HYDRODYNAMIC DISPERSION AT STAGNATION POINTS - SIMULATIONS AND EXPERIMENTS

The spreading of a passive tracer that is convected back and forth ins ide a porous medium depends both on the random characteristics of the medium and on the presence of stagnation points. We single out the eff ect of the latter in the present study of hydrodynamic dispersion in t he creeping (low Reynolds number) high Peclet number how around the si ngle stagnation point on a cylindrical obstacle in a Hele-Shaw cell [U . Oxaal, E. G. Flekkoy, and J. Feder, Phys. Rev. Lett. 72, 3514 (1994) ]. Employing both experiments and lattice Boltzmann simulations we ana lyze the dispersive spreading of a single tracer line, which is initia lly perpendicular to the how direction and then convected back and for th around the cylinder. The lattice Boltzmann model used is a modifica tion of the recently introduced two-dimensional lattice Bhatnagar-Gros s-Krook model for miscible fluid dynamics [E. G. Flekkoy, Phys. Rev. E 47, 4247 (1993)]. It includes the full three-dimensional viscous inte raction in the Hele-Shaw cell and, in the case of steady state how, it allows for a freely tunable Reynolds number. The diffusive behavior o f the system is explored extensively and excellent agreement between s imulations and experiment is observed. A method to determine very smal l molecular diffusion coefficients D, which relies on the combination of results from experiment and simulation, is proposed. It is demonstr ated that there is good agreement between the result of this method an d independent measurements that are carried out in the present case of relatively large D values.