Evaluation of the 1-point quadrature approximation in QMOM for combined aerosol growth laws

This work examines the applicability of various assumptions in implementation of the quadrature method of moments (QMOM) for solving problems in aerosol science involving simultaneous nucleation, surface growth and coagulation. The problem of aerosol growth and coagulation in a box and the problem of vapor condensation in a nozzle are reworked using quadrature method of moments. QMOM uses Gaussian quadrature to evaluate integrals appearing in the moment equations and therefore does not require any assumptions on the form of the size distribution function, the growth laws and coagulation kernels. Results are compared with calculations which assume a lognormal size distribution. The conditions for which one, two and higher quadrature points can be used in the quadrature formula and the issues regarding the accuracy are considered for combined aerosol nucleation, growth and coagulation processes. Results show that for these problems, the simplest 1-point quadrature scheme gives accuracy comparable with the lognormal calculations while using two and higher point quadrature gives highly accurate results. Some difficulties associated with the QMOM are discussed and some insights are provided.

[1]  S. Friedlander,et al.  Monodisperse particle production by vapor condensation in nozzles , 1988 .

[2]  F. Gelbard.  Modeling Multicomponent Aerosol Particle Growth By Vapor Condensation , 1990 .

[3]  S. Katz,et al.  Some problems in particle technology: A statistical mechanical formulation , 1964 .

[4]  J. C. Barrett,et al.  A comparison of some approximate methods for solving the aerosol general dynamic equation , 1998 .

[5]  J. R. Bates.  The Mechanism of the Reaction of Hydrogen Atoms with Oxygen , 1933 .

[6]  D. Wright,et al.  RETRIEVAL OF OPTICAL PROPERTIES OF ATMOSPHERIC AEROSOLS FROM MOMENTS OF THE PARTICLE SIZE DISTRIBUTION , 2000 .

[7]  Robert McGraw,et al.  Description of Aerosol Dynamics by the Quadrature Method of Moments , 1997 .

[8]  Robert McGraw,et al.  Chemically resolved aerosol dynamics for internal mixtures by the quadrature method of moments , 2003 .

[9]  S. Pratsinis.  Simultaneous nucleation, condensation, and coagulation in aerosol reactors , 1988 .

[10]  S. Friedlander.  DYNAMICS OF AEROSOL FORMATION BY CHEMICAL REACTION * , 1983 .

[11]  D. E. Rosner,et al.  Bivariate Extension of the Quadrature Method of Moments for Modeling Simultaneous Coagulation and Sintering of Particle Populations. , 2001, Journal of colloid and interface science.

[12]  S. Friedlander.  Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics , 2000 .

[13]  R. McGraw,et al.  Method of Moments Solutions for a Laminar Flow Aerosol Reactor Model , 2001 .

[14]  M. M. R. Williams,et al.  Aerosol Science: Theory and Practice , 1991 .

[15]  S. Schwartz,et al.  Six‐moment representation of multiple aerosol populations in a sub‐hemispheric chemical transformation model , 2000 .

[16]  Shaocai Yu,et al.  Retrieval of aerosol properties from moments of the particle size distribution for kernels involving the step function: cloud droplet activation , 2002 .

[17]  J. Seinfeld,et al.  Sectional representations for simulating aerosol dynamics , 1980 .

[18]  Roy G. Gordon,et al.  Error Bounds in Equilibrium Statistical Mechanics , 1968 .