Lattice Boltzmann method (LBM) is developed for solution of one-dimensional population balance equations (PBEs) with simultaneous growth, nucleation, aggregation and breakage. Aggregation and breakage, which act as source terms in PBEs, are included as force terms in LBM formulation. The force terms representing aggregation and breakage are evaluated by fixed pivot (FP) method. Multiscale analysis is used to derive the kinetic equations associated with LBM, whose long-time large-scale solution provides the solution of the PBE. A coordinate transformation is proposed, which allows the use of non-uniform grid for LBM to obtain accurate solution of PBE with moderate number of grid points. The performance of the proposed LBM-FP method is compared with finite volume (FV) and method of characteristics (MOC) combined with FP (MOC-FP) methods. Using benchmark examples, the proposed LBM-FP method is shown to be useful for solving PBEs due to its computational efficiency and ability to handle a wide range of problems.
Majumder, A., Kariwala, V., Ansumali, S., & Rajendran, A. (2012). Lattice Boltzmann method for population balance equations with simultaneous growth, nucleation, aggregation and breakage. Chemical Engineering Science, 69(1), 316-328. https://doi.org/10.1016/j.ces.2011.10.051