Chemical Bubble Dynamics and Quantitative Sonochemistry

Abstract

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 H2O. 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) ΓOH, 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 CCl4, which is pyrolyzed within collapsing bubblesare compatible with the efficient conversion of ultrasonic energy into transient cavitation. On this basis we calculate ΓOH = (1 ± 0.5) × 1017 molecules/J for R 0 = 2 μm bubbles optimally sonicated at 300 kHz and 2.3 W/cm2 by assuming mass and energy accommodation coefficients of α ≤ 7 × 10-3 and ε ≤ 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 ΓOH 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 104−105 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 O2, at variance with experimental evidence.

Single-bubble sonoluminescence

“…Models with unrealistically low accommodation coefficients a ϳ0.001, like that of Colussi et al (1998), on the other hand, could well be condensation limited.…”

Liquid compressibility effects during the collapse of a single cavitating bubble

“…At the interface [r ¼ R(t)], mass transfer is neglected, limiting the strict model applicability to forcing pressure wave frequencies above 100 kHz, where RP models have shown that the bubble dynamics is unaffected by evaporation/condensation. [26][27][28][29] Viscous stresses and radiation heat transfer are also neglected. Continuity, momentum, and energy transport equations applied to an infinitesimal shell about the interface yield the following relations, coupling bubble and liquid variables,…”

A reduced model of cavitation physics for use in sonochemistry

“…We assume that in sonochemistry applications, the cavitation is transient and the bubble breaks apart at the collapse, dispersing the chemical contents into the liquid (S&S; Colussi et al 1998). Therefore, we are only interested in the rst expansion and violent collapse, a typical example is shown in gure 1.…”