Hydrodynamic dispersion of water flowing through porous glasses with nominal pore sizes in the range $40\text{to}160\text{micrometers}$ 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, $⟨Z^2⟩\propto t^{0.84}$, in the absence of hydrodynamic flow to a superdiffusive, almost ballistic power law, $⟨Z^2⟩\propto t^{1.95}$, 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.

• Received 26 May 2006

DOI:https://doi.org/10.1103/PhysRevE.74.066309