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A theoretical analysis of gas-phase manufacture of particulates is presented using a discrete model for particulate dynamics in the free-molecular regime. Regardless of the reaction order and process conditions, two dimensionless groups suffice to determine the particle size distribution a t isothermal conditions. These groups are (1) the dimensionless reaction time, which is proportional to the ratio of the characteristic time for chemical reaction to the characteristic time for aerosol coagulation, and (2) the dimensionless residence time, which is proportional to the ratio of the residence time to the characteristic time for coagulation. The size distribution of a reaction-produced coagulating aerosol evolves to an asymptotic self-preserving size distribution that has a geometric standard deviation of 1.46. When the reaction is instantaneous, good agreement is obtained between model predictions and literature values for the time needed for the size distribution to obtain its asymptotic geometric standard deviation (self-preserving form). For noninstantaneous reactions, a self-preserving map is created in which the required time for attainment of the self-preserving form is given as a function of the dimensionless reaction time. The employed numerical model provides an accurate solution of the coagulation equations. This solution can be used to evaluate the accuracy of approximate models of aerosol dynamics that employ monodisperse, self-preserving, log-normal, or discrete-sectional representations of the aerosol size distribution.

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