On the stochastic simulation of particulate systems

The stochastic chemical kinetics approach provides one method of formulating the stochastic crystallization population balance equation (PBE). In this formulation, crystal nucleation and growth are modelled as sequential additions of solubilized ions or molecules (units) to either other units or an assembly of any number of units. Monte Carlo methods provide one means of solving this problem. In this paper, we assess the limitations of such methods by both (1) simulating models for isothermal and nonisothermal size-independent nucleation, growth and agglomeration; and (2) performing parameter estimation using these models. We also derive the macroscopic (deterministic) PBE from the stochastic formulation, and compare the numerical solutions of the stochastic and deterministic PBEs. The results demonstrate that even as we approach the thermodynamic limit, in which the deterministic model becomes valid, stochastic simulation provides a general, flexible solution technique for examining many possible mechanisms. Thus the stochastic simulation permits the user to focus more on modelling issues as opposed to solution techniques.