A Liquid drop Falling in Another Fluid: A Two-Phase Flow Phenomenon

Abstract

Liquid drops exist everywhere in daily life. However, such a common phenomenon involves complex mechanisms, and therefore has never been investigated thoroughly—the achievements of the studies are limited and unsatisfactory. In this article, the phenomenon of a liquid drop falling in another immiscible fluid (mostly its settling speed) was investigated. A series of experiments, in which liquid drops emerging from a syringe falls inside a measuring cylinder filled another fluid, was performed. Fluids used in the experiment include ethanol solutions and rice bran oil; for rice bran oil, its temperature-dependent viscosity was approximated by a function, which was proved effective on other similar oils. The dependence of the settling speed of the liquid drop on the density difference between the liquid drop and the surrounding fluid, as well as on the temperature of the surrounding fluid, was measured. Finite-Element Modeling (FEM) simulations were then carried out to model these situations, and lead to results that agreed with the experiments. It also visualized the flow field and revealed more details of the two-phase flow that were not detectable by our devices. Furthermore, inspired by some previous formulae, quantitative equations were derived semi-analytically by modifying an approximate drag formula originally developed for a rigid object at moderate Reynolds numbers. The form of the modification was never introduced in any other previous works. The equations were validated by simulations under ideal conditions.