Bivariate direct quadrature method of moments for coagulation and sintering of particle populations

The direct quadrature method of moments (DQMOM) is applied to a bivariate population balance equation governing the joint number density function n(v,a) of particle volume and area. Using a test case proposed by Wright et al. [2001. Bivariate extension of the quadrature method of moments for modeling simultaneous coagulation and sintering of particle populations. Journal of Colloid and Interface Science, 236, 242–251], it is shown that DQMOM reproduces the results found by using bivariate extensions of QMOM. The effects of the choice of bivariate moments and the order (N) of the quadrature approximation are also discussed. In general, it is found that for fixed N all non-singular sets of bivariate moments yield nearly identical results as reported by Wright et al. However, particular sets leading to lower condition numbers for the linear system used to compute the source terms in DQMOM are preferable for numerical reasons. For any value of N 3, the bivariate moment predictions are very similar. Overall, it is found that the coagulation and sintering kernels used in this test case are easily handled by lower-order moment methods, and are relatively insensitive to the choice of bivariate moments used for DQMOM.