A container designed for use as a disposable processing unit in a centrifuge includes first and second chambers connected by a bridge that allows transfer of fluid between the chambers. One of the chambers has a sloped floor that directs fluids to a smaller bottom portion for providing greater depth in the collected fluids. The container also includes cam surfaces that facilitate insertion of the container in a centrifuge in the desired orientation. As well, a key may be provided to ensure that the container is used in the correct centrifuge.
