A system is provided for separating a bodily fluid, such as blood, into two or more constituent parts. The system is configured to cooperate with a fluid flow circuit including a spinning membrane-type fluid separation chamber having a housing, with a fluid inlet port and at least one fluid outlet port. A rotor is positioned within the housing so as to define a gap between the rotor and an inside surface of the housing, with the rotor being rotatable relative to the housing about an axis. A membrane is mounted on the rotor and/or on the inside surface of the housing and faces the gap to separate bodily fluid within the housing into two or more constituent parts. The membrane includes an anti-thrombogenic material, which may be either incorporated into the material of the membrane or coated onto at least a portion of the membrane.