A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-00504
Acknowledgements: A. K. acknowledges support from International Academic Exchange Grant Program of the University of Tokyo and the Japan Society for the Promotion of Science. N.I. is supported by the Japan Society for the Promotion of Science (Grant No. 19340110) and KAUST, GRP (Grant No. KUK-I1-00504).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.