Abstract
The problem of nonlinear oscillations of the finite amplitude of an uncharged drop of an ideal incompressible conducting liquid in an external uniform electrostatic field is solved for the first time by analytical asymptotic methods. The problem is solved in an approximation quadratic in amplitude of the initial deformation of the equilibrium shape of the drop and in eccentricity of its equilibrium spheroidal deformation. Compared with the case of nonlinear oscillations of charged drops in the absence of the field, the curvature of the vertices of uncharged drops nonlinearly oscillating in the field is noticeably higher, whereas the number of resonant situations (in the sense of internal resonant interaction of modes) is much smaller.
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References
J. A. Tsamopoulos and R. A. Brown, J. Fluid Mech. 147, 373 (1984).
J. A. Tsamopoulos, T. R. Akylas, and R. A. Brown, Proc. R. Soc. London, Ser. A 401, 67 (1985).
R. Natarayan and R. A. Brown, Proc. R. Soc. London, Ser. A 410, 209 (1987).
Z. C. Feng, J. Fluid Mech. 333, 1 (1997).
S. O. Shiryaeva, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 173 (2001).
S. O. Shiryaeva, Zh. Tekh. Fiz. 72(4), 15 (2002) [Tech. Phys. 47, 673 (2002)].
S. O. Shiryaeva, Zh. Tekh. Fiz. 73(2), 19 (2003) [Tech. Phys. 48, 152 (2003)].
S. O. Shiryaeva, Pis’ma Zh. Tekh. Fiz. 29(17), 28 (2003) [Tech. Phys. Lett. 29, 714 (2003)].
A. N. Zharov, S. O. Shiryaeva, and A. I. Grigor’ev, Zh. Tekh. Fiz. 73(12), 9 (2003) [Tech. Phys. 48, 1511 (2003)].
S. O. Shiryaeva, A. N. Zharov, and A. I. Grigor’ev, Zh. Tekh. Fiz. 74(1), 10 (2004) [Tech. Phys. 49, 8 (2004)].
K. J. Cheng, Phys. Lett. A 112, 392 (1985).
A. I. Grigor’ev and O. A. Sinkevich, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 10 (1985).
Z. C. Feng, Quarterly Appl. Math. 47, 555 (1990).
Z. C. Feng and K. V. Beard, Proc. R. Soc. London 430, 133 (1990).
S. O. Shiryaeva and A. I. Grigor’ev, Zh. Tekh. Fiz. 66(9), 12 (1996) [Tech. Phys. 41, 865 (1996)].
Z. C. Feng and K. V. Beard, J. Fluid Mech. 227, 429 (1991).
A. I. Grigor’ev and S. O. Shiryaeva, Zh. Tekh. Fiz. 69(7), 10 (1999) [Tech. Phys. 44, 745 (1999)].
A. Bratz and I. Egry, J. Fluid Mech. 298, 341 (1995).
A. I. Grigor’ev, S. O. Shiryaeva, and M. V. Volkova, Zh. Tekh. Fiz. 73(11), 31 (2003) [Tech. Phys. 48, 1389 (2003)].
J. A. Tsamopolos and R. A. Brown, J. Fluid Mech. 127, 519 (1983).
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Translated from Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 75, No. 3, 2005, pp. 36–44.
Original Russian Text Copyright © 2005 by Shiryaeva, Volkova, Grigor’ev.
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Shiryaeva, S.O., Volkova, M.V. & Grigor’ev, A.I. Nonlinear oscillations of an uncharged conducting drop in an external uniform electrostatic field. Tech. Phys. 50, 321–329 (2005). https://doi.org/10.1134/1.1884731
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DOI: https://doi.org/10.1134/1.1884731