(369f) Bivariate Applications and Extensions of the Quadrature Method of Moments

Recent applications of the quadrature method of moments (QMOM) to the simulation of bivariate/multivariate particle populations [1,2,3] are presented, together with a preliminary description of several powerful extensions currently under development through 'hybridization' of the QMOM with principal components analysis (PCA), the spectral method called orthogonal collocation (OC), and empirical orthogonal function (EOF) methods. Applications of the PCA-QMOM will focus on:  (i) bivariate coagulation and sintering of irregular-shaped particle aggregates in laminar flames, and (ii) general mixing of multicomponent/multivariate particle populations under atmospheric conditions. Hybridization seeks to combine the best features of PCA, OC, and EOF with the QMOM. PCA provides an efficient and systematic way to assign quadrature points in higher dimensions. OC and EOF are fixed grid methods with generally higher resolution than the QMOM, which uses a smaller number of quadrature points optimally determined by the lower order moments of the particle distribution function. Thus, the QMOM has the intrinsic advantage of being an adaptive grid method. Combining these theoretical/numerical approaches should yield higher-resolution adaptive grids for the efficient simulation of multivariate nanoparticle populations evolving under complex environmental conditions including the nonlinear process of Brownian coagulation, with applications to combustion engineering, industrial crystallization, and atmospheric science. ________________________________

RLM: Adjunct Prof. Chemical Engineering, Yale University; Permanent address: Brookhaven National Laboratory, Upton, NY.

MAZ: Postdoctoral Visiting Research Scientist, Yale University; Permanent address: UNED-Madrid, Dept. Fluid Physics.

DER: Llewellyn West Jones Professor of Chemical Engineering, Yale University.

[1] Rosner, D.E., McGraw, R. and Tandon, P., Ind.&  Eng. Chem Res.(ACS) 42, 2699-2711(2003).

[2] Rosner, D.E., Ind.& Eng. Chem Res.(ACS) 44 ;  to appear: August 2005).

[3] Rosner, D.E., to appear in IJCRE: Proc. Tenth Intl. Conference on Chemical Reaction Engineering (CRE-X);Fall 2005.

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Prepared for Presentation at AIChE '05, Cincinnati OH , Oct.30-Nov.4, 2005