CELLULAR-AUTOMATON MODEL OF REACTION-TRANSPORT PROCESSES

The transport and chemical reactions of solutes are modelled as a cell ular automation in which molecules of different species perform a rand om walk on a regular lattice and react according to a local probabilis tic rule. The model describes advection and diffusion in a simple way, and as no restriction is placed on the number of particles at a latti ce site, it is also to describe a wide variety of chemical reactions. Assuming molecular chaos and a smooth density function, we obtain the standard reaction-transport equations in the continuum limit. Simulati ons on one- and two-dimensional lattices show that the discrete model can be used to approximate the solutions of the continuum equations. W e discuss discrepancies which arise from correlations between molecule s and how these disappear as the continuum limit is approached. Of par ticular interest are simulations displaying long-time behaviour which depends on long-wavelength statistical fluctuations not accounted for by the standard equations. The model is applied to the reactions a + b reversible c and a + b --> c with homogeneous and inhomogeneous initi al conditions as well as to systems subject to autocatalytic reactions and displaying spontaneous formation of spatial concentration pattern s.