An Energy Descriptor Unifying Acoustic and Physicochemical Effects on Radical Yields in Ultrasonic Cavitation

In water, ultrasound irradiation heats and pressurizes gaseous microbubbles resulting in spontaneous homolysis of H2O vapors to free radicals (e.g., •OH). Efficiently generating and utilizing these radicals requires a quantitative link between the energy used to power ultrasound waves and radical formation. This study establishes that link by quantifying the energy supplied to the bubble through compressive work, and the resulting distribution of that energy as internal energy. Work and internal energy changes are determined by simulating ultrasound-induced bubble expansion and compression. The amount of H2O vapor consumed and the total yield to radical products both increase linearly with the total internal energy change associated with chemical reactions, termed as the reaction energy. This linear trend persists across wide ranges of wave frequency (200-1100 kHz), wave pressure amplitude (1-10 bar), surface tension (20-72 mN m-1), and liquid density (700-1200 kg m-3). This reaction energy offers a unifying descriptor for the effects of wave and liquid properties—which govern bubble dynamics—on yields to useful radical initiators. Furthermore, a fractional decrease in liquid density or surface tension are found to produce a fractional increase in radical yield that is up to an order of magnitude larger, suggesting that substrates that lower these solution properties promote their own reactions in ultrasound reactors.