On the breakup of accelerating liquid drops

Abstract

An accelerating liquid drop, under the action of surface tension, is shown to be unstable to small disturbances above a first critical value of the Bond number. Both numerical and second-order asymptotic methods are employed in order to characterize the normal-mode response and the neutral-stable modes at larger values of the Bond number. The transient response of an initially spherical drop that is accelerated by the flow of an external gas is studied as an initial-value problem. A unified theory, that includes acceleration as well as aerodynamic effects, is presented in order to account for the complete dynamic range of Weber and Bond numbers. The results are compared with experimental observations that range from continuous vibration to irreversible aerodynamic distortion and unstable shattering.