FIGURE IIA.2 Predicted equilibrium bubble size distribution at three values of turbulent energy dissipation rates. Effect of energy dissipation rate on (a) group mass fraction and (b) total surface area.

dk and rk denote the diameter and radius of bubbles of group k. fBv is a breakage fraction and is defined in Eq. (11A.9), h0 and hf, used in Eq. (11A.7), denote initial and critical film (between two coalescing bubbles) thickness and are usually assumed to be 1 x 10-4 m (Kirkpatrick and Lockett, 1974) and 1x 10-8 m (Kim and Lee, 1987). Typical equilibrium bubble size distributions predicted by this model at three different values of turbulent energy dissipation rates and corresponding total interfacial area are shown in Fig. 11A.2a and 11A.2b respectively. As expected, the model predicts the shift towards finer bubble sizes at higher values of turbulent energy dissipation rates. Ongoing and future experimental and modeling studies are expected to lead towards enhanced understanding and better predictive capabilities. For example, recently Lehr and Mewes (2001) have proposed a new model to describe bubble breakage process, which was found to improve the predictions of bubble size distribution. Such new models of coalescence and breakage can be incorporated in the overall framework discussed here.

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