Controlled movement of a shape deforming bubble

The potential for the controlled movement of a gas bubble in a liquid through parametrically induced, finite amplitude, axisymmetric shape deformation is considered. In particular, the parametric excitation of a single odd shape mode via the fundamental resonance mechanism is studied using a model that accounts for viscous, thermal, and compressible damping together with shape mode interactions to the third order. Under a single frequency time-dependent acoustic forcing, the finite amplitude, parametrically excited shape mode gives rise to small, oscillatory translation only as a consequence of nonlinear shape mode interactions. Instead, if a dual-frequency forcing is used and provided that a second shape mode is not excited parametrically, then for a number of combinations of the driving frequencies, the small amplitude oscillations are superimposed on a longer timescale, sustained linear motion. The source of the linear motion is attributed to how the frequency component not causing the parametric excitation modifies the volume mode and, in turn, the shape mode interactions. In such cases, the resultant speed of the bubble is dependent on both the driving strengths and the ratio of the driving frequencies. The results are confirmed by considering a range of driving frequencies and strengths.