Representation of generally mixed multivariate aerosols by the quadrature method of moments: II. Aerosol dynamics

The quadrature method of moments (QMOM) is extended to generally mixed multicomponent particle populations using principal component analysis (PCA). The resulting PCA-QMOM provides a versatile method for moment closure illustrated for generally mixed, multivariate, particle populations evolving under condensation, coagulation, sintering, and simultaneous processes. The method is illustrated using a 2h-point quadrature version of the PCA-QMOM, where h is the number of coordinate dimensions, developed in the preceding paper (Paper I). Calculations for multiple particle populations interacting through coagulation are also presented. A theory is developed for the time-dependence of the covariance matrix of a multicomponent particle population evolving under a size-independent coagulation rate. It is found that the rank of the h×h covariance matrix, for h components, approaches unity at long time as the particle population evolves to an internally mixed, self-preserving size distribution state.