Electrohydrodynamical study of the instability of a thin liquid metal film: Application to planar liquid metal ion sources

Liquid metal ion sources are of interest in diverse areas of technology since they provide a high brightness, quasipoint source of ions and droplets for microfabrication, surface analysis, ultrathin film deposition, and other potential applications. N. M. Miskovsky, M. Chung, P. H. Cutler, T. E. Feuchtwang, and E. Kazes [J. Vac. Sci. Technol. A 6, 2992 (1988)] have developed an electrohydrodynamic capillary wave theory for ion and droplet emission in electrically stressed conducting viscous fluids based on a mathematical formalism introduced by J. R. Melcher and C. V. Smith [Phys. Fluids 12, 778 (1969)] and S. Grossmann and A. Muller [Z. Phys. B 57, 161 (1984)]. As the simplest analytical application of this theory they chose a model consisting of a planar fluid of thickness ''a'' supported on a rigid electrode. A parallel planar counter electrode is at a distance ''b'' from the unperturbed surface. The Navier--Stokes equation was solved subject to a dynamical Laplace--Young stress boundary condition (which includes the frictional tensor) to obtain the dispersion relation used to investigate the stability of the system