Shapes and terminal velocities of a drop rising in stagnant liquids

The effects of the density ratio η, the viscosity ratio λ, the inverse viscosity number Nf, and the Eötvös number Eo on the shapes and terminal velocities of a drop rising in stagnant liquids are studied numerically using a front tracking method. It is found that mild variation of η barely changes the drop shape and terminal velocity while keeping the other non-dimensional parameters fixed, whereas λ, Nfand Eo significantly affect the drop dynamics. With the increase of λ, Nfor Eo, the drop becomes either more dimpled or more crescent. The flow details inside and around the drop are also investigated. A recirculation zone is observed for small λ or large Eo, and it becomes larger with the decrease of λ and increase of Eo. In addition, the qualitative and quantitative relationships between Fr, the non-dimensional terminal velocity of the drop, and λ, Nfand Eo are proposed based on the simulation results.