Analytical results for soot concentration, average particle size, and a of the size distribution are obtained for a free radical soot growth model which includes a constant nucleation source, growth, and coagulation. Results are obtained with and without coagulation included and for a size independent growth rate as well as growth rate proportional to the surface area. Neither this model nor a nucleation pulse model is able to account for all the results on soot formation for shock tube and pyrolysis experiments. INTRODUCTION Soot produced in fires is a major concern. The emission of radiation from soot plays a dominant role in fire spread. The reduced visibility caused by soot is a significant impediment to persons escaping from fires. The deposition of soot in the respiratory tract is a potential health hazard especially in the case of repeated exposures by firemen. On the other hand, a low concentration of soot is adequate to activate a smoke detector alarm and thus provide a warning of a fire. While there has been a large amount of experimental work concerning soot formation under a wide variety of conditions, as evidenced by some 388 references in a recent review article by Haynes and Wagner [1], there has been relatively little theoretical effort to integrate the various processes leading to soot formation and growth into a model capable of predicting soot concentration and particle size. Jensen [2] has developed such a model for predicting soot generation from methane fuel in an exhaust jet. The approach taken here is similar in spirit to Jensen's method though with less structure in the individual processes. The advantage of our model is that it can be solved analytically, and this allows a more general understanding of the effect of the various growth processes on the final particle size. The model includes the formation of soot nuclei, surface growth, and coagulation. The nucleation process is modeled as a thermal pyrolysis leading to a free radical species. The growth stage is first treated in a manner analogous to chain polymerization. Growth proportional to the surface area is also considered. For the combined growth model, the soot concentration, the average particle size, and the width of the size distributions are determined. The model assumes a homogeneous isothermal system and for that reason the most direct validation is with shock tube experiments and pyrolysis experiments rather than with flame data. The model results are compared with the available data. FIRE SAFETY SCIENCE-PROCEEDINGS OF THE FIRST INTERNATIONAL SYMPOSIUM 709 Copyright © International Association for Fire Safety Science FREE RADICAL SOOT GROWTH MODEL This model is very similar to what is called polymerization without termination in the polymer literature. The first step involves the thermal pyrolysis of the fuel to yield free radical species. k 1 F -+ R 1 + a where R1 indicates the incipient soot nuclei and Ra indicates a gaseous radical such as H atoms. The rate constant k1 is taken to have an activation energy, Ea' Of course, the chemistry leading to the soot precursor in an actual system is not a simple elementary reaction so this is a global expression of the kinetics. The free radical R1 initiates the chain polymerization. k 2 R1 + F -+ R2 k 2 -+ The symbols, F, R1, Rj, etc. represent species in the equations above; we use the same symbols to represent concentration in the kinetic equations developed below. The rate constant k2 is taken to be a constant independent of particle size. It is assumed that the fuel adds directly to the radical species. The polymer species Rj are considered to be soot particles. We denote by N the total number concentration of soot.