Influence of local geometry and transition to dispersive regime by mechanical mixing in porous media

We study dispersion without diffusion via mechanical mixing, starting from the early ballistic regime where the mean-square displacement (MSd)<(xi- )2)> proportional to t(2) grows as the elapsed time squared, to the long-time, decoherent, asymptotic regime, where, MSd grows linearly in time. We find in the early time regime, the propagator has a fingerprint of local geometry. The quadratic t(2) term in the MSd may persist if a mechanical parameter aleph, long-range velocity deviation, which characterizes the deviation of the long-range mean velocity seen by each particle from the long-range mean velocity of the entire ensemble, is nonzero. The time dependence of dispersion coefficient, even in absence of diffusion, shows a behavior similar to that found in Telegraph equation for diffusion with drift.