Mathematical Problems in Engineering
Volume 4 (1998), Issue 3, Pages 233-246

Asymptotic solution of nonlinear moment equations for constant-rate aerosol reactors

B. D. Shaw

Mechanical and Aeronautical Engineering Department, University of California, Davis 95616, CA, USA

Received 8 August 1996

Copyright © 1998 B. D. Shaw. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonlinear evolution equations based upon moments of the aerosol size distribution function are solved asymptotically for constant-rate aerosol reactors (i.e., where condensible monomer is added at a constant rate) operating in the free-molecular limit. The governing equations are nondimensionalized and a large parameter that controls nucleation behavior is identified. Asymptotic analyses are developed in terms of this parameter. Comparison of the asymptotic results with direct numerical integration of the governing equations is favorable. The asymptotic results provide a simplified analytical approach to estimating average particle sizes, particle number densities, and peak supersaturation values for constant-rate aerosol reactors.