On the breakup of an air bubble injected into a fully developed turbulent flow.: Part 2.: Size PDF of the resulting daughter bubbles

Based on energy principles, we propose a statistical model to describe the bubble size probability density function of the daughter bubbles resulting from the shattering of a mother bubble of size D-0 immersed in a fully developed turbulent water flow. The model shows that the bubble size p.d.f. depends not only on D-0, but also on the value of the dissipation rate of turbulent kinetic energy of the underlying turbulence of the water, epsilon. The phenomenological model is simple, yet it predicts detailed experimental measurements of the transient bubble size p.d.f.s performed over a range of bubble sizes and dissipation rates e in a very consistent manner. The agreement between the model and the experiments is particularly good for low and moderate bubble turbulent Weber numbers, We(t) = rho Delta u(2)(D-0)D-0/sigma where the assumption of the binary breakup is shown to be consistent with the experimental observations. At larger values of We(t), it was found that the most probable number of daughter bubbles increases and the assumption of tertiary breakup is shown to lead to a better fit of the experimental measurements.