Abstract: A dispenser for dispensing flowable materials and in particular anaerobic materials. This dispenser has a material inlet which allows the flowable material to flow into a pump cylinder, and a material passage through which the flowable material exits the pump cylinder. The material is positively displaced from the pump cylinder by a material displacement assembly of the ball-nut follower-type. A flexible plastic diaphragm which has sufficient porosity to permit oxygen to flow therethrough is biased toward a closed position by a pressurized air supply which applies pressurized air against an outside surface of the diaphragm, enabling the diaphragm to function as a one-way shut-off valve. The diaphragm extends across the material passage formed in the pump cylinder and a material outlet through which the material exits the dispenser.