In this paper a new method for the calculation of the diameter of a partially-sintered particle is introduced and shown to be more accurate than the standard d(p) = 6v/a formula. The method was used to determine the particle sintering rates in a flame producing SiO2 nanoparticles. The results of the simulations return a value for the average particle fractal dimension closer to the experimental values than is obtained using the standard formula. The particle ensemble was simulated using an efficient bivariate stochastic particle method, which for the first time, was applied to the non-isothermal environment of a premixed laminar flame. The transition from a bimodal particle size distribution to a unimodal particle size distribution for the silica particles was observed. This paper also contains the results of a test simulation which examines the stochastic algorithm under various simple starting conditions and determines its convergence properties. (c) 2005 Elsevier Ltd. All fights reserved.