An interpretation of the translation of drops and bubbles at high Reynolds numbers in terms of the vorticity field

The steady translation of a drop is reconsidered in the high Reynolds number flow limit, ℛ ≫ 1. The standard approach for determining the drag on a spherical drop is to calculate the total energy dissipation in the fluid with the velocity field approximated using the potential flow solution outside the drop and Hill's spherical vortex inside. Kang and Leal [Phys. Fluids 31, 233 (1988)] provide the first calculation of the drag for a spherical bubble by integrating the normal stresses over the bubble surface. Their detailed calculation shows that the drag coefficient up to O(ℛ^-1) depends only on the O(1) vorticity distribution along the bubble surface and is independent of the vorticity distribution in the fluid. Here, this conclusion regarding the role of vorticity js extended to the case of any steady high Reynolds number bubble shape compatible with the steady trarislational speed; there is no restriction to sphericity. The results are demonstrated without explicit calculations and follow from the representation of the energy dissipation for translating drops in terms of the vorticity field.