After quenching a partially miscible, initially homogeneous, critical liquid mixture to a temperature T deeply below its critical point of miscibility, we observed the formation of rapidly coalescing droplets, whose size grows linearly with time, thus indicating that the phase separation process is driven by convection. Eventually, when their size reaches a critical length, which is roughly equal to one-tenth of the capillary length, the nucleating drops start sedimenting and the two phases rapidly segregate by gravity. This behavior was observed for both densitysegregated and quasi-isopycnic systems, showing that gravity cannot be the driving force responsible for the enhancement of the coalescence among the nucleating drops. This result is in line with previous theoretical works based on the diffuse interface model, predicting that the phase separation of low-viscosity liquid mixtures is a convection-driven process, induced by a body force which is proportional to the chemical potential gradients. Finally, at later times, following the evolution of isolated drops of the secondary emulsion, we saw that their size grows in time like t(1/3).