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Received February 7, 2011
Accepted April 1, 2011
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The effect of an electrostatic field on the rupture of a thin viscous static film by van der Waals attractions
Department of Chemical Engineering, The University of Seoul, 90 Jeonnong-dong, Dongdaemun-gu, Seoul 130-743, Korea
hkim@uos.ac.kr
Korean Journal of Chemical Engineering, November 2011, 28(11), 2122-2129(8), 10.1007/s11814-011-0085-6
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Abstract
This research examines rupture phenomena of a horizontal static thin viscous layer on a solid plate under an electrostatic field generating from a charged foil above the film. The dynamics of the electrified liquid film is formulated to derive a long-wave evolution equation of local film thickness. It determines two-dimensional nonlinear behavior of the film subject to surface tension, viscous, electrically induced forces, and van der Waals attractions. Linear stability analysis is used to obtain the maximum growth rate of a periodic disturbance and its corresponding wavenumber. To see the development of film rupture the strongly nonlinear partial differential equation is numerically solved for the unlimited or limited foil length as part of an initial-value problem with spatially periodic boundary conditions. The stronger electric forces make the thin layer more unstable and speed up its rupture.
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References
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Scheludko A, Adv. Colloid Interface Sci., 1, 391 (1967)
Williams MB, Davis SH, J. Colloid Interface Sci., 90, 220 (1982)
Burelbach JP, Bankoff SG, Davis SH, J. Fluid Mech., 195, 463 (1988)
Kim H, Bankoff SG, Miksis MJ, Phys. Fluids A., 4, 2117 (1992)
Griffing EM, Bankoff SG, Miksis MJ, Schluter RA, ASME I: J. Fluids Eng., 128, 276 (2006)
Schaffer E, Thurn-Albrecht T, Russell TP, Steiner U, Nature., 403, 874 (2000)
Schaffer E, Thurn-Albrecht T, Russell TP, Steiner U, Europhys. Lett., 53, 518 (2001)
Lin ZQ, Kerle T, Russell TP, Schaffer E, Steiner U, Macromolecules, 35(10), 3971 (2002)
Blyth MG, J. Fluid Mech., 595, 221 (2008)
Tseluiko D, Papageorgiou DT, SIAM J. Appl. Math., 67, 1310 (2007)
Tilley BS, Petropoulos PG, Papageorgiou DT, Phys. Fluids., 13, 3547 (2001)
Savettaseranee K, Papageorgiou DT, Petropoulos PG, Tilley BS, Phys. Fluids., 15, 641 (2003)
Landau LD, Lifshitz EM, Pitaevskii LP, Electrodynamics of Continuous Media, 2nd Ed., Pergamon, New York (1984)
Morse PM, Feshbach H, Methods of Theoretical Physics, McGraw-Hill, New York (1953)
