Stochastic coalescence-redispersion model for molecular diffusion and chemical reactions. 1. Methodology

A population balance model for simulation of molecular diffusion and chemical reactions, using a Monte Carlo method, is developed. In this model the system is divided into cells assigned by spatial coordinates. Pairs of adjacent cells are sampled randomly, and their properties mixed. The parameters of the model are the sampling frequency and a partition parameter that determines the fraction of property transferred from one cell to its neighbor. An equation for the mass flux is formulated from the model and found to be a finite difference approximation to Fick's law of diffusion. Correlations between the diffusion coefficient and the parameters of the model for specified coordinate systems (Cartesian, cylindrical, and polar) are derived. Two sampling methods are developed: (1) uniform sampling and (2) sampling according to concentration gradients. Chemical reactions are decoupled from the transport process by alternate mixing-chemistry operations. The major advantage of the present stochastic approach is the simplicity of the numerical treatment. In the following paper, simulation examples of molecular diffusion with chemical reactions are illustrated.