Abstract
The equilibrium shape of a drop in the electrostatic field of a point charge and a point dipole is asymptotically calculated in terms of the dimensionless deformation of the shape and a ratio between the drop’s radius and the distance to the point charge (dipole). Irrespective of the degree of nonuniformity of the field, the prolate spheroidal deformation (typical of the uniform field) is shown to be the main reason for the change in the equilibrium shape of the spherical drop. When the nonuniformity of the field grows, the equilibrium shape becomes more and more asymmetric and different from the spheroidal one. This, all other things being equal, may influence the critical conditions for the instability of the drop’s surface against an induced charge. It follows from the aforesaid that the drop in the field of the dipole will be the first to undergo instability with the electrostatic pressure on the drop being the same.
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References
A. Doyle, D. R. Moffet, and B. Vonnegut, J. Colloid Sci. 19, 136 (1964).
T. G. O. Berg, R. J. Trainor, and U. Vaughan, J. Atmos. Sci. 27, 1173 (1970).
J. D. Schweizer and D. N. Hanson, J. Colloid Int. 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(8), 1 (2002).
D. Duft, T. Achtzehn, R. Muller, et al., Nature 421, 128 (2003).
R. L. Grimm and J. L. Beauchamp, J. Phys. Chem. B 109, 8244 (2005).
J. W. Strutt (Lord Rayleigh), Philos. Mag. 14, 184 (1882).
A. I. Grigor’ev, A. N. Zharov, and S. O. Shiryaeva, Tech. Phys. 50, 1006 (2005).
S. O. Shiryaeva, Tech. Phys. 51, 1284 (2006).
S. O. Shiryaeva, A. I. Grigor’ev, and P. V. Moksheev, Tech. Phys. 52, 422 (2007).
S. O. Shiryaeva, A. I. Grigor’ev, and P. V. Moksheev, Tech. Phys. 53, 296 (2008).
O. V. Kim and P. F. Dunn, Langmuir 26, 15807 (2010).
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981).
S. O. Shiryaeva and A. I. Grigor’ev, Charged Drop in Storm Cloud (YarGU, Yaroslavl’, 2008).
A. I. Grigor’ev, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 50 (1989).
S. O. Shiryaeva and A. I. Grigor’ev, Sov. Phys. Tech. Phys. 37, 1071 (1992).
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Original Russian Text © S.O. Shiryaeva, A.I. Grigor’ev, A.A. Shiryaev, 2013, published in Zhurnal Tekhnicheskoi Fiziki, 2013, Vol. 83, No. 11, pp. 44–51.
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Shiryaeva, S.O., Grigor’ev, A.I. & Shiryaev, A.A. On the equilibrium shapes of a conducting drop in a uniform and nonuniform electric field. Tech. Phys. 58, 1592–1599 (2013). https://doi.org/10.1134/S1063784213110236
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DOI: https://doi.org/10.1134/S1063784213110236