The buoyancy-driven motion of a single skirted bubble or drop rising through a viscous liquid

The buoyancy-driven motion of a single skirted bubble or drop rising through a viscous liquid is computationally explored by way of 3d-axisymmetric computations. The Navier-Stokes equations for incompressible two-fluid flow are solved numerically in which the coupled level-set and volume-of-fluid method is used to simulate the deforming bubble/drop boundary and the interface jump conditions on the deforming boundary are enforced through a sharp interface numerical treatment. Dynamic, block structured adaptive grid refinement is employed in order to sufficiently resolve the thin skirts. Results on the sensitivity of the thickness of trailing bubble/drop skirts to the density ratio and viscosity ratio are reported. It is shown that both the density ratio (not the density difference) and the viscosity ratio effect the skirt thickness. Previous theory for predicting skirt thickness can be refined as a result of our calculations. It is also discovered that the formation of thin skirts for bubbles and drops have little effect on the rise velocity. In other words, the measured Re number for cases without skirt formation have almost the same values for Re as cases with a thin skirt.