Internal flow and deformation of a liquid CO$_{2}$ drop rising through water

We report computations of the steady axisymmetric flow in and around a deformable liquid drop of CO$_{2}$ ascending through a water column under the action of buoyancy, a problem relevant to risk assessment for sub-seabed carbon sequestration and storage. In these initial computations, we consider several drop densities, corresponding to different depths in the ocean, and neglect dissolution of CO$_{2}$ into the surrounding water and formation of a hydrate film at the drop/water interface. The results, which extend our previous work (Bozzi et al., \textit{J. Fluid Mech.}, \textbf{336}, 1-32, 1997) to the case in which the dynamic viscosities of the dispersed and continuous phases are unequal, show that the degree of deformation and internal circulation depend strongly on drop size.