Numerical simulations of bubble oscillations in liquid water irradiated by an ultrasonic wave are performed under the experimental condition for single-bubble sonochemistry reported by Didenko and Suslick [Nature (London) 418, 394 (2002)]. The calculated number of OH radicals dissolving into the surrounding liquid from the interior of the bubble agrees sufficiently with the experimental data. OH radicals created inside a bubble at the end of the bubble collapse gradually dissolve into the surrounding liquid during the contraction phase of an ultrasonic wave although about 30% of the total amount of OH radicals that dissolve into the liquid in one acoustic cycle dissolve in 0.1 micros at around the end of the collapse. The calculated results have indicated that the oxidant produced by a bubble is not only OH radical but also O atom and H2O2. It is suggested that an appreciable amount of O atom is produced by bubbles inside a standing-wave-type sonochemical reactor filled with water in which oxygen is dissolved as in the case of air.

Numerical simulations of nonequilibrium chemical reactions inside an air bubble in liquid water irradiated by ultrasound have been performed for various ambient bubble radii. The intensity of sonoluminescence (SL) has also been calculated taking into account electron-atom bremsstrahlung, radiative attachment of electrons to neutral molecules, radiative recombination of electrons and ions, chemiluminescence of OH, molecular emission from nitrogen, etc. The lower bound of ambient radius for an active bubble in SL and sonochemical reactions nearly coincides with the Blake threshold for transient cavitation. The upper bound is in the same order of magnitude as that of the linear resonance radius. In actual experiments, however, the distribution of ambient radius for active bubbles may be narrow at around the threshold ambient radius for the shape instability. The threshold peak temperature inside an air bubble for nitrogen burning is higher than that for oxidant formation. The threshold peak temperatures depend on ultrasonic frequency and acoustic amplitude because chemical reactions inside a bubble are in nonequilibrium. The dominant emission mechanism in SL is electron-atom bremsstrahlung except at a lower bubble temperature than 2000 K, for which molecular emissions may be dominant.

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Numerical simulations of bubble pulsations have been performed for a system of two bubble clouds in order to study the experimentally observed bubble motion under an ultrasonic horn by high-speed video camera. The comparison between the calculated results and the experimental observation of the bubble pulsation has indicated that the bubble pulsation is strongly influenced by the interaction with surrounding bubbles. The expansion of a bubble during the rarefaction phase of ultrasound is strongly reduced by the bubble-bubble interaction. Some bubbles move toward the horn tip due to the secondary Bjerknes force acting from the bubbles near the horn tip. It has also been shown that the acoustic amplitude in the liquid is strongly reduced by cavitation due to the decrease in acoustic radiation resistance.

The mechanism of the effect of particle addition on sonochemical reaction is studied through the measurements of frequency spectrum of sound intensity for evaluating the cavitation noise and the absorbance for the liberation of iodine from an aqueous solution of KI as an index of oxidation reaction by ultrasonic irradiation in the presence or absence of alumina particles. As it is expected that both the acoustic noise and a rise in temperature in the liquid irradiated by intense ultrasound will increase with the number of collapsing bubbles, these are supposed to be the best tools for evaluating the relative number of bubbles. In the present investigation, it has been shown that the addition of particles with appropriate amount and size results in an increase in the absorbance when both the acoustic noise and the rise in the liquid temperature due to cavitation bubbles also increase. This suggests that the enhancement in the yield of sonochemical reaction by appropriate particle addition comes from an increase in the number of cavitation bubbles. The existence of particle in liquid provides a nucleation site for cavitation bubble due to its surface roughness, leading to the decrease in the cavitation threshold responsible for the increase in the number of bubbles when the liquid is irradiated by ultrasound. Thus, from the present investigation, it is clarified that the particle addition has a potential to enhance the yield in the sonochemical reaction.

There are two main mysteries in bulk nanobubbles which are cavitation nuclei. One is the mechanism of stability of a bulk nanobubble. The other is the problem whether OH radicals are produced from bulk nanobubbles without a dynamic stimulus. For the former problem, several proposed models are briefly reviewed. The dynamic equilibrium model is discussed in details that a bulk nanobubble is stabilized by a partial coverage of the bubble surface by a hydrophobic material. The TEM images of bulk nanobubbles seem to support the dynamic equilibrium model. For the latter problem, numerical simulations of dissolution of an air nanobubble are reviewed, which suggest that no OH radical is produced from a dissolving nanobubble. A possible role of HO generated during bulk nanobubble production using hydrodynamic cavitation is briefly discussed in relation to the experimental results of "OH radical" detection.

The dynamic equilibrium model for a bulk nanobubble partly covered with hydrophobic material in water is theoretically and numerically studied. The gas diffusion into a bubble near the peripheral edge of the hydrophobic material on the bubble surface balances that out of the bubble from the other part of the uncovered bubble surface. In the present model, gas diffusion in quiescent liquid is assumed and there is no liquid flow. The total changes of energy and entropy are both zero as it is a kind of equilibrium state. The main origin of the dynamic equilibrium state is the gradient of chemical potential of gas near the peripheral edge of the hydrophobic material. It is caused by the permanent attractive potential of a hydrophobic material to gas molecules dissolved in liquid water as there is permanent repulsion of a hydrophobic material against liquid water. Thus, the gas supply will not terminate. It is numerically shown that stable nanobubble could be present when the fraction of surface coverage by hydrophobic material is from about 0.5 to 1. The stable size of a nanobubble changes with the liquid temperature as well as the degree of gas saturation of water. In slightly degassed water, not only a nanobubble but also a microbubble could be stable in mass balance when the fraction of surface coverage for a microbubble is on the order of 10 or less. For hydrophilic materials, however, a bubble could not be stable unless the fraction of the surface coverage is exactly 1. It is suggested that in many experiments of bulk nanobubbles there could be aggregates of nanobubbles.

Numerical simulations of nonequilibrium chemical reactions in a pulsating air bubble have been performed for various ultrasonic frequencies (20 kHz, 100 kHz, 300 kHz, and 1 MHz) and pressure amplitudes (up to 10 bars). The results of the numerical simulations have indicated that the main oxidant is OH radical inside a nearly vaporous or vaporous bubble which is defined as a bubble with higher molar fraction of water vapor than 0.5 at the end of the bubble collapse. Inside a gaseous bubble which is defined as a bubble with much lower vapor fraction than 0.5, the main oxidant is H2O2 when the bubble temperature at the end of the bubble collapse is in the range of 4000-6500 K and O atom when it is above 6500 K. From the interior of a gaseous bubble, an appreciable amount of OH radical also dissolves into the liquid. When the bubble temperature at the end of the bubble collapse is higher than 7000 K, oxidants are strongly consumed inside a bubble by oxidizing nitrogen and the main chemical products inside a bubble are HNO2, NO, and HNO3.