Bubble population phenomena in sonochemical reactor: II. Estimation of bubble size distribution and its number density by simple coalescence model calculation

A simple bubble population model, with emphasis on the bubble–bubble coalescence, is proposed. In this model, the bubble size distribution is simulated through the iteration of fundamental bubble population process: generation, dissolution, and coalescence. With this simple modelling, the bubble size distribution experimentally observed by the pulsed laser diffraction method and the void rate obtained by the capillary system at 443 kHz were successfully simulated. The experimental results on the bubble population growth by the repetitive pulsed sonication and the effect of pulse width on the bubble population were recreated by the numerical simulation in a semi-quantitative manner. The importance of coalescence of bubbles especially for the effect of addition of surfactant is demonstrated. By decreasing the coalescence frequency by one order of magnitude in the simulation, both the drastic decrease in the total bubble volume as well as the depression of bubble size distribution centring from a few tens of microns in water to a few microns in a dilute surfactant solution can be simultaneously derived.