Direct Simulation and Mass Flow Stochastic Algorithms to Solve a Sintering-Coagulation Equation

In this paper we develop an efficient stochastic method to solve the time evolution of a bivariate population balance equation which has been developed for modelling nano-particle dynamics. We have adapted the existing stochastic models used in the study of coagulation dynamics to solve a variant of the sintering-coagulation equation proposed by Xiong & Pratsinis. Hitherto stochastic models based on Markov jump processes have not taken into account the surface area evolution. We produce numerical results efficiently with the direct simulation and mass flow algorithms and study the convergence behaviour as the number of stochastic particles increases. We find a marked preference for using the mass flow algorithm to determine the higher order volume and area moments of the particle size distribution function. The computational efficiency of these algorithms is remarkable when compared to the sectional method that has been used previously to study this equation.