LAMELLAR MODELING OF REACTION, DIFFUSION AND MIXING IN A 2-DIMENSIONAL FLOW

We present a one-dimensional model of reaction, diffusion and mixing i n 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 arra y. The lamellae are assumed to have a uniform thickness. Mixing is inc luded as a single parameter i.e. the average stretch rate of the flow. Results are compared with full two-dimensional simulations of the con centration fields. Given the very simple nature of the one-dimensional model and the complexity of the full system, remarkably good agreemen t is obtained with a considerable saving in computational effort. For a competitive-consecutive reaction the predicted yields agree to withi n 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-d imensional 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. (C ) 1998 Elsevier Science S.A. All rights reserved.