On the rising motion of a drop in stratified fluids

Abstract

The rising dynamics of a deformable drop in a linearly stratified fluid is numerically obtained using a finite-volume/front-tracking method. Our results show that the drag coefficient of a spherical drop in a stratified fluid enhances as \documentclass[12pt]{minimal}\begin{document}$C_{d,s}/C_{d,h}-1\sim Fr_d^{-2.86}$\end{document}Cd,s/Cd,h−1∼Frd−2.86 for drop Froude numbers in the range of 4 < Frd < 16. The role of the deformability of the drop on the temporal evolution of the motion is investigated along with stratification and inertial effects. We also present the important role of stratification on the transient rising motion of the drop. It is shown that a drop can levitate in the presence of a vertical density gradient. The drop undergoes a fading oscillatory motion around its neutrally buoyant position except for high viscosity ratio drops where the oscillation occurs around a density level lighter than the neutral buoyancy level. In addition, a detailed characterization of the flow signature of a rising drop in a linearly stratified fluid including the buoyancy induced vortices and the resultant buoyant jet is presented.