Three‐dimensional simulation of liquid drop dynamics within unsaturated vertical Hele‐Shaw cells

Abstract

A three‐dimensional, multiphase fluid flow model with volume of fluid‐interface tracking was developed and applied to study the multiphase dynamics of moving liquid drops of different sizes within vertical Hele‐Shaw cells. The simulated moving velocities are significantly different from those obtained from a first‐order analytical approximation, based on simple force‐balance concepts. The simulation results also indicate that the moving drops can exhibit a variety of shapes and that the transition among these different shapes is largely determined by the moving velocities. More important, there is a transition from a linear moving regime at small capillary numbers, in which the capillary number scales linearly with the Bond number, to a nonlinear moving regime at large capillary numbers, in which the moving drop releases a train of droplets from its trailing edge. The train of droplets forms a variety of patterns at different moving velocities.