Laboratory investigation of lateral dispersion within dense arrays of randomly distributed cylinders at transitional Reynolds number

Relative (effective) lateral dispersion of a passive solute was examined at transitional Reynolds numbers within a two-dimensional array of randomly distributed circular cylinders of uniform diameter d. The present work focuses on dense arrays, for which previously developed theory [Y. Tanino and H. M. Nepf, J. Fluid Mech. 600, 339 (2008)] implies that the asymptotic (long-time/long-distance) dispersion coefficient, when normalized by the mean interstitial fluid velocity, u, and d, will only exhibit a weak dependence on Reynolds number, Re-d equivalent to ud/nu, where nu is the kinematic viscosity. However, the advective distance required to reach asymptotic dispersion is expected to be controlled by pore-scale mixing, which is strongly Re-d-dependent prior to the onset of full turbulence. Laser-induced fluorescence was used to measure the time-averaged lateral concentration profiles of solute released continuously from a point source in arrays of solid volume fraction phi=0.20 and 0.35 at Re-d=48-120. Results are compared to previous measurements at higher Re-d. Lateral dispersion reaches the same rate as asymptotic dispersion in fully turbulent flow at x approximate to 154d at (phi,Re-d)=(0.20,110-120) and at x approximate to 87d at (phi,Re-d)=(0.35,300-390). In contrast, dispersion does not reach the fully turbulent flow limit at Re-d < 100 within the range of x considered. Also, concentration profiles deviate further from a Gaussian distribution at phi=0.35 than at 0.20 for similar Re-d and x phi/d. From these observations, it can be inferred that the pre-asymptotic regime extends farther downstream, in terms of the number of cylinders spanned, at lower Re-d and at larger phi.