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 as t−(d+α)/αt−(d+α)/α, where dd is the number of spatial dimensions and αα is the fractional derivative exponent.

► We study mixing driven reactions with multidimensional space fractional dispersion. ► Reactions occur in regions precluded by classical Fickian theory. ► Zero reaction zones in Fickian case become maximum reaction for anomalous systems. ► Fractional dispersion changes how quickly mixing and mixing-driven reactions occur.