Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors.

We study the evolution of velocity in time, which fundamentally controls the way dissolved substances are transported and spread in porous media. Experiments are conducted that use tracer particles to track the motion of substances in water, as it flows through transparent, 3-D synthetic sandstones. Particle velocities along streamlines are found to be intermittent and strongly correlated, while their probability density functions are lognormal and nonstationary. We demonstrate that these particle velocity characteristics can be explained and modeled as a continuous time random walk that is both Markovian and mean reverting toward the stationary state. Our model accurately captures the fine-scale velocity fluctuations observed in each tested sandstone, as well as their respective dispersion regime progression from initially ballistic, to superdiffusive, and finally Fickian. Model parameterization is based on the correlation length and mean and standard deviation of the velocity distribution, thus linking pore-scale attributes with macroscale transport behavior for both short and long time scales.