Abstract—
The dispersion relation for capillary waves of an arbitrary azimuthal symmetry on an elliptic cross-section jet in a uniform electrostatic field which is perpendicular to the axis of symmetry of the jet is derived. The stability of the first three azimuthal modes is investigated. It is shown that the stability of capillary waves on the jet reduces with increase in the external electrostatic field strength and the related eccentricity of transverse jet cross-section, as well as with increase in the polarization charge on the jet surface. Comparison with a jet in a radial electrostatic field is carried out. In the case of the transverse electrostatic field the instability growth rates of the capillary waves of any symmetry on the jet surface are turned out to be significantly higher than those in the case of the radial electrostatic field.
Similar content being viewed by others
REFERENCES
Kozhenkov, V.I. and Fuks, N.A., Electrohydrodynamic atomization of liquids (A Review), Usp. Khimii, 1976, vol. 45, no. 12. pp. 2274–2284.
Bailey, A.G., Electrostatic atomization of liquids (revue), Atomization and Spray Technology, 1986, vol. 2, pp. 95−134.
Fenn, J.B., Mann, M., and Meng, C.K., Electrospray ionization for mass spectrometry of large biomolecules (revue), Science, 1989, vol. 246, no. 4926, pp. 64–71.
Cloupeau, M. and Prunet Foch, B., Electrostatic spraying of liquids: main functioning modes, J. Electrostatics, 1990, vol. 25, pp. 165–184.
Cloupeau, M. and Prunet Foch, B., Electrohydrodynamic spraying functioning modes: a critical review, J. Aerosol Sci., 1994, vol. 25, no. 6, p. 1021–1035.
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., Control production by in-flight electrospraying, Langmuir, 2010, vol. 26, pp. 15807–15813. https://doi.org/10.1021/la102793j
Verdoolda, S., Agostinhoc, L.L.F., Yurterib, C.U., and Marijnissenb, J.C.M., A generic electrospray classification. J. Aerosol Sci., 2014, vol. 67, pp. 87–103.
Grigor’ev, A.I., Petrushov, N.A., and Shiryaeva, S.O., Nonlinear analysis of governing laws of realization of the wave motion on the surface of a charged jet moving with respect to a material medium, Fluid Dynamics, 2012, vol. 47, no. 1, pp. 58–69. https://doi.org/10.1134/S0015462812010073
Grigor’ev, A.I., Petrushov, N.A., and Shiryaeva, S.O., Nonlinear analysis of the wave motion on the surface of a jet moving through a dielectric medium in the longitudinal electric field, Zh. Tekh. Fiz., 2012, vol. 82, no. 8, pp. 35–41.
Amini, G. and Dolatabadi, A., Capillary instability of elliptic liquid jets, Phys. Fluids, 2011, vol .23, no. 084109, pp. 1–9. https://doi.org/10.1063/1.3626550
Amini, G., Yu, Lv, Dolatabadi, A., and Ihme, M., Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis, Phys. Fluids, 2014, vol. 26, no. 114105, pp. 1–22. https://doi.org/10.1063/1.4901246
Strutt, J.W. (Lord Rayleigh), The Theory of Sound, vol. 2, Cambridge: University Press, 2011.
Strutt, J.W. (Lord Rayleigh), On the instability of jets, Proc. London Math. Soc., 1878, vol. 10, pp. 4–13.
Strutt, J.W. (Lord Rayleigh), On the instability of cylindrical fluid surfaces, Phil. Mag., 1892, vol. 34, Series 5, pp. 145–154.
Cheng, K.J., Capillary oscillations of a drop in an electric field, Phys. Lett., 1985, vol. A112, no. 11, pp. 392–396.
Frenkel, Ya.I., On the Tonks theory of liquid surface rupture by a uniform electric field in vacuum, Zh. Eksper. Teoret. Fiz., 1936, vol. 6, no. 4, pp. 348–350.
Landau, L.D. and Lifshitz, E.M., The Classical Theory of Fields (3rd ed.), Pergamon Press, 1971; Moscow: Nauka, 1973.
Naifeh, A.H., Perturbation Methods, New York: Wiley, 1973; Moscow: Mir, 1976.
Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Ed. by Abramowitz, M., and Stegun, I.A., Washington: Gov. Print. Off., 1964; Moscow: Nauka, 1979.
Levich, V.G., Physicochemical Hydrodynamics, Englewood Cliffs, NJ: Prentice-Hall, 1962; Moscow: Fizmatgiz, 1959.
Shiryaeva, S.O., Grigor’ev, A.I., Levchuk, T.V., and Rybakova, M.V., On the stability of nonaxisymmetric charged jet of a viscous conducting liquid, Zh. Tekh. Fiz., 2003, vol. 73, no. 4, pp. 5–12.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by E.A. Pushkar
Rights and permissions
About this article
Cite this article
Grigor’ev, A.I., Shiryaeva, S.O. Stability of Capillary Waves of an Arbitrary Symmetry on a Jet in a Uniform Electrostatic Field. Fluid Dyn 56, 178–188 (2021). https://doi.org/10.1134/S001546282102004X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S001546282102004X