Lamellar modelling of reaction, diffusion and mixing in a two-dimensional flow

We present a one-dimensional model of reaction, diffusion and mixing in a two-dimensional flow. The model assumes that initially segregated reactants are stretched and folded into a lamellar structure. Reaction and diffusion are simulated within this one-dimensional lamellar array. The lamellae are assumed to have a uniform thickness. Mixing is included as a single parameter i.e. the average stretch rate of the flow. Results are compared with full two-dimensional simulations of the concentration fields. Given the very simple nature of the dimensional model and the complexity of the full system, remarkably good agreement is obtained with a considerable saving in computational effort. For a competitive-consecutive reaction the predicted yields agree to within 6%. A typical one-dimensional simulation on a Silicon Graphics R5000 workstation takes around 1 min compared to 25 h on a 1024-node nCUBE 2 parallel computer for the concentration field simulations. The one-dimensional lamellar simulations are not limited by the relative rates of diffusion, reaction and advection, and are generally applicable to complex two-dimensional and, in principle, three-dimensional flows.