  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 stably-stratified 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 Rayleigh-Darcy 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.
