We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling for the growth of the mixing region, which was observed in recent two-dimensional simulations. To this purpose, we use a Hele-Shaw cell. The flow configuration consists of a heavy fluid layer overlying a lighter fluid layer, initially separated by a horizontal, flat interface. When small perturbations of concentration and velocity fields occur at the interface, convective mixing is eventually produced: Perturbations grow and evolve into large finger-like convective structures that control the transition from the initial diffusion-dominated phase of the flow to the subsequent convection-dominated phase. As the flow evolves, diffusion acts to reduce local concentration gradients across the interface of the fingers. When the gradients become sufficiently small, the system attains a stablystratified state and diffusion is again the dominant mixing mechanisms. We employ an optical method to obtain high-resolution measurements of the density fields, and we perform experiments for values of the RayleighDarcy number (i.e., the ratio between convection and diffusion) sufficiently large to exhibit all the flow phases just described, which we characterize via the mixing length, a measure of the extension of the mixing region. We are able to confirm that the growth of the mixing length during the convection-dominated phase follows the superlinear scaling predicted by previous simulations.
