A method of multiple-parameter perturbations with an application to drop oscillations in an electric field
Author:
James Q. Feng
Journal:
Quart. Appl. Math. 48 (1990), 555-567
MSC:
Primary 76W05; Secondary 76B99, 78A99
DOI:
https://doi.org/10.1090/qam/1074971
MathSciNet review:
MR1074971
Full-text PDF Free Access
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Abstract: A formulation of a perturbation technique with several small parameters is presented. As a particular example, this method is used to study the axisymmetric oscillations of an inviscid conducting drop in an electric field. It is shown that all characteristic frequencies of the axisymmetric oscillations decrease as the electric field strength increases, which is in general agreement with simplified models based on the assumption of spheroidal deformations.
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J. A. Tsamopoulos and R. A. Brown, Resonant oscillations of inviscid charged drops, J. Fluid Mech. 147, 373–395 (1984)
G. I. Taylor, Disintegration of water drops in an electric field, Proc. Roy. Soc. Lond. Ser. A 280, 383–397 (1964)
P. R. Brazier-Smith, M. Brook, J. Latham, C. P. Saunders, and M. H. Smith, The vibration of electrified water drops, Proc. Roy. Soc. Lond. Ser. A 322, 523–534 (1971)
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J. R. Carruthers, The application of drops and bubbles to the science of space processing of materials, Proc. Int. Colloq. Drops and Bubbles (eds. D. J. Collins, M. S. Plesset and M. M. Saffren), Pasadena: Jet Propulsion Laboratory (1974)
C. E. Rosenkilde, A dielectric fluid drop in an electric field, Proc. Roy. Soc. Lond. Ser. A 312, 473–494 (1969).
S. B. Sample, B. Raghupathy, and C. D. Hendricks, Quiescent distortion and resonant oscillations of a liquid drop in an electric field, Internat. J. Engrg. Sci. 8, 97–109 (1970)
C. A. Morrison, R. P. Leavitt, and D. E. Wortman, The extended Rayleigh theory of the oscillation of liquid droplets, J. Fluid Mech. 104, 295–309 (1981)
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J. A. Tsamopoulos and R. A. Brown, Nonlinear oscillations of inviscid drops and bubbles, J. Fluid Mech. 127, 519–537 (1983)
P. M. Adornato and R. A. Brown, Shape and stability of electrostatically levitated drops, Proc. Roy. Soc. Lond. Ser. A 389, 101–117 (1983)
J. W. S. Rayleigh, On the capillary phenomena of jets, Proc. Roy. Soc. Lond. Ser. A 29, 71–97 (1879)
A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, Wiley-Interscience, 1979
D. D. Joseph, Domain perturbations: the higher order theory of infinitesimal water waves, Arch. Rational Mech. Anal. 51, 295–303 (1973)
J. A. Tsamopoulos and R. A. Brown, Resonant oscillations of inviscid charged drops, J. Fluid Mech. 147, 373–395 (1984)
G. I. Taylor, Disintegration of water drops in an electric field, Proc. Roy. Soc. Lond. Ser. A 280, 383–397 (1964)
P. R. Brazier-Smith, M. Brook, J. Latham, C. P. Saunders, and M. H. Smith, The vibration of electrified water drops, Proc. Roy. Soc. Lond. Ser. A 322, 523–534 (1971)
R. J. Pfeifer and C. D. Hendricks, Charge-to-mass relationships for electrohydrodynamically sprayed liquid droplets, Phys. Fluids 10, 2149–2154 (1967)
J. R. Carruthers, The application of drops and bubbles to the science of space processing of materials, Proc. Int. Colloq. Drops and Bubbles (eds. D. J. Collins, M. S. Plesset and M. M. Saffren), Pasadena: Jet Propulsion Laboratory (1974)
C. E. Rosenkilde, A dielectric fluid drop in an electric field, Proc. Roy. Soc. Lond. Ser. A 312, 473–494 (1969).
S. B. Sample, B. Raghupathy, and C. D. Hendricks, Quiescent distortion and resonant oscillations of a liquid drop in an electric field, Internat. J. Engrg. Sci. 8, 97–109 (1970)
C. A. Morrison, R. P. Leavitt, and D. E. Wortman, The extended Rayleigh theory of the oscillation of liquid droplets, J. Fluid Mech. 104, 295–309 (1981)
L. D. Landau and E. M. Lifshitz, Electrodynamics of continuous media, Addison-Wesley, 1959
J. A. Tsamopoulos and R. A. Brown, Nonlinear oscillations of inviscid drops and bubbles, J. Fluid Mech. 127, 519–537 (1983)
P. M. Adornato and R. A. Brown, Shape and stability of electrostatically levitated drops, Proc. Roy. Soc. Lond. Ser. A 389, 101–117 (1983)
J. W. S. Rayleigh, On the capillary phenomena of jets, Proc. Roy. Soc. Lond. Ser. A 29, 71–97 (1879)
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Article copyright:
© Copyright 1990
American Mathematical Society
