On the transport of droplets and bubbles through density transition layers

The transport of droplets or bubbles through density interfaces is a common phenomenon in nature. For instance, in the ocean, oil droplets from spills or rising air bubbles may encounter variations in the surrounding fluid's temperature. These temperature differences can significantly alter the density and viscosity of the ambient fluid, thereby affecting the transport dynamics and fateof the droplets or bubbles.In this work, we consider the rising motion of a droplet or bubble through a sharp density interface. The study considers varying the droplet/bubble Bond number (Bo), Galilei number (Ga)and the stratification strength of the ambient fluid, which is governed by the Froude number (Fr). The simulations are implemented viathree-dimensional DNS using a LevelContour Reconstruction Method (LCRM) -a hybrid level-set front-tracking method to accurately capture the motion and the interaction of the droplet or bubble with the sharp density interface. The Galilei numbers considered in this work are relatively moderate(Ga<100), and the density stratification is modeled using an error function formulation, ρ_f(z)=ρ₁+ 0.5(ρ₂−ρ₁)[(1−erf(z/H)], where z indicates the vertical position, H is the height of the density transition layer, and ρ₁ and ρ₂ are the undisturbed fluid densities above and below the stratification interface, respectively. This study begins by examining how density variations in the ambient fluid, caused by temperature differences, affect the transport of droplets or bubbles. The work then investigates the role of coupling the effects of variable fluid viscosity on their transportand deformation