Simulation of micro-behaviors including nucleation, growth, and aggregation in particle system

A new method for the solution of population balance equations (PBE) describing the micro-processes such as nucleation, growth, aggregation of particle swarms in a multiphase system is proposed. The method is based on the fixed pivot moment and allows arbitrary number of moments to be tracked simultaneously. By expressing PBEs for both batch and continuous operations in a general form, and using weighted residual method to derive the moment equations, different moments can be tracked directly. The numerical density function is assumed to be a summation of several weighted Dirac Delta functions, and the integral and derivative terms in PBEs are transformed to a summation in order to reduce computational cost. Simulations of a batch nucleation-growth process and a continuous aggregation-growth process have demonstrated good agreement with the corresponding analytical solutions, with relative errors less than 10^-8%. Simulation of a combined nucleation-growth-aggregation process, which does not have an analytical solution, is also included, so as to reproduce the micro-behaviors of such a complex system, demonstrating the feasibility and reliability of this method.