A mathematical model for the dynamics of particle growth during synthesis of ultra fine particles in diffusion flames is presented. The model includes the kinetics of particle coalescence and coagulation, and when combined with a calculation of the temperature, velocity and gas composition distribution in the flame, the effluent aerosol characteristics are calculated. The model is validated by comparison with an experimental study of the synthesis of alumina particles by combustion of Al-tri-sec-butoxide. Two parameters of the coalescence kinetics are estimated by regression of the model predictions to the measured specific surface area of the product particles. The estimated kinetics can be used to predict the surface area and shape of the particles for a wide range of synthesis conditions.