Simulation of chemical reaction via particle tracking: Diffusion-limited versus thermodynamic rate-limited regimes

Chemical reactions may be simulated without regard to local concentrations by applying simple probabilistic rules of particle interaction and combination. The forward reaction A + B -> C is coded by calculating the probability that any A and B particles will occupy the same volume over some time interval. This becomes a convolution of the location densities of the two particles. The backward reaction is a simple exponential decay of C particles into A and B particles. When the mixing of reactants is not a limiting process, the classical thermodynamic reaction rates are reproduced. When low mixing (as by diffusion) limits the reaction probabilities, the reaction rates drop significantly, including the rate of approach to global equilibrium. At long enough times, the law of mass action is reproduced exactly in the mean, with some irreducible deviation in the local equilibrium saturations (the equilibrium constant divided by the mass action expression) away from unity. The saturation variability is not sensitive to numerical parameters but depends strongly on how far from equilibrium the system is initiated. This is simply due to a relative paucity of particles of some species as the reaction moves far to one side or the other.