In addition to bubble number density, bubble size distribution is an important population parameter governing the activity of acoustic cavitation bubbles. In the present paper, an iterative numerical method for equilibrium size distribution is proposed and combined to a model for bubble counting, in order to approach the number density within a population of acoustic cavitation bubbles of inhomogeneous sizing, hence the sonochemical activity of the inhomogeneous population based on discretization into homogenous groups. The composition of the inhomogeneous population is analyzed based on cavitation dynamics and shape stability at 300 kHz and 0.761 W/cm2 within the ambient radii interval ranging from 1 to 5 µm. Unstable oscillation is observed starting from a radius of 2.5 µm. Results are presented in terms of number probability, number density, and volume probability within the population of acoustic cavitation bubbles. The most probable group having an equilibrium radius of 3 µm demonstrated a probability in terms of number density of 27%. In terms of contribution to the void, the sub-population of 4 µm plays a major role with a fraction of 24%. Comparisons are also performed with the homogenous population case both in terms of number density of bubbles and sonochemical production of HO●, HO2●, and H● under an oxygen atmosphere.
An alternative technique for determining the number density of acoustic cavitation bubbles in sonochemical reactors
