Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers

Abstract

Numerical solutions have been obtained for steady streaming flow past an axisymmetric drop over a wide range of Reynolds numbers (0.005 [les ] Re [les ] 250), Weber numbers (0.005 [les ] We [les ] 14), viscosity ratios (0.001 [les ] λ [les ] 1000), and density ratios (0.001 [les ] ζ [les ] 1000). Our results indicate that at lower Reynolds numbers the shape of the drop tends toward a spherical cap with increasing We, but at higher Re the body becomes more disk shaped with increasing We. Unlike the recirculating wake behind an inviscid bubble or solid particle, the eddy behind a drop is detached from the interface. The size of the eddy and the separation distance from the drop depend on the four dimensionless parameters of the problem. The motion of the fluid inside the drop appears to control the behaviour of the external flow near the body, and even for cases when λ and ζ [Lt ] 1 (a ‘real’ bubble), a recirculating wake remains unattached.