Mixing-Driven Equilibrium Reactions in Multidimensional Fractional Advection Dispersion Systems.
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 ast-(d+α)/α, wheredis the number of spatial dimensions andαis the fractional derivative exponent.
Environmental Fluid Dynamics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, IN, USA.
Diogo
D
Bolster
David A
DA
Benson
Mm
M
Meerschaert
Boris
B
Baeumer
Fractional Dispersion; Multiple Dimensions; Reactions