Modelling Reaction-Diffusion Dynamics in Microsystems

The commonly used macroscale techniques based on the continuum approximation cannot always be readily adapted to describe chemical reactions and transport processes that take place at the microscale. By contrast, particle-based mesoscale methods possess the unique ability to model relatively large physical systems, and, at the same time, effectively capture the essential features of the micro- and nanoscale structures. The lattice Boltzmann method (LBM) is a powerful mesoscopic computational tool for simulating complex flows and has the ability to efficiently solve the reaction-diffusion-advection equation (RDA). Typically reaction is incorporated into LBM by a macroscopic reaction source term similar in structure to the kinetic equations that are used when solving RDA problems by conventional numerical methods. A more accurate approach is to include reaction into LBM simulations at a meso or microscopic level and mimic collisions of reactive particles. In this study we present a novel algorithm based on an effective reaction cross section that is able to capture the underlying dynamics of reaction mechanism.