We present a general theoretical framework designed to interpret the effect of centrifugation of ternary fluids that exhibit weak aggregation. The model includes a buoyancy term with thermodynamic description given by a Flory-Huggins model of ternary systems containing a hydrotrope. The system octanol-ethanol-water used as a numerical example is one of several ternary systems that exhibit dynamic aggregates even far from the critical point and undergo a spontaneous emulsification upon dilution with water (Ouzo effect). The model proposes an explanation from first principles of an increased responsiveness to the centrifugal fields. We illustrate the usage of this system in intensified extraction efficiency of hydrophobic solutes that is at the basis of the dispersive liquid-liquid extraction, and show that its capabilities can be extended from analytical to continuous preparative extraction.