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The pressure threshold for 1/2 order subharmonic (SH) emissions and perioddoubling during the oscillations of ultrasonically excited bubbles is thoughtto be minimum when the bubble is sonicated with twice its resonance frequency(fr). This estimate is based on studies that simplified or neglected theeffects of thermal damping. In this work, the nonlinear dynamics ofultrasonically excited bubbles is investigated accounting for the thermaldissipation. Results are visualized using bifurcation diagrams as a function ofpressure. Here we show that, and depending on the gas, the pressure thresholdfor 1/2 order SHs can be minimum at a frequency between 0.5fr<f<0.6fr. In thisfrequency range, the generation of 1/2 order SHs are due to the occurrence of5/2 order ultra-harmonic resonance. The stability of such oscillations are sizedependent. For an air bubble immersed in water, only bubbles bigger than 1microns in diameter are able to emit non-destructive SHs in these frequencyranges.

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