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The destabilization of an infinite plane surface of liquid metal by a normal electric field in a vacuum has been the subject of different theoretical articles: above a critical field peaks grow on the liquid interface. A wavelength can be attributed to the resulting pattern. The electric field at onset and the corresponding wavelength only depends of the density and the surface tension of the liquid. Above this critical field a whole range of wavelengths are excited, each growing with a different growth time: the fastest is the dominant wavelength. We shall present the influence of dynamics of the liquid viscosity and of the liquid bath depth: it can be shown that the dominant wavelength is smaller with higher fields but differs if the liquid film is thick or thin, inviscid, or viscous.
G. Neron de Surgy,Jean Pierre Chabrerie, andJ. E. Wesfreid
"Emission of a liquid metal interface in vacuum", Proc. SPIE 2259, XVI International Symposium on Discharges and Electrical Insulation in Vacuum, (1 May 1994); https://doi.org/10.1117/12.174569
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G. Neron de Surgy, Jean Pierre Chabrerie, J. E. Wesfreid, "Emission of a liquid metal interface in vacuum," Proc. SPIE 2259, XVI International Symposium on Discharges and Electrical Insulation in Vacuum, (1 May 1994); https://doi.org/10.1117/12.174569