Dynamics of the Disintegration of a Drop by Electrical Forces

Abstract

TECHNIQUES have recently been developed for modelling the dynamics of the flow of incompressible fluids using a high-speed computer^1,2. The dynamical equations were solved by representing the fluid by a series of marker particles moving in a cartesian mesh, and assuming that each particle experiences a linear acceleration during a selected short interval of time. By computing the new positions and velocities of the marker particles at the end of successive time intervals, accurate calculations can be made of the motion of the fluid throughout the period of interest. This marker-and-cell technique has been applied to a study of the instability of an uncharged liquid drop of radius R and surface tension T situated in an electric field strength E. This problem, which is important in certain situations in cloud physics³, has previously been treated analytically⁴ by assuming that the drop retains a spheroidal shape throughout the period of deformation until the instability point is attained. The calculated instability criteria, namely, the E(R/T)^&12frac; = 1.625 when the ratio of the semi-major to semi-minor axes a/b = 1.9, agree well with experimental measurements. The present numerical calculations permit a quantitative assessment to be made of the validity of the spheroidal assumption and, of greater importance, provide a description of the dynamics of the disintegration of a drop subjected to intense electrical forces. In order to save computer time the initial condition was assumed to be that a spheroidal drop of undistorted radius 0.2 cm and surface tension 70 dynes cm⁻¹, possessing a degree of deformation represented by a/b =1.9, was introduced into a field of strength E=9,500 V cm⁻¹, which is 4 per cent greater than the critical value deduced on the basis of the spheroidal assumption.