Fractured and porous media are in general heterogeneous across scales ranging from the pore to regional and global scales. Spatial heterogeneity is key for the understanding of the dynamics of flow, transport and reaction processes. The heterogeneity impact on transport has traditionally been quantified in terms of dispersion. From pore to Darcy-scale, this refers to hydrodynamic dispersion, from Darcy to regional scale, macrodispersion. Dispersion quantifies the impact of small scale velocity fluctuations on solute transport, in analogy to Brownian motion, in which molecular-scale thermal fluctuations of particle velocities are quantified through a constant diffusion coefficient. Deviations from the dispersion paradigm manifest, for example, in the non-Fickian evolution of plume widths, forward and backward tails of spatial concentration distributions, heavy tails of solute breakthrough curves, and anomalous reaction and mixing behaviors. Here we provide a view on these phenomena that revolves around mixing or rather incomplete mixing and the notion of local physical non-equilibrium. We first review the characteristics of physical equilibrium in terms of Lagrangian and Eulerian transport frameworks and its breakdown in the presence of spatial heterogeneity. Then we discuss the causes and mechanisms of mixing and anomalous behaviors in heterogeneous media, and the scale-dependent breakdown of local equilibrium.
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