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.
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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.
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.
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.
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.
Eggers, J. and Willermaux, E., Physics of Liquid Jets, Rep. Prog. Phys., 2008, vol. 71, no. 036601, pp. 1–79.
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.
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.
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.
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.
Saville, D.A., Elecrohydrodynamic Stability: Fluid Cylinders in Longitudinal Electric Fields, Phys. Fluids, 1970, vol. 13, no. 12, pp. 2987–2994.
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.
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.
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.
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.
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.
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.
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.
Cloupeau, M. and Prunet Foch, B., Electrostatic Spraying of Liquids: Main Functioning Modes, J. Electrostatics, 1990, vol. 25, pp. 165–184.
Jaworek, A. and Krupa, A., Classification of the Modes of EHD Spraying, J. Aerosol Sci., 1999, vol. 30, no. 7, pp. 873–893.
Kim, O.V. and Dunn, P.F., Controlled Production of Droplets by In-Flight Electrospraying, Langmuir, 2010, vol. 26, pp. 15807–15813.
Abramovitz, M. and Stigan, I., Spravochnik po spetzial’nym funktziyam (Handbook on the Special Functions), Moscow: Nauka, 1979.
Barry, J.D., Ball Lightning and Bead Lightning, New-York: Plenum, 1980.
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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.
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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
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DOI: https://doi.org/10.3103/S1068375511050097