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

• Published in: Chemical engineering journal (Lausanne, Switzerland : 1996) Vol. 71; no. 1; pp. 49 - 56
• Main Authors: Clifford, Michael J., Cox, Stephen M., Roberts, E.P.L
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.1998; Elsevier
• Subjects: Chemically reactive flows; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Lamellar modelling; Lamellar structure; Physics; Reactive, radiative, or nonequilibrium flows; Two-dimensional flow; Lamellar modelling; Lamellar structure; Two-dimensional flow; Mixing; Digital simulation; Theoretical study; Competitive reaction; Chemical reactions; Advection diffusion equation; Two dimensional flow; Reaction diffusion equation; Laminar flow; Reacting flow; One dimensional model; Chaotic systems; Concentration distribution; Successive reaction
• ISSN: 1385-8947; 1873-3212
• DOI: 10.1016/S1385-8947(98)00107-7

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 one-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.