Stability and Shape of Isolated and Pairs of Water Drops in an Electric Field

Abstract

A numerical method of calculating the correct stable equilibrium shape of a conducting drop subject to electrical forces is described. Its application to the problem of the stability of an isolated water drop of undistorted radius R and surface tension T situated in an electric field E indicates that a drop is unstable if E(R/T)12 exceeds a value of 1.603 and its maximum stable deformation expressed as a/b, the ratio of the major to minor axes is 1.83. The numerical method is also applied to a study of the stability of drop pairs. The results show that the critical value of E(R/T)12 depends upon the initial separation X of the drops. For X = 0, E(R/T)12 is zero and its value increases as X increases, tending to a value of 1.603. Finally, the relevance of these results to the behavior of drops in the atmosphere is discussed.