To continuously separate solid matter in a slurry by supplying the slurry contg. solid matter to divided subsections located in the lower part of a solid-liquid separation drum section that is a freely-rotatable annular cylindrical body and passing a liquid fraction of the slurry through a mother liquor permeation section, to subject the slurry to solid-liquid separation and then, conveying the separated solid matter to the outside through a solid matter introduction section.

In this separator, a slurry to be treated is supplied to an intermediate annular space section 5 through a slurry supply section 52 and then allowed to flow downward along the inner peripheral surface of a solid-liquid separation drum section 2 rotating at a low speed and introduced into each of solid-liquid separation divided subsections 23 located in an almost lower part of the solid-liquid separation drum section 2. A liquid fraction of the introduced slurry, namely, a mother liquor is filtered and passed through a mother liquor permeation section 28 and allowed to flow downward to a storage section 41 of a mother liquor receiver 4 and also, immediately thereafter, the separated solid matter is washed with washing water that is supplied from a washing water supply section and sprayed on the solid matter. The washed solid matter remaining on a filter medium in each of the solid-liquid separation divided subsections 23, is moved toward the upper part with the rotation of the solid-liquid separation drum section 2 and then, allowed to fall by its own weight and recovered within a pipe 31 drum of a conveyance section 3 and thereafter, discharged to the next process stage from a discharge port 37 of an outside conveyance part 35.