Growth by rectified diffusion of strongly acoustically forced gas bubbles in nearly saturated liquids.

The growth or dissolution of small gas bubbles (R0<15 microm) by rectified diffusion in nearly saturated liquids, subject to low frequencies (20 kHz<f<100 kHz) and high driving acoustic fields (1 bar<p<5 bars), is investigated theoretically. It is shown that, in such conditions, the rectified diffusion threshold radius merges with the Blake threshold radius, which means that a growing bubble is also an inertially oscillating bubble. On the assumption that such a bubble keeps its integrity up to the shape instability threshold predicted by single-bubble theory, a numerical estimation and a fully analytical approximation of its growth rate are derived. On the one hand, the merging of the two thresholds raises the problem of the construction and self-sustainment of acoustic cavitation fields. On the other hand, the lifetime of the growing inertial bubbles calculated within the present theory is found to be much shorter than the time necessary to rectify argon. This allows an alternative interpretation of the absence of single-bubble sonoluminescence emission in multibubble fields, without resorting to the conventional picture of shape instabilities caused by the presence of other bubbles.