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Mixing-driven equilibrium reactions in multidimensional fractional advection–dispersion systems

Authors
Journal
Physica A Statistical Mechanics and its Applications
0378-4371
Publisher
Elsevier
Publication Date
Volume
392
Issue
10
Identifiers
DOI: 10.1016/j.physa.2012.12.040
Keywords
  • Fractional Dispersion
  • Reactions
  • Multiple Dimensions

Abstract

Abstract We study instantaneous, mixing-driven, bimolecular equilibrium reactions in a system where transport is governed by a multidimensional space fractional dispersion equation. The superdiffusive, nonlocal nature of the system causes the location and magnitude of reactions that take place to change significantly from a classical Fickian diffusion model. In particular, regions where reaction rates would be zero for the Fickian case become regions where the maximum reaction rate occurs when anomalous dispersion operates. We also study a global metric of mixing in the system, the scalar dissipation rate and compute its asymptotic scaling rates analytically. The scalar dissipation rate scales asymptotically as t−(d+α)/α, where d is the number of spatial dimensions and α is the fractional derivative exponent.

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