Assessment of Numerical Techniques for Micro-Drop Fluid Mechanics

Abstract

Are currently available CFD techniques able to model the motion of a submilimiter-scale liquid drop falling in another (quiescent) liquid? In this work we define a very simple two-dimensional test: An initially circular drop of water of diameter 0.1 mm is placed at the center of a square box (size 0.6 mm) filled with oil (relative density 0.8). The goal is to compute the fall of the drop towards the bottom of the box, which would take several seconds based on typical terminal velocities found in the problem. It seems easy, doesn’t it? We have tested several CFD techniques on this problem: FOAM (two available VOF-based methods within FOAM’s platform), GERRIS (free software from Popinet’s group), level-set finite elements (interface capturing) and finally ALE finite elements (interface tracking). The aim is to illustrate on the serious limitations this methodologies have to accurately and efficiently track the dropet’s trajectory.