Growth of the Boundary Layer on a Spherical Gas Bubble

Abstract

The unsteady flow of a pure viscous liquid past a gas bubble starting impulsively from rest is investigated theoretically. The Reynolds number is considered to be large so that boundary-layer ideas are applicable, but the bubble is nevertheless so small that it remains nearly spherical under the action of surface tension. This theory describes the growth of boundary layer due to an initial discontinuity in tangential stress at the bubble surface; the results also show how the flow changes from the irrotational motion to the steady-state boundary-layer flow described by Moore. The drag coefficient of the bubble is evaluated from the energy dissipation in the liquid; it is initially finite—by contrast with the case of flow with a boundary layer at a rigid wall, for which it is initially infinite—and, at a given instant, of smaller order than that for a solid sphere.