On the threshold of 1/2 order subharmonic emissions in the oscillations of ultrasonically excited bubbles

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 pressure. Here we show that, and depending on the gas, the pressure threshold for 1/2 order SHs can be minimum at a frequency between 0.5fr≤f≤0.6fr. 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 is size dependent. For an air bubble immersed in water, only bubbles bigger than 1 μm in diameter are able to emit non-destructive SHs in these frequency ranges. •Nonlinear behavior of bubbles is studied accounting for thermal dissipation.•Thermal damping may have a significant effect on the pressure threshold of 1/2 order subharmonics•The minimum pressure threshold for the onset of subharmonics may not be at resonance (fr) or 2fr.•Minimum pressure threshold of the onset of subharmonics may be at 0.5fr≤f≤0.6fr.