An apparatus for contacting and separating at least two immiscible liquids into separate phases, comprising, in combination, a) a vessel having an interior space; b) a shroud positioned vertically within the interior space, the shroud having top and bottom portions and an outer wall enclosing a downward fluid flow path; c) a plurality of vertical hanging fibers defining a vertical axis and being contained in the downward fluid flow path, the fibers configured to allow an admixture of at least two immiscible liquids to contact the hanging fibers and to flow in a downward direction parallel to the vertical axis; d) a disengagement device connected to the bottom portion of the shroud and defining an enhanced coalescing zone, where the disengagement device has one or more openings that are configured to allow a portion of the admixture of liquids to exit the disengagement device following a flow path that is not parallel to the vertical axis; e) a gravity settling zone located in the interior space of vessel but not including the downward fluid flow path, where the gravity settling zone is configured to allow the formation of a lower layer comprising the higher density liquid and the formation of an upper layer comprising the lower density liquid; f) a coalescing surface comprised in the disengagement device that is positioned in or adjacent to the one or more openings,. wherein the coalescing surface is wrapped around or inserted within a support structure having one or more openings, or wherein the disengagement device comprises an annulus having inner and outer walls (22, 21) each having one or more openings and the coalescing surface positioned between the inner and outer walls (22, 21) adjacent to the one or more openings. a) a vessel having an interior space; b) a shroud positioned vertically within the interior space, the shroud having top and bottom portions and an outer wall enclosing a downward fluid flow path; c) a plurality of vertical hanging fibers defining a vertical axis and being contained in the downward fluid flow path, the fibers configured to allow an admixture of at least two immiscible liquids to contact the hanging fibers and to flow in a downward direction parallel to the vertical axis; d) a disengagement device connected to the bottom portion of the shroud and defining an enhanced coalescing zone, where the disengagement device has one or more openings that are configured to allow a portion of the admixture of liquids to exit the disengagement device following a flow path that is not parallel to the vertical axis; e) a gravity settling zone located in the interior space of vessel but not including the downward fluid flow path, where the gravity settling zone is configured to allow the formation of a lower layer comprising the higher density liquid and the formation of an upper layer comprising the lower density liquid; f) a coalescing surface comprised in the disengagement device that is positioned in or adjacent to the one or more openings,. wherein the coalescing surface is wrapped around or inserted within a support structure having one or more openings, or wherein the disengagement device comprises an annulus having inner and outer walls (22, 21) each having one or more openings and the coalescing surface positioned between the inner and outer walls (22, 21) adjacent to the one or more openings.