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.

Reverse movement and coalescence of water microdroplets in electrohydrodynamic atomization

“…Grimm and Beauchamp [30] also investigated the formation of these sprays. They found that neutral droplets exhibited the same prolate elongation mentioned by Brazier-Smith [29] with symmetric "cone jets" of positive and negative progeny droplets. Droplets with a net charge q take the form of asymmetric tear shapes and emit a single charged jet.…”

“…Consequently, the instabilities mentioned by Refs. [29][30][31] can be seen even when the droplet charge is way below its Rayleigh limit.…”

“…It is possible that not only is the applied electric field an important factor to consider in theses cases, as reported by [26,29,30], but so is the droplet's inertia. To better understand these different interactions we examined the stability of these droplets in the applied electric field, the coalescence phenomenon, and droplet mechanics.…”

“…Among these phenomena one can mention the work of Fuchs et al [19,20], who rediscovered Armstrong's [21] rope of water and published a series of papers about this "floating water bridge," the influences of EF on liquid-liquid coalescence [22][23][24][25][26][27], the work of Ristenpart et al [28], who has reported on the noncoalescence of oppositely charged droplets immersed in strong EF, and the deformation of droplets immersed in strong electric fields [29,30]. The last three examples are especially important for the good understanding of this paper; and therefore will be better explored in the following paragraphs.…”

“…Many authors investigated these effects both for charged and uncharged droplets [29][30][31]. Commonly referred to as Taylor cones [6], these structures result from a balance of charge-induced pressure from the applied EF and surface tension stresses resisting interfacial deformation [25].…”