Translation and shape deformation of a microbubble driven by an acoustic traveling wave

The forcing of a micron sized gas bubble by an acoustic traveling wave in water is considered using a model which includes axisymmetric shape mode interactions to third order. In all cases, the resultant bubble motion is predicted to consist of small scale periodic oscillations superimposed upon a longer timescale, monotonically changing profile. For driving amplitudes below those necessary to cause parametrically induced instabilities to grow on the surface of the bubble, the long timescale bubble speed increases as the amplitude of the forcing increases but the resultant bubble motion induces markedly small scale deformation of the bubble surface which is dominated by the ellipsoidal mode. For cases where parametric instabilities grow but the driving pressure is not sufficient to cause bubble splitting or fragmentation, saturation due to nonlinear shape mode interactions occurs resulting in observable, sustained, finite amplitude shape deformation dominated by the parametrically excited mode. The induced shape deformation is found in turn to modify the bubble motion. In particular the speed of the long timescale monotonic translation is reduced to a new constant value and for sufficiently large forcing, this motion is found to reverse.