Drop ejection from an oscillating rod

The dynamics of a liquid drop which is supported on a solid rod that is for ced to undergo large-amplitude, time-periodic oscillations along its axis i s studied using a computational approach based on the Galerkin/finite eleme nt method and an adaptive mesh generation technique which enables discretiz ation of overturning interfaces and analysis of drop breakup. When the forc ing amplitude is small, the drop deformations are small and the drop remain s intact as it undergoes shape oscillations. Larger forcing amplitudes resu lt in the formation of a liquid thread, or neck, which connects two fluid m asses: the fluid adjacent to the rod and a nearly globular fluid mass. If t he drop deforms such that its length is sufficiently large, the thread rupt ures and the globular fluid mass-a so-called primary drop-is ejected from t he fluid remaining on the rod. The critical forcing amplitude A(c) necessar y to attain this length and hence drop breakup, the interface shape at brea kup, and the volume of the ejected primary drop are determined computationa lly as functions of the Reynolds number, forcing frequency, and drop size. Over a wide range of values of the forcing amplitude above A(c) ejection oc curs as the drop recedes from its maximum length during its second period o f oscillation. These results show that Ac increases as Reynolds number and/ or drop size decreases. The maximum length the drop reaches prior to ejecti on and the position and velocity of the rod for times approaching breakup a re shown to profoundly affect the dynamics of drop breakup and the resultin g interface shapes. These results show that the forcing amplitude and/or fr equency can be chosen so as to prevent the formation of long liquid necks, which typically favor the formation of satellite droplets after breakup. Be cause drop ejection does not rely on external forces other than those due t o rod motion, this method of drop formation holds promise for microgravity applications as well as terrestrial drop-on-demand technologies in which gr avitational force is negligible compared to surface tension force. (C) 2001 Academic Press.