Bivariate extension of the quadrature method of moments for modeling simultaneous coagulation and sintering of particle populations

We extendthe application of moment methods to multivariate suspended partic le population problems-those for which size alone is insufficient to specif y the state of a particle in the population. Specifically, a bivariate exte nsion of the quadrature method of moments (QMOM) (R. McGraw, Aerosol Sci. T echnol. 27, 255 (1997)) is presented for efficiently modeling the dynamics of a population of inorganic nanoparticles undergoing simultaneous coagulat ion and particle sintering. Continuum regime calculations are presented for the Koch-Friedlander-Tandon-Rosner model, which includes coagulation by Br ownian diffusion (evaluated for particle fractal dimensions, D-f, in the ra nge 1.8-3) and simultaneous sintering of the resulting aggregates (P. Tando n and D. E. Rosner, J. Colloid Interface Sci. 213, 273 (1999)). For evaluat ion purposes, and to demonstrate the computational efficiency of the bivari ate QMOM, benchmark calculations are carried out using a high-resolution di screte method to evolve the particle distribution function rt(nu, a) for sh ort to intermediate times (where nu and a are particle volume and surface a rea, respectively). Time evolution of a selected set of 36 low-order mixed moments is obtained by integration of the full bivariate distribution and c ompared with the corresponding moments obtained directly using two differen t extensions of the QMOM. With the more extensive treatment, errors of less than 1% are obtained over substantial aerosol evolution, while requiring o nly a few minutes (rather than days) of CPU time. Longer time QMOM simulati ons lend support to the earlier finding of a self-preserving limit for the dimensionless joint (nu, a) particle distribution function under simultaneo us coagulation and sintering (Tandon and Rosner, 1999; D. E. Rosner and S, Yu, AIChE J., 47 (2001)). We demonstrate that, even in the bivariate case, it is possible to use the QMOM to rapidly model the approach to asymptotic behavior, allowing an immediate assessment of when previously established a symptotic results can be applied to dynamical situations of current/future interest. (C) 2001 Academic Press.