In an embodiment, axially-fed slurry can be continuously separated into clarified liquid, stripped gas, and thickened sludge in radial counterflow between counter-rotating coaxial centrifugal impellers. One impeller comprises an annular crossflow filter through which liquids are extracted. At the periphery of the impellers, where they are narrowly separated, the sludge is shear thickened into an extruded paste. Suspended solids in the feed pass over the surface of the rotating annular crossflow filter by the shear lift effect, and the vortex-wall interaction jets water radially inward from the periphery, dewatering the sludge. Evolved gases, oils, and fractions lighter than water flow radially inward to the impeller axis through radial vortices in a shear layer between the impellers, and are extracted through an axial exhaust conduit. Feed has long residence time so that separation is complete and continuous. Municipal wastewater, produced water, beverages, food, and scrubber sludge are discussed.