Dependence on Amplitudes

The positional stability lines of a bubble in a bimodal driving field depends on the amplitude of the second added frequency. FIGs. 3 show the results of the sum of forces on a $4\mu m$ bubble and the stability lines at different pressures. While the amplitude of the first harmonic is fixed at $1.4bars$ the pressure of the second harmonic is varied in 4 steps from $0.07$ to $0.7bars$. The large oscillations of the stable bubble position as a function of the temporal phase is seen. Their amplitudes increase with increasing second harmonic driving pressure. At $0.35bars$ pressure the zero-force lines surround small islands in the force landscape. Also lines showing spatially unstable bubble behaviour are seen. The complexity increases at $0.7bars$ where multiple coexisting stability lines are present with unstable connections. A bubble can oscillate stably along the stability lines marked by filled symbols and would sometimes jump by a discrete amount if the temporal phase is changed. FIG. 4 shows results for a bubble of $4.25\mu m$ ambient radius. Different collapse radii as a function of position and phase difference are shown together with the stability lines. It is seen that the collapse radius changes along the stability lines. Bjerknes and and buoyancy force keep the bubble away from regions with a very high energetic collapse.

In the multiple stability regime the different bubble positions are associated with vastly different dynamics. While at some points the bubble hardly oscillates others show enormous compression rations needed for sonoluminescence. Also shown are parametrically (surface) unstable bubbles [18]. Bubbles driven at these phases/positions will show a dancing behaviour with less radial compression.