders in Longitudinal Electric Fields, Phys. Fluids, 1970, vol. 13, no. 12, pp. 2987–2994.

    Article  MATH  Google Scholar 

  11. Shkadov, V.Ya. and Shutov, A.A., Stability of a Surface-Charged Viscous Jet in an Electric Field, Izv. RAN. Mekh. Zhidk. i Gaza, 1998, no. 2, pp. 29–40.

  12. Shiryaeva, S.O., Grigor’ev, A.I., and Volkova, M.V., On the Possibility of the Full Stabilization of the Capillary Instability of a Dielectric Liquid Jet by a Longitudinal Static Field Surface Engineering and Applied Electrochemistry, 2009, vol. 45, no. 3, pp. 193–198.

    Article  Google Scholar 

  13. Shiryaeva, S.O., On Capillary Stability of a Cylindrical Dielectric Liquid Jet in a Longitudinal Electrostatic Field, Zh. Theor. Phyz., 2010, vol. 80, no. 2, p. 47–51.

    Google Scholar 

  14. Grigor’ev, A.I., Voronina, N.V., and Shiryaeva, S.O., Asymptotical Studies of Nonlinear Non-Axially Symmetric Waves on The Surface of an Uncharged Dielectric Jet in a Longitudinal Electrostatic Field, Zh. Theor. Phyz., 2010, vol. 80, no. 10, p. 22–29.

    Google Scholar 

  15. Shiryaeva, S.O., On Stability of a Volume-Charged Jet of a Dielectric Liquid Moving with Acceleration in a Collinear Jet of an Electric Field, Izv. RAN. Mekh. Zhidk. i Gaza, 2010, no. 3, p. 57–68.

  16. Grigor’ev, A.I., Shiryaeva, S.O., Petrushov, N.A., and Volkova, M.V., On the Effect of Medium Density on Stability of Capillary Waves on the Surface of a Liquid Jet Moving with Reference to a Medium, Electronic Journal “Studied in Russia”, http://zhurnal.ape.relarn.ru/articles/2010/017.pdf, 2010, pp. 232–240.

  17. Grigor’ev, A.I., Shiryaeva, S.O., Petrushov, N.A., and Volkova, M.V., Instability of the Lateral Surface of Strongly Charged Jets in a Collinear Flow of Material Environment, Surface Engineering and Applied Electrochemistry, 2010, vol. 46, no. 3, pp. 218–222.

    Article  Google Scholar 

  18. Cloupeau, M. and Prunet Foch, B., Electrostatic Spraying of Liquids: Main Functioning Modes, J. Electrostatics, 1990, vol. 25, pp. 165–184.

    Article  Google Scholar 

  19. Jaworek, A. and Krupa, A., Classification of the Modes of EHD Spraying, J. Aerosol Sci., 1999, vol. 30, no. 7, pp. 873–893.

    Article  Google Scholar 

  20. Kim, O.V. and Dunn, P.F., Controlled Production of Droplets by In-Flight Electrospraying, Langmuir, 2010, vol. 26, pp. 15807–15813.

    Article  Google Scholar 

  21. Abramovitz, M. and Stigan, I., Spravochnik po spetzial’nym funktziyam (Handbook on the Special Functions), Moscow: Nauka, 1979.

    Google Scholar 

  22. Barry, J.D., Ball Lightning and Bead Lightning, New-York: Plenum, 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. I. Grigor’ev.

Additional information

Original Russian Text © A.I. Grigor’ev, S.O. Shiryaeva, N.A. Polyantsev, 2011, published in Elektronnaya Obrabotka Materialov, 2011, No. 5, pp. 43–49.

About this article

Cite this article

Grigor’ev, A.I., Shiryaeva, S.O. & Polyantsev, N.A. The effect of the density of the medium on the stability of a dielectric liquid jet moving collinearly to a uniform electrostatic field. Surf. Engin. Appl.Electrochem. 47, 413–418 (2011). https://doi.org/10.3103/S1068375511050097

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068375511050097

Keywords

Navigation