Transport in fractal media: an effective scale-invariant approach

Self-similar Turing patterns: An anomalous diffusion consequence

In this work, we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through diffusion-driven instability. We also find spiral patterns and patterns with mixtures of rotational symmetries. The type of anomalous diffusion discussed in this work, either subdiffusion or superdiffusion, is a consequence of the medium heterogeneity, and it is modeled through a space-dependent diffusion coefficient with a power-law functional form.

Implications of the change in confinement status of a heterogeneous aquifer for scale-dependent dispersion and mass-transfer processes

A series of experimental tracer tests were performed to explore the implications of the change in the pressure status of a heterogeneous bimodal aquifer for scale-dependent dispersion and mass-transfer processes. The sandbox was filled with sands and gravel channels and patches to form an alluvial-like bimodal aquifer. We performed multiple injections of a conservative tracer from 26 different locations of the sandbox and interpreted the resulting depth-integrated breakthrough curves (BTCs) at the central pumping well to obtain a scale-dependent distribution of local and field-integrated apparent longitudinal dispersivity (respectively, α_L^loc and α_L^app). We repeated the experiments under confined (CS) and unconfined (UNS) pressure status, keeping the same heterogeneous configuration. Results showed that α_L^loc(associated with transport through gravel zones) was poorly influenced by the change in aquifer pressure and the presence of channels. Instead, α_L^app(i.e. macrodispersion) strongly increased when changing from CS to UNS. In specific, we found α_L^app≈0.03r for the CS and α_L^app≈0.15r for the UNS (being r the distance from the well). Second-to-fourth-order temporal moments showed strong spatial dependence in the UNS and no spatial dependence in the CS. These results seem consistent with a "vadose-zone-driven" kinetic mass-transfer process occurring in the UNS but not in the CS. The vadose zone enhances vertical flow due to the presence of free surface and large contrasts in hydraulic conductivity triggered by the desaturation of gravel channels nearby the pumping well. The vadose zone enhances vertical mixing between gravel and sands and generates BTC tailing. In the CS vertical mixing is negligible and anomalous transport is not observed.

Fractal continuum model for tracer transport in a porous medium

A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.