Disintegration of Pairs of Drops Raised to Equal and Opposite Potentials

Abstract

In order to assess quantitatively the role of drop disintegrations in producing the electrification of warm clouds, it is necessary to establish the electrohydrodynamical equations governing the stability of drops subjected to electrical forces. In the present paper a theoretical and experimental study is presented of the disintegration of drops raised to equal and opposite potentials. In his theoretical treatment of the deformation and disintegration of individual water drops of undistorted radius R0 raised to a potential V, Taylor assumed that the drop retained a spheroidal shape until the instability point was reached and that the equations of equilibrium between the stresses due to surface tension T, the potential V, and the difference between the external and internal pressures was satisfied at the poles and the equator. He showed that since there is no stationary value for V as the elongation a/b increases, the only stable condition is when the drop is stable and V(πR0T)?½ < 4. Taylor's spheroidal assumption has been applied to the problem of the deformation and disintegration of pairs of drops raised to equal and opposite potentials. In this case directionality is imposed upon the problem by the attractive forces between the drops which provide a contribution, increasing with decreasing separation, to the outwardly-directed stresses in their surfaces. Stationary values of V were found to exist at values of a/b > 1, and the corresponding values of V(πR0T)?½ were less than 4.0 by a factor which increased rapidly as the initial separation was decreased. These critical values of V(πR0T)?½ at the disintegration point ranged from Rayleigh's value of 4.0 at infinite separations to 3.117, 6.842 ? 10?1, 2.880 ? 10?2 and 8.654 ? 10?4 for initial separations of 10, 1, 0.1 and 0.01 radii, respectively. These values of V(πR0T)?½ are slightly reduced for larger drops owing to the influence of the hydrostatic pressure difference between their vertical extremities. These calculations were tested experimentally on suspended drops of water, aniline and benzene, and good agreement was obtained in all cases. High speed photographs indicated that the process of disintegration was similar to that observed by Taylor, with an extremely rapid transformation (<10?8 sec) from an approximately spheroidal shape to a conical profile. Measurements taken from the photographs demonstrated that the radius of curvature and the elongation of a drop at the moment of disintegration agreed quite closely with the predicted values.