A mesoscale approach for population balance modeling of bubble size distribution in bubble column reactors

- We propose a new physical constraint to population balance equations.
- It is relevant to the mesoscale energy dissipation due to breakage and coalescence.
- A correction factor for coalescence rate is then derived from the new constraint.
- CFD-PBM simulation of bubble size with the new corrector agrees with experiments.
- The new corrector model can adapt the kernel functions used.

Prediction of bubble size distribution is of paramount importance for the study of bubble column reactors. Current kernel functions for coalescence or breakage in CFD-PBM simulation are usually derived from the isotropic turbulence theory and overestimate bubble size distribution with increasing gas flow rate. Based on the energy-minimization multi-scale concept, we develop a new approach to calculate the coalescence rate through the so-called stability condition and the meso-scale energy dissipation relevant to bubble breakage and coalescence (Yang et al., 2010). The approach is independent of specific kernel functions, and provides a new constraint to the kernel functions of coalescence or breakage which were previously only related to the turbulence properties through isotropic turbulence theory. New correctors for coalescence rate could then be derived for various kernel models. Our simulation indicates that this new approach can adapt to different coalescence or breakage kernel function models, and can achieve better prediction for bubble size distribution.