A device for separating immiscible fluids of different densities from an emulsion containing at least one liquid, comprising a longitudinal rotary drum having a longitudinal axis of rotation, and in which the drum comprises, internally, longitudinally from upstream to downstream and between at least one upstream inlet and a number of downstream outlets (49, 72): a solid body rotation stage having at least one chamber, inside which is arranged at least one longitudinal inner partition for causing circumferential solid body rotation delimiting at least one flow space communicating with said inlet; a migration and coalescence stage having at least one chamber, inside which is arranged at least one longitudinal interior partition for causing circumferential solid body rotation, delimiting a plurality of longitudinal flow channels exhibiting respectively one upstream extremity communicating with said flow space of said solid body rotation stage and one downstream extremity connected to said outlets, said partition comprising at least one longitudinal partition delimiting at least one of said longitudinal channels and extending as far as said downstream extremity; and an extraction stage comprising at least one liquid overflow comprising an overflow edge turned facing towards said axis of rotation and extending along a longitudinal flow space communicating, upstream, with said longitudinal channels of the migration and coalescence stage via at least one longitudinal passageway, and comprising, downstream, a downstream liquid discharge space communicating with the longitudinal flow space and connected to one of said downstream outlets; in which the said upstream inlet discharges into a section of the flow space of the solid body rotation stage situated close to the axis of rotation; and in which the drum is equipped with a radial interior wall separating the chamber of the solid body rotation stage and the chamber of the migration and coalescence stage, said radial interior wall being provided with through passageways. a solid body rotation stage having at least one chamber, inside which is arranged at least one longitudinal inner partition for causing circumferential solid body rotation delimiting at least one flow space communicating with said inlet; a migration and coalescence stage having at least one chamber, inside which is arranged at least one longitudinal interior partition for causing circumferential solid body rotation, delimiting a plurality of longitudinal flow channels exhibiting respectively one upstream extremity communicating with said flow space of said solid body rotation stage and one downstream extremity connected to said outlets, said partition comprising at least one longitudinal partition delimiting at least one of said longitudinal channels and extending as far as said downstream extremity; and an extraction stage comprising at least one liquid overflow comprising an overflow edge turned facing towards said axis of rotation and extending along a longitudinal flow space communicating, upstream, with said longitudinal channels of the migration and coalescence stage via at least one longitudinal passageway, and comprising, downstream, a downstream liquid discharge space communicating with the longitudinal flow space and connected to one of said downstream outlets; in which the said upstream inlet discharges into a section of the flow space of the solid body rotation stage situated close to the axis of rotation; and in which the drum is equipped with a radial interior wall separating the chamber of the solid body rotation stage and the chamber of the migration and coalescence stage, said radial interior wall being provided with through passageways.