Effect of viscosity and density ratios on two drops rising side by side

We study the dynamics of a pair of initially spherical drops rising side by side in a surrounding, denser, fluid. Our primary focus is on liquid-liquid systems, and a range of viscosity and density ratios is explored by three-dimensional numerical simulations. Interesting dynamics are reported, which cannot be extrapolated from previously known dynamics of gas-liquid systems. Similar to two air bubbles though, we find that two liquid drops move away from each other as they rise, in cases where a single drop would rise vertically. A pair of light drops always remains in two-dimensional motion, and higher drop viscosity increases the tendency of wobbling. This is in contrast with the dynamics of a single drop that follows a highly three-dimensional trajectory at very low drop viscosity, but is restricted to two-dimensional motion at higher drop viscosity. On the other hand, a pair of heavier drops displays three-dimensional behavior at low drop viscosity and two-dimensional behavior at high viscosity. We find that a pair of drops is far less sensitive to viscosity contrast than a single drop is, in our parameter range. In contrast to gas-liquid systems, where the shape change of the bubble was tied to nonlinear dynamics of the trajectory, we find in liquid-liquid systems that interesting drop trajectories can occur without corresponding large shape changes. It is found that the separation distance between the drops exhibits a nonmonotonic trend with an increase in the density ratio. The physical reason for this nonmonotonic trend is simple and explained by inspecting the velocity components