Shapes and terminal velocity of a drop rising in stagnant liquids - Liu, Lili. (2012)
In this project, the effects of the density ratio ?, the viscosity ratio ?, the inverse viscosity number ? ?, 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 ? barely changes the drop shape or terminal velocity, whereas ?, ? ? and Eo significantly affect the drop dynamics. With the increase of ?, ? ?, or Eo, the drop becomes either more dimpled or more crescent. When the drop is dimpled or ellipsoidal-cap, there is no recirculation flow in its rear. The recirculation zone appears and becomes larger when ? decreases or Eo increases. From the simulation results, the relationships between Fr, the non-dimensional terminal velocity of the drop, and ?, ? ? and Eo are determined. For the correlation between Fr and ?, it is found that Fr= ?(1+ ?1 ?)/(2+ ?2 ?) for 5< ? ?<38, where ?1 = 1.245±0.165, and ?2 = 3.43±0.35, whereas Fr is a constant around 0.602 for 50< ? ?<100. The correlation between Fr and ? ? follows a logarithmic trend for ? ?<50. And Fr is also found to decrease with the increase of Eo.