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) )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.