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Conflict of Interest: In relation to this article, we declare that there is no conflict of interest.

Publication history: Received January 17, 2005
Accepted March 31, 2005

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Finite-Amplitude Surface Waves on a Thin Film Flow Subject to a Unipolar-Charge Injection

Hyo Kim^†

Department of Chemical Engineering, University of Seoul, 90 Jeonnong-dong, Dongdaemun-gu, Seoul 130-743, Korea

hkim@uos.ac.kr

Korean Journal of Chemical Engineering, July 2005, 22(4), 495-502(8), 10.1007/BF02706633

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Abstract

The interaction of an electric field with a dielectric liquid film is investigated as it drains under gravity down an inclined plane electrode emitting uniform positive ions into the liquid region. By applying long-wave approximation to the governing equations, the evolution equation for the free surface is derived up to the first order of a thin film parameter ξ. To investigate the space charge effect on the development of a finite-amplitude surface wave, a neutral stability condition is obtained as a critical Reynolds number through a linear stability analysis, and the amplitude and velocity of a periodic disturbance are also calculated within a supercritically stable flow region. The presence of a unipolar space charge in the fluid makes a steady surface wave take on even higher amplitude and faster wave speed compared with the case of no space charge.

Keywords

Finite-Amplitude Surface Waves Unipolar-Charge Injection Dielectric Liquid Film Critical Reynolds Number

References

Atten P, IEEE Trans. Dielectr. Electr. Insul., 3(1), 1 (1996)
Benjamin TB, J. Fluid Mech., 2, 554 (1957)
Benney DJ, J. Math. Phys., 45, 150 (1966)
Castellanos A, Agrait N, IEEE Trans. Ind. Appl., 28(3), 513 (1992)
Gjevik B, Phys. Fluids, 13, 1918 (1970)
Gonzalez A, Catellanos A, Phys. Rev. E, 53(4), 3573 (1996)
Kim H, Bankoff SG, Miksis MJ, Phys. Fluids A., 4, 2117 (1992)
Kim H, Korean J. Chem. Eng., 20(5), 803 (2003)
Kim H, Korean J. Chem. Eng., 14(1), 41 (1997)
Kunhardt EE, Christophorou LG, Luessen LH, The Liquid State and Its Electrical Properties, NATO ASI Series B: Physics Vol. 193, Plenum Press, New York (1988)
Schneider JM, Watson PK, Phys. Fluids, 18, 1407 (1975)
Yih CS, Phys. Fluids, 5, 321 (1963)