Shapes and terminal velocities of a drop rising in stagnant liquids

The effects of the density ratio eta, the viscosity ratio lambda, the inverse viscosity number N-f, and the Eotvos 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 eta barely changes the drop shape and terminal velocity while keeping the other non-dimensional parameters fixed, whereas lambda, N-f and Eo significantly affect the drop dynamics. With the increase of lambda, N-f or 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 lambda or large Eo, and it becomes larger with the decrease of lambda and increase of Eo. In addition, the qualitative and quantitative relationships between Fr, the non-dimensional terminal velocity of the drop, and lambda, N-f and Eo are proposed based on the simulation results. (C) 2013 Elsevier Ltd. All rights reserved.