Electrically charged conducting drops revisited
Author:
James Q. Feng
Journal:
Quart. Appl. Math. 55 (1997), 525-536
MSC:
Primary 76B45; Secondary 35Q35, 76W05
DOI:
https://doi.org/10.1090/qam/1466146
MathSciNet review:
MR1466146
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Abstract: Since its publication in 1882, Rayleigh’s work on electrically charged conducting drops has been widely quoted, but its rigorous derivation has not been given in the literature. By means of the domain perturbation technique, this work presents a rigorous derivation of Rayleigh’s results, following his approach with Lagrange’s equation. With the systematic procedure, it becomes explicit that the first-order surface deformations result in a deviation of the drop surface potential of only second-order significance. Besides providing mathematical details, this work also reveals an apparent error in Rayleigh’s original result for two-dimensional (cylindrical) drops.
Lord Rayleigh, On the equilibrium of liquid conducting masses charged with electricity, Philos. Mag. 5 (14), 184–186 (1882)
C. D. Hendricks and J. M. Schneider, Stability of a conducting droplet under the influence of surface tension and electrostatic forces, Amer. J. Phys. 31, 450–453 (1963)
- Daniel D. Joseph, Domain perturbations: the higher order theory of infinitesimal water waves, Arch. Rational Mech. Anal. 51 (1973), 295–303. MR 339656, DOI https://doi.org/10.1007/BF00250536
J. A. Tsamopoulos and R. A. Brown, Dynamic centering of liquid shells, Phys. Fluids 30, 27–35 (1987)
- James Q. Feng, A method of multiple-parameter perturbations with an application to drop oscillations in an electric field, Quart. Appl. Math. 48 (1990), no. 3, 555–567. MR 1074971, DOI https://doi.org/10.1090/qam/1074971
C. E. Weatherburn, Differential Geometry of Three Dimensions, Cambridge University Press, 1927
- John David Jackson, Classical electrodynamics, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1975. MR 0436782
J. A. Tsamopoulos and R. A. Brown, Resonant oscillations of inviscid charged drops, J. Fluid Mech. 147, 373–395 (1984)
J. Q. Feng and K. V. Beard, Three-dimensional oscillation characteristics of electrostatically deformed drops, J. Fluid Mech. 227, 429–447 (1991)
Lord Rayleigh, On the equilibrium of liquid conducting masses charged with electricity, Philos. Mag. 5 (14), 184–186 (1882)
C. D. Hendricks and J. M. Schneider, Stability of a conducting droplet under the influence of surface tension and electrostatic forces, Amer. J. Phys. 31, 450–453 (1963)
D. D. Joseph, Domain perturbations: The higher order theory of infinitesimal water waves, Arch. Rational Mech. Anal. 51, 294–303 (1973)
J. A. Tsamopoulos and R. A. Brown, Dynamic centering of liquid shells, Phys. Fluids 30, 27–35 (1987)
J. Q. Feng, A method of multiple-parameter perturbations with an application to drop oscillations in an electric field, Quart. Appl. Math. 48, 555–567 (1990)
C. E. Weatherburn, Differential Geometry of Three Dimensions, Cambridge University Press, 1927
J. D. Jackson, Classical Electrodynamics, John Wiley and Sons, 1975
J. A. Tsamopoulos and R. A. Brown, Resonant oscillations of inviscid charged drops, J. Fluid Mech. 147, 373–395 (1984)
J. Q. Feng and K. V. Beard, Three-dimensional oscillation characteristics of electrostatically deformed drops, J. Fluid Mech. 227, 429–447 (1991)
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Article copyright:
© Copyright 1997
American Mathematical Society
