Abstract: A blood processing system such as a dialysis system may be primed by passing priming solution in a first direction of flow through at least one of the sets, to cause the priming solution to enter an in-line chamber carried by the one set in a flow direction that is retrograde to the normal direction of blood flow through the chamber. Preferably, the in-line chamber carries a filter. Simultaneously, one removes air from the one set through a port. In another, preferably simultaneous step of the process, one passes priming solution in the second, reverse direction of flow to the first direction, through the blood processing unit and connected sets for continuing to remove air from the system through the port, to complete priming of the system.

Abstract: A female tube connector defining a tapered socket having an open, inner end communicating with the lumen of a tube, and a sealing cap proportioned to close the connector and to seal the tapered socket. The sealing cap comprises a cap body and a tapered projection proportioned to sealingly fit within the tapered socket. The projection is carried by the cap body and extends beyond the cap body by a distance to permit the projection to substantially completely occupy the whole length of the tapered socket when the cap is closing the female connector. The projection has an outer surface that carries an antiseptic material, so that upon such closure the interior of the tube connector can be sterilized between uses.