Three-dimensional simulation of ligament formation and breakup caused by external vibration

Abstract

Ligament formation followed by breakup is the primary process that controls external vibration-driven liquid atomization. In this paper, single-mode Faraday instabilities with detailed interfacial dynamics are studied via three-dimensional simulations with a validated numerical methodology. The detailed mechanisms of ligament formation and its breakup are illuminated. Colliding flow from adjacent troughs results in a pressure increase at the root of the crest. This nonlinear flow structure produces a local maximum pressure point that liberates the liquid region above it from the bulk liquid layer that synchronously moves with the bottom substrate. The appearance of the maximum pressure point can thus be recognized as the indicator of ligament formation. The freed ligament with capillary waves on its surface continues to grow until successive breakup occurs at its tip, which is driven by the “short-wave mode” breakup mechanism. It is found that the tip contraction dynamics of Faraday-type ligament can be well described by a one-dimensional theoretical model of a low-speed liquid jet under temporally periodic acceleration. Finally, the development behaviors of Faraday-type ligament and liquid jet are compared quantitatively, which reveals the analogy in their breakup dynamics in the tip regions.