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

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

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 10, 2513-2525

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.

Keywords: Fractional dispersion; Reactions; Multiple dimensions (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:10:p:2513-2525

DOI: 10.1016/j.physa.2012.12.040

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