The Pressure Threshold of the 1/2 Order Subharmonic Emissions in the Oscillations of Ultrasonically Excited Uncoated Air Bubbles Is Not at Twice the Resonance Nor It Is It at the Resonance Frequency

The pressure threshold for 1/2 order subharmonic (SH) emissions and period doubling during the oscillations of ultrasonically excited bubbles is thought to be minimum when the bubble is sonicated with twice its resonance frequency ( fr). This estimate is based on studies that simplified or neglected the effects of thermal damping. In this work, the nonlinear dynamics of ultrasonically excited bubbles is investigated accounting for the thermal dissipation. Results are visualized using bifurcation diagrams as a function of excitation pressure. Here we show that contrary to the common belief, for an uncoated Air bubble, the pressure threshold for 1/2 order SHs is minimum at a frequency between .5 f_{r}\leq f\leq 0.6f_{r}$. In this frequency range, the generation of 1/2 order SHs are due to the occurrence of 5/2 order ultra-harmonic resonance. The stability of such oscillations are size dependent. For an air bubble immersed in water, only bubbles bigger than 1 μm in diameter are able to emit nondestructive SHs in these frequency ranges.