Circulation in Liquid Drops

A number of aspects of the motion of drops through liquids are discussed with a view to clarifying the physical picture of the mechanism by which the liquid/liquid interface influences the transfer of momentum and mass across it. Internal motion and distortion are shown to affect drag characteristics at relatively high Reynolds numbers (100 to 1000). The Hadamard and Hill vortex models are compared. The internal velocity distribution in a spherical drop is shown to agree with both models but external motion in the Stokesian region is only predicted by the former. At higher Reynolds numbers where a potential flow regime prevails, the external motion is more closely described by Hill’s model. Vortices do not form in a drop until the Reynolds number reaches a critical value depending on the state of the interface and the viscosity of the drop liquid. Bond & Newton (1928) predicted that interfacial tension was the only variable affecting the transition but additional effects due to impurities and to the polarities of the component liquid molecules are also important, not only regarding the onset of vortex formation but also in relation to the extensiveness of circulation when under way. The presence of impurities such as very small concentrations of surface-active agents, although lowering the interfacial tension, greatly reduces the velocity of circulation in the vortex.