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

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  • Bolster, Diogo
  • Benson, David A.
  • Meerschaert, Mark M.
  • Baeumer, Boris

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.

Suggested Citation

  • Bolster, Diogo & Benson, David A. & Meerschaert, Mark M. & Baeumer, Boris, 2013. "Mixing-driven equilibrium reactions in multidimensional fractional advection–dispersion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2513-2525.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:10:p:2513-2525
    DOI: 10.1016/j.physa.2012.12.040
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
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    Cited by:

    1. Zhang, Yong & Sun, HongGuang & Stowell, Harold H. & Zayernouri, Mohsen & Hansen, Samantha E., 2017. "A review of applications of fractional calculus in Earth system dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 29-46.

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