The vibration of electrified water drops

Abstract

Pressure has been used as the principal parameter in calculations of the fundamental vibrational frequencies of spherical drops of radius R , density ρ, and surface tension T carrying a charge Q or uncharged spheroidal drops of axial ratio a / b situated in a uniform electric field of strength E . Freely vibrating charged drops have a frequency f = f 0 ( 1 - Q 2 /16π R 3 T ) ½ , as shown previously by Rayleigh (1882) using energy considerations; f 0 is the vibrational frequency of non-electrified drops (Rayleigh 1879). The fundamental frequency of an uncharged drop in an electric field will decrease with increasing field strength and deformation a / b and will equal zero when E ( R )/ T ) ½ = 1.625 and a / b = 1.86; these critical values correspond to the disintegration conditions derived by Taylor (1964). An interferometric technique involving a laser confirmed the accuracy of the calculations concerned with charged drops. The vibration of water drops of radius around 2 mm was studied over a wide range of temperatures as they fell through electric fields either by suspending them in a vertical wind tunnel or allowing them to fall between a pair of vertical electrodes. Photographic analysis of the vibrations revealed good agreement between theory and experiment over the entire range of conditions studied even though the larger drops were not accurately spheroidal and the amplitude of the vibrations was large.