Nonlinear electrohydrodynamic instability of a jet
Authors:
R. Kant and S. K. Malik
Journal:
Quart. Appl. Math. 43 (1986), 407-419
MSC:
Primary 76E25; Secondary 76X05
DOI:
https://doi.org/10.1090/qam/846153
MathSciNet review:
846153
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Abstract: A weakly nonlinear theory of an electrohydrodynamic jet held together by capillary forces is investigated. The evolution of two-dimensional wave packets on the surface of the jet is shown to be governed by a nonlinear Schrödinger equation. It is found that the wave train of constant amplitude is unstable against modulation. The instability sets in at higher wave numbers as compared to the case of an unelectrified jet.
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J. R. Melcher, Field coupled surface waves, M.I.T. Press, 1963
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M. C. Yuen, Nonlinear capillary instability of a liquid, J. Fluid Mech. 33, 151 (1968)
A. H. Nayfeh, Nonlinear stability of a liquid jet, Phys. Fluids 13, 841 (1970)
T. Kakutani, Y. Inoue and T. Kan, Nonlinear capillary waves on the surface of liquid column, J. Phy. Soc. Japan 37, 529 (1974)
L. Crane, S. Birch and P. D. McCormack, The effect of mechanical vibrations on the break-up of a cylindrical water jet in air, Brit. J. Appl. Phys. 15, 743 (1964)
R. J. Donnelly and W. Glaberson, Experiments on the capillary instability of a liquid jet, Proc. Roy. Soc. (London) 290A, 547 (1966)
K. C. Chaudhary and T. Maxworthy, The nonlinear capillary instability of a liquid jet. Part 2. Experiments on jet behaviour before droplet formation, J. Fluid Mech. 96 part 2, 275 (1980)
- S. K. Malik and M. Singh, Nonlinear breakup of an electrohydrodynamic jet, Quart. Appl. Math. 41 (1983/84), no. 3, 273–287. MR 721418, DOI https://doi.org/10.1090/S0033-569X-1983-0721418-7
J. R. Pierce, An interesting wave amplifier, IRE Transactions on Electron Devices, ED-7, 3 (1960)
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V. I. Karpman, Nonlinear waves in dispersive media, Pergamon Press, 1975
R. Kant, R. K. Jindia and S. K. Malik, Finite amplitude surface waves in electrohydrodynamics, Quart. Appl. Math. 39, No. 1, 23 (1981)
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Lord Rayleigh, The theory of sound, Vol. 2, Dover, 1945
J. R. Melcher, Field coupled surface waves, M.I.T. Press, 1963
D. H. Michael, Note on the electrostatic instability of a jet, Can. J. Phys. 45, 3179 (1967)
M. C. Yuen, Nonlinear capillary instability of a liquid, J. Fluid Mech. 33, 151 (1968)
A. H. Nayfeh, Nonlinear stability of a liquid jet, Phys. Fluids 13, 841 (1970)
T. Kakutani, Y. Inoue and T. Kan, Nonlinear capillary waves on the surface of liquid column, J. Phy. Soc. Japan 37, 529 (1974)
L. Crane, S. Birch and P. D. McCormack, The effect of mechanical vibrations on the break-up of a cylindrical water jet in air, Brit. J. Appl. Phys. 15, 743 (1964)
R. J. Donnelly and W. Glaberson, Experiments on the capillary instability of a liquid jet, Proc. Roy. Soc. (London) 290A, 547 (1966)
K. C. Chaudhary and T. Maxworthy, The nonlinear capillary instability of a liquid jet. Part 2. Experiments on jet behaviour before droplet formation, J. Fluid Mech. 96 part 2, 275 (1980)
S. K. Malik and M. Singh, Nonlinear break-up of an electrohydrodynamic jet, Quart. Appl. Math. 41, No. 3, 273 (1983)
J. R. Pierce, An interesting wave amplifier, IRE Transactions on Electron Devices, ED-7, 3 (1960)
G. B. Whitman, Linear and nonlinear waves, John Wiley, New York, 1974
V. I. Karpman, Nonlinear waves in dispersive media, Pergamon Press, 1975
R. Kant, R. K. Jindia and S. K. Malik, Finite amplitude surface waves in electrohydrodynamics, Quart. Appl. Math. 39, No. 1, 23 (1981)
V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Phys., J.E.T.P. 34 (1972)
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Article copyright:
© Copyright 1986
American Mathematical Society
