The drag coefficient for a spherical bubble in a uniform streaming flow

Abstract

The drag coefficient C_D=48/R for a spherical bubble in a uniform streaming flow at high Reynolds number, which was first obtained via a dissipation method by Levich [Zh. Eksp. Teor. Fiz. 1 9, 18 (1949)], is rederived here by direct integration of the normal stress over the bubble surface. The present study also shows that the drag coefficient up to O(R⁻¹) depends only on the O(1) vorticity distribution right on the bubble surface, and is independent of the vorticity distribution in the fluid. Therefore the drag coefficient up to O(R⁻¹) is completely determined by the irrotational flow solution, which is perfectly consistent with the dissipation method.