The role of surface tension on the growth of bubbles by rectified diffusion

Rectified diffusion has wide and important applications in sonochemistry, ultrasonic cleaning and medical ultrasound. Recent experimental results have demonstrated that the addition of surfactant substantially enhances bubble growth rate. As a hypothesis, this was widely attributed to the acoustic microstreaming and mass transfer resistance caused by surfactants. In this research, the effects of the surfactant of sodium dodecyl sulphate on the rectification have been simulated by considering only the variation of the surface tension coefficient due to the surfactant. The computations are carried out using a newly developed tractable model based on the multi-scale method and the method of matched asymptotic expansions, which allows the prediction of bubble growth taking place over millions of oscillation cycles. The rate of bubble growth observed in the experiments is accurately predicted by our computations, for a range for bulk surfactant SDS concentrations less than or equal to 2.4 mM. Contrary to the widely held hypothesis in the published literature, this has demonstrated that the dominant physical mechanisms remain the shell and area effects in this range of bulk surfactant concentrations. The further enhancement of bubble growth rate provided by either acoustic microstreaming or the resistance to mass transfer is only evident at higher bulk surfactant concentrations. Therefore, the role of surface tension in rectified diffusion for aqueous surfactant solutions is more significant than previously understood. The new results also show that the bubble growth rate is sensitive to small changes in the bubble radius which may account for its unpredictability in applications of sonochemistry.