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

• Main Author: Shaw B. D.
• Format: Article
• Language: English
• Published: Hindawi Limited 1998-01-01
• Series: Mathematical Problems in Engineering
• Subjects: Asymptotic Expansions; Perturbations; Asymptotic Approximations; Heat And Mass Transfer; Phase Changes; Miscellaneous Topics
• Online Access: http://www.hindawi.net/access/get.aspx?journal=mpe&volume=4&pii=S1024123X98000805

<p>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.</p>