Exact solution of the problem of the equilibrium configuration of the charged surface of a liquid metal

A broad class of exact solutions is obtained for the problem of the equilibrium configuration of the charged surface of a conducting liquid allowing for capillary forces. An analysis of the solutions showed that when the amplitudes of the perturbations reached certain critical values, the region occupied by the liquid ceases to be singly connected, which corresponds to the formation of liquid metal droplets. It is shown that a steady-state liquid metal profile may exist for which appreciable local amplification of the electric field can be achieved. Zh. éksp. Teor. Fiz. 116, 1990–2005 (December 1999)