Abstract
A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a cylindrical jet of an ideal incompressible dielectric liquid subjected to an electrostatic field aligned with the symmetry axis of the jet. It is shown that only long axisymmetric waves can experience capillary instability in such a system. The wavenumber range into which unstable waves fall begins with a zero value, and its width depends on the permittivities of the liquid and ambient and on the electrostatic field strength squared. As the field strength grows, the wavenumber range for unstable waves rapidly narrows and the capillary instability growth rate, as well as the wavenumber of the wave with the greatest growth rate, decreases.
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References
J. W. Strutt (Lord Rayleigh), Proc. London Math. Soc. 10, 4 (1878).
J. W. Strutt (Lord Rayleigh), The Theory of Sound (Dover, New York, 1945; Gostekhizdat, Moscow, 1955), Vol. 2.
V. M. Entov and A. L. Yarin, Itogi Nauki Tekh., Ser.: Mekh. Zhidk. Gaza 17, 112 (1984).
E. V. Ametistov, V. V. Blazhenkov, A. K. Gorodov, et al., Monodispersion of Matter: Principles and Applications, Ed. by V. A. Grigor’ev (Energoatomizdat, Moscow, 1991) [in Russian].
S. O. Shiryaeva, A. I. Grigor’ev, and M. V. Volkova, Spontaneous Capillary Disintegration of Charged Jets (Yaroslavsk. Gos. Univ., Yaroslavl’, 2007) [in Russian].
J. Eggers and E. Willermaux, Rep. Prog. Phys. 71, 036601 (2008).
Ya. I. Frenkel’, Zh. Eksp. Teor. Fiz. 6, 348 (1936).
N. K. Nayyar and G. S. Murty, Proc. Phys. Soc. 75, 369 (1960).
G. A. Glonti, Zh. Eksp. Teor. Fiz. 34, 1328 (1958) [Sov. Phys. JETP 7, (1958)].
R. J. Raco, AIAA J. 6, 979 (1968).
D. A. Saville, J. Fluid. Mech. 48, 815 (1971).
A. J. Mestel, J. Fluid. Mech. 312, 311 (1996).
A. A. Shutov, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 52 (2006).
D. F. Belonozhko and A. I. Grigor’ev, Zh. Tekh. Fiz. 74(11), 22 (2004) [Tech. Phys. 49, 1422 (2004)].
V. G. Levich, Physicochemical Hydrodynamics (Fizmatgiz, Moscow, 1959; Prentice Hall, Englewood Cliffs, 1962).
M. Cloupeau and B. Prunet Foch, J. Electrost. 25, 165 (1990).
A. Jaworek and A. Krupa, J. Aerosol Sci. 30, 873 (1999).
S. O. Shiryaeva and A. I. Grigor’ev, J. Electrost. 34, 51 (1995).
S. O. Shiryaeva, A. I. Grigor’ev, and A. A. Svyatchenko, RF Preprint No. 25, IMI RAN (Institute of Microelectronics and Informatics RAN, Yaroslavl’, 1993).
A. I. Grigor’ev, Zh. Tekh. Fiz. 77(2), 31 (2007) [Tech. Phys. 52, 173 (2007)].
A. I. Grigor’ev and D. M. Pozharitskii, Zh. Tekh. Fiz. 78(10), 40 (2008) [Tech. Phys. 53, 1289 (2008)].
A. F. Aleksandrov, V. L. Bychkov, L. P. Grachev, et al., Zh. Tekh. Fiz. 76(3), 38 (2006) [Tech. Phys. 51, 330 (2006)].
A. I. Grigor’ev and S. O. Shiryaeva, Zh. Tekh. Fiz. 62(12), 9 (1992) [Sov. Phys. Tech. Phys. 37, 1136 (1992)].
N. B. Zolotoi, G. V. Karpov, and V. E. Skurat, Zh. Tekh. Fiz. 58, 315 (1988) [Sov. Phys. Tech. Phys. 33, 193 (1988)].
S. O. Shiryaeva and A. I. Grigor’ev, Zh. Tekh. Fiz. 63(8), 162 (1993) [Tech. Phys. 38, 715 (1993)].
S. O. Shiryaeva, A. I. Grigor’ev, T. V. Levchuk, and M. V. Rybakova, Zh. Tekh. Fiz. 73(5), 5 (2003) [Tech. Phys. 48, 527 (2003)].
S. O. Shiryaeva, A. I. Grigor’ev, and T. V. Levchuk, Zh. Tekh. Fiz. 73(11), 22 (2003) [Tech. Phys. 48, 1380 (2003)].
A. I. Grigor’ev, N. V. Voronina, and S. O. Shiryaeva, Zh. Tekh. Fiz. 78(2), 33 (2008) [Tech. Phys. 53, 173 (2008)].
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Original Russian Text © S.O. Shiryaeva, 2010, published in Zhurnal Tekhnicheskoǐ Fiziki, 2010, Vol. 80, No. 2, pp. 45–50.
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Shiryaeva, S.O. On the capillary stability of a cylindrical dielectric liquid jet in a longitudinal electrostatic field. Tech. Phys. 55, 204–209 (2010). https://doi.org/10.1134/S1063784210020076
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DOI: https://doi.org/10.1134/S1063784210020076