Integral formulation of the population balance equation using the cumulative QMOM

The integral formulation of the population balance equation using the CQMOM presents a novel and hierarchical method to couple the QMOM and the physically evolving particle size distribution. Here, not only is the cumulative number density function reconstructed, but also its low-order moments. The numerical analysis of the method shows two desirable properties: First, it can be considered as a free-mesh method, since the solution of each integral equation at the current grid point does not depend on the other ones. Second, the accuracy of the targeted low-order cumulative moments depend only on the nodes and weights of the cumulative Gauss-Christoffel quadrature, but not on sampling the continuous low-order cumulative moments. So, the CQMOM is a general integral formulation of the population balance equation and is an effective numerical scheme in which the QMOM is imbedded as a limiting case.