We model the collapse of a bubble by taking into account all the energy forms involved (i.e., mechanical, thermal, chemical, and radiative) and compare the calculated radical yields with sonochemical data in H_2O. Water decomposition plays a critical role in the energy balance, but trails equilibrium even in bubbles collapsing at subsonic speeds. Integration of the equation of bubble motion coupled with a full chemical mechanism reveals that (1) terminal gas temperatures and Mach numbers M_L increase in cooler water, (2) Γ_(OH), the number of OH-radicals produced per unit applied work at maximum M_L-when bubbles become unstable and disperse into the liquid-decreases at small and very large sound intensities. We show that available data on the sonochemical decomposition of volatile solutes-such as CCl_4, which is pyrolyzed within collapsing bubbles-are compatible with the efficient conversion of ultrasonic energy into transient cavitation. On this basis we calculate Γ_(OH) = (1 ± 0.5) * 10~(17) molecules/J for R_0 = 2 μm bubbles optimally sonicated at 300 kHz and 2.3 W/cm~2 by assuming mass and energy accommodation coefficients of α ≤ 7 * 10~(-3) and ∈ ≤ 0.04, respectively, in gas-liquid collisions, and values about 3-fold smaller after averaging over the nuclei size distribution. Since there is negligible radical recombination during dispersal, these Γ_(OH) values represent available oxidant yields, that agree with experimental data on iodide sonochemical oxidation. Bubbles emit little radiation, suggesting that only radial shock waves may heat small regions to the 10~4-10~5 K range required by some sonoluminescence experiments. The contribution of this sonoluminescent core to sonochemical action is, however, insignificant. We show that much larger accommodation coefficients would lead to higher temperatures, but also to O atoms rather than OH radicals and ultimately to excess O_2, at variance with experimental evidence.
展开▼
