Breakdown of Ovchinnikov-Zeldovich Segregation in the A+B-->0 Reaction under Lévy Mixing.

Abstract

Density fluctuations in the transient $A+B\ensuremath{\rightarrow}0$ reaction, at stoichiometric conditions, cause the Ovchinnikov-Zeldovich segregation which slows down the reaction process. Continuous mixing that homogenizes the reactants can suppress the role of the fluctuations. L\'evy walks which lead to an anomalous diffusion provide such a mixing mechanism. For L\'evy walks with the number of steps distributed as $P(n)\ensuremath{\sim}{n}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\gamma}},n>0,1<\ensuremath{\gamma}<2$, we demonstrate that segregation disappears in $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ dimensions for $\ensuremath{\gamma}<3/2$. Particle densities and particle-particle correlation functions are presented. The erosion of the segregation is an example of L\'evy mixing.