Shape stability of unsteadily translating bubbles

In this paper the problem of shape stability is considered, for a bubble with time-dependent radius, translating unsteadily in a flow. This situation can be brought about, for example, by forcing with an acoustic traveling wave. The equation governing translation was derived in a previous work [Reddy and Szeri (unpublished)]. Here, the equations governing the amplitudes of shape modes are derived using domain perturbation theory, following a classical paper by Plesset. Contrary perhaps to intuition, results show that driving at the natural frequency of volume oscillations is not necessarily the ideal forcing to engender a shape instability. Moreover, severe radial oscillations can have a stabilizing effect on shape oscillations. The results suggest the possibility of destroying bubbles selectively by size.