Abstract: This invention relates to a method and apparatus for the fractionation of a suspension of finely divided solid particles differing in sedimentation velocity, such as platelets and other blood cells. The separation of, for instance, platelet-rich plasma (PRP) from whole blood is accomplished by centrifuging the blood sample in a bag and by injecting into its outer centrifugal end a volume of saline which displaces the PRP from the blood sample after red cells have been sedimented away from the other end of the bag. The preferred apparatus is designed as a closed system of interconnected bags held in a support made to fit a large centrifuge bucket. The flow of liquid is generated by placing the saline-containing bag closer to the center of rotation while positioning the collection bag at a farthest distance from this center. The discharge of PRP from the separation bag into the collection bag is facilitated by making the inner centrifugal end of the separation bag to collapse in response to centrifugal force.