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

TL;DR

This study investigates the pressure thresholds for subharmonic emissions in ultrasonically excited bubbles, revealing that thermal effects and bubble size influence the optimal frequency for subharmonic generation, especially around 0.5 to 0.6 times the resonance frequency.

Contribution

It introduces a detailed analysis of thermal damping effects on subharmonic emissions, showing that optimal frequencies vary with gas type and bubble size, extending previous models.

Findings

Threshold for subharmonic emissions can be below resonance frequency due to thermal effects.

Generation of subharmonics linked to ultra-harmonic resonance in a specific frequency range.

Bubbles larger than 1 micron can emit non-destructive subharmonics in these conditions.

Abstract

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 are size dependent. For an air bubble immersed in water, only bubbles bigger than 1 microns in diameter are able to emit non-destructive SHs in these frequency ranges.