Hydrodynamic dispersion at stagnation points: Simulations and experiments

Abstract

The spreading of a passive tracer that is convected back and forth inside a porous medium depends both on the random characteristics of the medium and on the presence of stagnation points. We single out the effect of the latter in the present study of hydrodynamic dispersion in the creeping (low Reynolds number) high P\'eclet number flow around the single stagnation point on a cylindrical obstacle in a Hele-Shaw cell [U. Oxaal, E. G. Flekko/y, and J. Feder, Phys. Rev. Lett. 72, 3514 (1994)]. Employing both experiments and lattice Boltzmann simulations we analyze the dispersive spreading of a single tracer line, which is initially perpendicular to the flow direction and then convected back and forth around the cylinder. The lattice Boltzmann model used is a modification of the recently introduced two-dimensional lattice bathnagar-Gross-Krook model for miscible fluid dynamics [E. G. Flekko/y, Phys. Rev. E 47, 4247 (1993)]. It includes the full three-dimensional viscous interaction in the Hele-Shaw cell, and, in the case of steady state flow, it allows for a freely tunable Reynolds number. The diffusive behavior of the system is explored extensively and excellent agreement between simulations and experiment is observed. A method to determine very small molecular diffusion coefficients D, which relies on the combination of results from experiment and simulation, is proposed. It is demonstrated that there is good agreement between the result of this method and independent measurement that are carried out in the present case of relatively large D values.