On the Approximate Solution and Modeling of the Kernel of Nonlinear Breakage Population Balance Equation

The study of collision-induced nonlinear breakage phenomenon is mostly unexplored but is important in the area of particulate processes. In this work, the volume and time dependent collisional breakage kernel function is modeled based on the population balance modeling approach. To solve the nonlinear breakage population balance equation, the weighted finite volume scheme for linear breakage process from Kumar, Saha, and Tsotsas [SIAM J. Numer. Anal., 53 (2015), pp. 1672--1689] is extended for the case of collision-induced breakage process. The weighted finite volume scheme is developed in such a way that it conserves the total mass of the system while preserving the total number of particles in the system. Moreover, an event-driven constant number Monte Carlo simulation algorithm is presented, and the simulation results are used as an alternative to experimental results. The volume dependency of the collisional breakage kernel is incorporated successfully in the Monte Carlo simulation for the first time while selecting particles for collision events. Some essential properties of any particulate process, such as the total number of particles and the size distribution of particles, are validated successfully for several breakage distribution functions using the Monte Carlo results. This offers new insights into the estimation and interpretation of collision-induced nonlinear breakage kinetics.