Reversible and Irreversible Tracer Dispersion in an Oscillating Flow Inside a Model Rough Fracture

Abstract

We study the mixing dynamics of a dyed and a clear miscible fluid by an oscillating flow inside an Hele-Shaw cell with randomly distributed circular obstacles. A transparent setup allows us to analyze the distribution of the two fluids and the reversible and irreversible mixing components. At the lower Péclet numbers Pe (based on the averaged absolute fluid velocity), geometrical dispersion due to the disordered flow field between the obstacles is dominant: the corresponding dispersivity is constant with Pe and, at constant Pe, increases with the amplitude of the oscillations and is negligible at small ones. Compared to echo dispersion with only one injection–suction cycle, oscillating flows are shown to provide additional information when the number of oscillations and, as a result, the distance of transverse mixing are varied. Geometrical dispersion is dominant up to a limiting Pe increasing with the amplitude. At higher Pe′s, the results are similar to those of Taylor dispersion in cells with smooth walls.