Abstract
The problem of nonlinear vibrations of a charged drop of an ideal incompressible conducting fluid in an electrostatic suspension is analytically solved in an approximation quadratic in two small parameters: vibration amplitude and equilibrium deformation of the shape of the drop in an electrostatic field. To solve the problem analytically, the desired quantities are expanded in semiinteger powers of the small parameters. It is shown that the charge of the drop and the gravitational field influence the shape of the drop, nonlinear corrections to the vibration frequencies, and critical conditions for instability of the drop against the surface charge. At near-critical values of the charge, the shape of the nonlinearly vibrating drop falls far short of being a sphere or a spheroid, which should be taken into account in treating experimental data.
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References
J. A. Tsamopoulos and R. A. Brown, J. Fluid Mech. 147, 373 (1984).
Z. Feng, J. Fluid Mech. 333, 1 (1997).
S. O. Shiryaeva, Pis’ma Zh. Tekh. Fiz. 26(22), 76 (2000) [Tech. Phys. Lett. 26, 1016 (2000)].
S. O. Shiryaeva, Pis’ma Zh. Tekh. Fiz. 29(17), 28 (2003) [Tech. Phys. Lett. 29, 714 (2003)].
S. O. Shiryaeva, A. I. Grigor’ev, and M. V. Volkova, Zh. Tekh. Fiz. 75(3), 36 (2005) [Tech. Phys. 50, 321 (2005)].
S. O. Shiryaeva, A. I. Grigor’ev, and M. V. Volkova, Zh. Tekh. Fiz. 75(7), 40 (2005) [Tech. Phys. 50, 856 (2005)].
K. J. Cheng, Phys. Lett. A 112, 392 (1985).
Z. C. Feng and K. V. Beard, J. Fluid Mech. 227, 429 (1991).
S. O. Shiryaeva, Pis’ma Zh. Tekh. Fiz. 22(4), 84 (1996) [Tech. Phys. Lett. 22, 171 (1996)].
A. Doyle, D. R. Moffet, and B. Vonnegut, J. Colloid Sci. 19, 136 (1964).
M. A. Abbas and J. Latham, J. Fluid Mech. 30, 663 (1967).
T. G. O. Berg, R. J. Trainor, and U. Vaughan, J. Atmosph. Sci. 27, 1173 (1970).
J. W. Schweizer and D. N. Hanson, J. Colloid Interface Sci. 35, 417 (1971).
M. Roulleau and M. Desbois, J. Atmos. Sci. 29, 565 (1972).
D. Duft, H. Lebius, B. A. Huber, et al., Phys. Rev. Lett. 89, 1 (2002).
A. I. Grigor’ev, S. O. Shiryaeva, and E. I. Belavina, Zh. Tekh. Fiz. 59(6), 27 (1989) [Sov. Phys. Tech. Phys. 34, 602 (1989)].
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Original Russian Text © S.O. Shiryaeva, 2006, published in Zhurnal Tekhnicheskoĭ Fiziki, 2006, Vol. 76, No. 3, pp. 93–95.
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Shiryaeva, S.O. Nonlinear vibrations of a charged drop in an electrostatic suspension. Tech. Phys. 51, 385–388 (2006). https://doi.org/10.1134/S1063784206030169
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DOI: https://doi.org/10.1134/S1063784206030169