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

Abstract

The growth or dissolution of small gas bubbles (R0 < 15 μm) by rectified diffusion in nearly satu- rated liquids, subject to low frequencies (20 kHz < f < 100 kHz), high driving acoustic fields (1 bar < p < 5 bar) 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. From one hand, the merging of the two thresholds raises the problem of the construction and self-sustainment of acoustic cavitation fields. From the other hand, the lifetime of the growing inertial bubbles calculated within the present the- ory 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 (SBSL) emission in multi-bubble fields, without resorting to the conventional picture of shape instabilities caused by the presence of other bubbles.