Apparatus and a method for the provision of TNP therapy to a wound are described, the apparatus comprising: a sealing membrane for covering a wound to from a wound cavity; one end of an aspirant conduit operably associated with the wound cavity; vacuum means provided at a distal end of the aspirant conduit for applying a vacuum to the wound cavity; and, air bleed means in fluid communication with the wound cavity. Various embodiments of air bleed port members are also described.