Efficient stochastic simulation of simultaneous reaction and diffusion in a gas-liquid interface

A stochastic simulation of simultaneous reaction and diffusion is proposed for the gas-liquid interface formed in the surface of a gas bubble within a liquid. The interface between a carbon dioxide bubble and an aqueous solution of calcium hydroxide was simulated as an application example, taken from the integrated production of calcium carbonate. First Gillespie’s stochastic simulation algorithm was applied in separate reaction and diffusion simulations. The results from these simulations were consistent with deterministic solutions based on differential equations. However it was observed that stochastic diffusion simulations are extremely slow. The sampling of diffusion events was accelerated applying a group molecule transfer scheme based on the binomial distribution function. Simulations of the reaction-diffusion in the gas-liquid interface based on the standard Gillespie’s stochastic algorithm were also slow. However the application of the binomial distribution function scheme allowed to compute the concentration profiles in the gas-liquid interface in a fraction of the time required with the standard Gillespie’s stochastic algorithm.