A fluid circuit for cell washing is provided that comprises a spinning membrane separator and a fluid management system comprising a cassette that defines the fluid pathways, and including internally mechanical valving, pressure sensing and air sensing for controlling flow through the fluid pathways, thus minimizing the volume of the fluid circuit. Additionally, the fluid circuit comprises syringes that are acted on by syringe pumps associated with the hardware component of the system to provide pressure for moving fluid through the circuit. Preferably, the syringes are connected directly to the cassette, or formed integrally within the cassette housing, thus further minimizing the volume of the fluid circuit.