  We investigate the impact of buoyancy on the solute mass transport in an
evaporating liquid mixture (non-volatile solute $+$ solvent) confined in a slit
perpendicular to the gravity. Solvent evaporation at one end of the slit
induces a solute concentration gradient which in turn drives free convection
due to the difference between the densities of the solutes and the solvent.
From the complete model coupling mass transport and hydrodynamics, we first use
a standard Taylor-like approach to derive a one dimensional non-linear
advection-dispersion equation describing the solute concentration process for a
dilute mixture. We then perform a complete analysis of the expected regimes
using both scaling analysis and asymptotic solutions of this equation. The
validity of this approach is confirmed using a thorough comparison with the
numerical resolution of both the complete model and the 1D advection-dispersion
equation. Our results show that buoyancy-driven free convection always impacts
solute mass transport at long time scales, dispersing solutes in a steadily
increasing length scale along the slit. Beyond this confined drying
configuration, our work also provides an easy way for evaluating the relevance
of buoyancy on mass transport in any other microfluidic configuration involving
concentration gradients.
