Passive tracer dispersion in oscillating Poiseuille liquid flows of zero net velocity is studied experimentally in a Hele-Shaw cell and numerically by 2D simulations: this study is particularly focused on the time dependence and local properties of the dispersion. The dispersion mechanism is found to be controlled by the ratio τ m /T of the molecular diffusion time across the gap and the oscillation period (when molecular diffusion parallel to the flow is negligible). The 2D numerical

more »

... s complement the experiments by providing the local concentration c(x, z,t) at a given distance z from the cell walls (instead of only the average over z). Above a time lapse scaling like τ m , the variation of c with the distance x along the flow becomes a Gaussian of width constant with z while the mean distancex may depend both on z and t. For τ m /T 2, the front spreads through Taylor-like dispersion and the normalized dispersivity scales as τ m /T. The front oscillates parallel to the flow with an amplitude constant across the gap; its width increases monotonically at a rate modulated at twice the flow frequency, due to variations of the instantaneous dispersivity. For τ m /T 20, the molecular diffusion distance during a period of the flow is smaller than the gap and the normalized dispersivity scales as (τ m /T) −1 . The oscillations of the different points of the front follow the local fluid velocity: this produces a reversible modulation of the global front width at twice the flow frequency and in quadrature with that in the Taylor-like regime. C 2015 AIP Publishing LLC.