The apparatus for the continuous separation of liquid and relatively fine particles from a liquid slurry includes one or more centrifuge vessels disposed about a longitudinal axis of rotation, and a driver for rotating the centrifuge vessel or vessels. A feed inlet introduces the liquid slurry into each centrifuge vessel, each of which extends at an oblique angle to the axis. A first outlet is provided adjacent to the inner end for the lighter liquid component, and a second outlet is provided adjacent to the outer end for the heavier solid particle component. The inlet of the each centrifuge vessel is preferably located between the first end and the second end, and the second outlet preferably comprises a plurality of solids removal capillary passages connected to a continuous solids removal tube, which can be connected to a source of vacuum to form a vacuum chamber for withdrawing the solids. A supernatant liquid collection chamber is also connected to the first outlet for receiving the supernatant liquid.