Sub- and superdiffusive molecular displacement laws in disordered porous media probed by nuclear magnetic resonance

Hydrodynamic dispersion of water flowing through porous glasses with nominal pore sizes in the range 40 to 160 micrometers was studied with the aid of a pulsed gradient nuclear magnetic resonance technique compensating for coherent flow velocities. The crossover from effectively subdiffusive mean square displacement, proportional variant t0.84, in the absence of hydrodynamic flow to a superdiffusive, almost ballistic power law, proportional, variant t1.95, at the highest flow rates was observed. At intermediate flow rates, a gradual conversion between these two limiting power laws occurs. As a function of the Péclet number, the effective dispersion coefficient is in accordance with a power law with an exponent 1.2.