Boundary layer development in the case of a spherical gas bubble

An analysis is made for a gas bubble starting impulsively from rest with a constant velocity in a quiescent liquid of infinite extent. The Reynolds nu mber is considered to be large so that boundary-layer ideas are applicable; but the bubble is nevertheless so small that it re-retains nearly spherica l under the action of surface tension. Simultaneous solutions of the unstea dy boundary layer equations for both the outside and inside flows of the bu bble are obtained by considering that tangential velocity components and sh ear stresses on both sides of the interface are equal. Satisfactory results are obtained for spherical air bubbles in water as well as in some organic liquids. The theoretical results are applicable at early times to any flui d sphere started impulsively in a substantially immiscible, viscous liquid provided that the flow separation is negligible and the Reynolds number is sufficiently large.