Mixing in reaction dynamics under enhanced diffusion conditions

• Published in: Physics reports Vol. 290; no. 1; pp. 157 - 171
• Main Authors: Zumofen, G., Klafter, J., Shlesinger, M.F.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.1997
• Subjects: 05.40.+j; 82.20.Db
• ISSN: 0370-1573; 1873-6270
• DOI: 10.1016/S0370-1573(97)00065-3

We first review the Lévy-flight approach for the description of enhanced diffusion and then study the effects of mixing on the transient A + B → 0 reaction at stoichiometric conditions in d = 1−3 dimensions under enhanced diffusion conditions. The particles are assumed to follow Lévy walks, characterized by an index γ, which result in enhanced diffusion for 1 < γ < 2. Particle density decays and particle-particle correlation functions are calculated using deterministic reaction diffusion equations and computer simulations of this multi-particle problem. We concentrate on the segregation phenomenon and demonstrate that, depending on γ, segregation may disappear in d = 3 dimensions under enhanced diffusion conditions. Hence, Lévy walks lead to an efficient mixing of reacting particles.