A novel algorithm for solving population balance equations: the parallel parent and daughter classes. Derivation, analysis and testing

A novel numerical method, the parallel parent and daughter classes (PPDC) technique, for solving population balance equations (PBEs) is presented in this paper. In many practical applications, the PBE of particles under investigation is coupled with the thermo-fluid dynamics of the surrounding fluid. Hence, the PBE needs to be implemented in a computational fluid dynamics (CFD) code, which leads to an additional computational load. The computational cost becomes intractable when techniques such as methods of classes (CM) or Monte Carlo method are used. Quadrature method of moments (QMOM) and direct quadrature method of moments (DQMOM) are accurate and require a relatively low additional computational cost when applied to CFD. The PPDC is shown to be as accurate as QMOM and DQMOM, and even more accurate in some cases, when the same number of classes is used. In the present work, the PPDC technique has been derived and tested. This technique can be used for solving a wide class of problems involving PBE such as polymerization, aerosol dynamics, bubble columns, etc. Numerical simulations have been carried out on aggregation processes with different kernels and on simultaneous aggregation and breakage processes. The numerical predictions are compared either with analytical solutions, when available, or with the numerical solutions obtained by methods of classes.