In previous works, We showed that the spinodal decomposition of low-viscosity liquid mixtures is driven by the convection induced by chemical potential gradients. In this article, we study the impact of this driving force on the phase separation of low-viscosity liquid mixtures in which a strong initial concentration gradient is present within a few-millimeter-thick layer. This region was created by keeping an initially demixed mixture at a higher-than-critical temperature for 0.5 h and allowing it to mix by diffusion. After a deep and rapid quench within the spinodal range. the mixtures at first remained macroscopically unchanged; then micron-sized drops appeared; and finally, after few seconds, a sharp interface suddenly formed with droplet sizes never exceeding 10 mum. As it took hours for diffusion and only seconds for phase separation, this result shows that the latter process cannot be driven by diffusion, This conclusion was reinforced by adding glass particles to the mixture and observing the velocity pattern, which had speeds exceeding 0.5 mm/s, thus demonstrating that the process is driven by convection. The impact of gravity was ruled out, as the morphology of a density-segregated mixture as it phase separates appears to be the same as that of an isodensity mixture. These effects can be explained considering that the large initial concentration gradient induces a body force that drives small drops toward one or the other of the homogeneous phases, where they are rapidly reabsorbed, thus explaining why larger drops were not observed during the separation process. In addition, the measured bulk velocities correlate with the magnitude of the chemical potential gradients, in agreement with the theoretical model.