An investigation of the behaviour of drops and drop-pairs subjected to strong electrical forces

A numerical model is described which simulates irrotational, incompressible flow on a computer. It has been applied to the problems of the deformation of uncharged drop-pairs separated in an electric field of critical strength and isolated drops charged to the Rayleigh limit in the absence of an electric field. In the case of pairs of drops of radius R, separated by an initial distance X in an electric field equal to that predicted by Brazier-Smith (1971) to cause disruption two types of interaction were identified. For values of X/R less than about 1.2 the drops deform and their surfaces accelerate towards each other and make contact. For X/R greater than about 1.2 the drops deform, a concavity appears at the near poles and then the near surfaces assume a conical profile of angle equal to that predicted by Taylor (1964). The subsequent issuance of liquid from these jets could not be studied with the present model. The computations predict that an isolated drop carrying the critical charge calculated by Rayleigh (1882) will deform, while retaining an approximately spheroidal shape, until the axial ratio achieves a value of about 2.5, whereupon cones possessing the Taylor angle are formed at each end of the drop, from which liquid will issue in the form of a jet. Experiments were performed in which uncharged water drops of radius R and surface tension T were directed towards a highly polished, earthed electrode at a shallow angle in an electric field of strength E. Each drop experienced the same electric forces as would result if the earthed electrode were removed and replaced by an identical drop twice as far away. Stroboscopic photographs of drops and their optical image in the polished electrode illustrated their deformation and eventual disintegration. The experimentally determined relation between normalized disintegration field $E(R/T)^{\frac{1}{4}}$ and both X/R and the elongation a/b agreed well with theory over a wide range of separations.