A study of the instabilities in the interaction of an electrostatic field with a thin liquid film flowing under gravity down an inclined plane is presented. First, the long-wave stability conditions are studied by perturbing the evolution equation of film height about its steady-state solution. Three limits of flow systems are considered, i.e., static state, Reynolds number Re=O(1) and Re=O(1/ξ). Here ξ(≪1)is the ratio of the characteristic length scale parallel to the flow to the primary film thickness. Next, the long-wave behavior of the thin film flow is examined with the electrostatic potential of a Gaussian function in the two limits of Reynolds number, i.e., Re=O(1) and Re=O(1/ξ). These results are also compared with those from a full-scale explicit calculation. Finally, wave-growth rates are calculated from the Orr-Sommerfeld equation to show the stability to wave number with and without the electric field. The effect of the electric field is to lessen the range of the wave number in which the thin film flow remains stable.
[References]
Yih CS, Quart. Appl. Math., 13, 434, 1955
Banjamin TB, J. Fluid Mech., 2, 554, 1957
Yih CS, Phys. Fluids, 5, 321, 1963
Benney DJ, J. Math. Phys., 45, 150, 1966
Lin SP, J. Fluid Mech., 63, 417, 1974
Gjevik B, Phys. Fluids, 13, 1918, 1970
Pumir A, Manneville P, Pomeau Y, J. Fluid Mech., 135, 27, 1983
Alekseenko SV, Nakoryakov VE, Pokusaev BG, Int. J. Multiph. Flow, 11, 607, 1985
Kim H, Miksis MJ, Bankoff SG, Proc. Eighth Symp. on Space Nuclear Power Systems, Albuquerque, NM, CONF-910116, 1280, 1991
Kim H, Bankoff SG, Miksis MJ, Phys. Fluids A, 4, 2117, 1992
Kim H, Bankoff SG, Miksis MJ, AIAA J. Propulsion Power, 9, 245, 1993
Thomas S, Hankey WL, Faghri A, Swanson TD, Proc. Natl. Heat Transfer Conf., 110, 103, 1989
Rahman MM, Faghri A, Hankey WL, Swanson TD, Proc. Natl. Heat Transfer Conf., 110, 161, 1989
Hirt CW, Nichols BD, Romero NC, "SOLA-A Numerical Solution Algorithm for Transient Fluid Flow," Los Alamos Scientific Lab., Los Alamos, NM, 1975