Shape deformation of a gas bubble forced by a dual frequency time-dependent pressure field

The nonlinear volume oscillations and shape deformation of a gas bubble in water driven by a spatially uniform, time-dependent dual frequency acoustic source is considered. Employing a model that includes shape mode interactions to third order, the respective, distinct frequency values of the driving pressure are chosen in order to parametrically excite two different axisymmetric shape modes via the fundamental resonance. It is shown that the shape modes develop on different timescales with their relative growth rates controlling the resultant dynamics. For suitably chosen driving strengths, intermediate steady state shape oscillations are observed. In particular, for cases where the higher order shape mode grows fastest and subsequently saturates first, then steady state shape oscillations dominated by this mode are observed for a finite time. However, as the lower mode grows, the higher mode decays and if the lower mode saturates, the resultant steady state oscillations are dominated by the lower mode, indicating that this mode is a preferential oscillation state. For cases where the shape modes develop on similar timescales, the balance between the driving strengths results in either the lower mode growing unbounded or one of the shape modes suppressing the parametric growth of the other mode.