Mass transport with sorption in porous media

Small-scale models in the form of random walks, combining Gaussian jumps, advection by mean flow field and possibly very long sorbing durations, correspond to experimental data in many porous media, in the laboratory and in the field. Within this frame-work, solutes are observed in two phases, which are mobile and immobile. For such random walks, in the hydrodynamic limit, the densities of that phases are linked by a relationship involving a fractional integral. This implies that the total density of tracer evolves according to a fractional variant of Fourier’s law.