A 3D-PTV two-projection study of pre-asymptotic dispersion in porous media which are heterogeneous on the bench scale

Abstract

Velocity fluctuations over evolving scales of motion, on the scale of observation, often lead to anomalous dispersion of conservative tracers in heterogeneous porous media. Recent theories of anomalous dispersion lead to space-time non-local constitutive models for the flux of concentration. We review one such model, which has its foundations in non-equilibrium statistical mechanics. The basic premise is that knowledge of the evolution of the self-part of the intermediate scattering function, G , is all that is required to model the phenomena of interest. We review the basic integro-partial-differential equation that G satisfies and solve the inverse problem to obtain the kernels, and then use these to describe the wave-vector and frequency dependent dispersive process. Subsequently we use this information to study the transition from anomalous to Fickian regime. We also make use of the finite size Lyapunov exponent in the description of the dispersive process. Two-camera, three-dimensional particle tracking velocimetry experiments are undertaken to study dispersion within matched-index porous media. Particle trajectories, mean square displacements, velocity covariance’s, intermediate scattering functions, classical dispersion tensors, wave-vector and frequency dependent generalized dispersion tensors, and the finite-size Lyapunov exponents are obtained. Comparisons are made in the small frequency and small wave vector limits to obtain the transition from pre-asymptotic to asymptotic dispersion.