Effect of viscosity and density ratios on two bubbles rising side-by-side

We study the dynamics of a pair of initially spherical `bubbles' of fluid rising side-by-side in a surrounding, denser, fluid. 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 bubbles move away from each other as they rise, in cases where a single bubble would rise vertically. A pair of light bubbles always remains in two-dimensional motion, and higher bubble viscosity increases the tendency of wobbling. This is in contrast with the dynamics of a single bubble that follows a highly three-dimensional trajectory at very low bubble viscosity, but is restricted to two dimensional motion at higher bubble viscosity. On the other hand, a pair of heavier bubbles displays three-dimensional behaviour at low bubble viscosity and two dimensional behaviour at high viscosity. We find that a pair of bubbles is far less sensitive to viscosity contrast than a single bubble is, in our parameter range. In contrast to gas-liquid systems, where shape change of the bubble was tied to nonlinear dynamics of the trajectory, we find in liquid-liquid systems that interesting bubble trajectories can occur without corresponding large shape changes.