A diaphragm pump (also called a Membrane pump) is a positive displacement pump that runs on the mixture of the reciprocating action of a rubber, thermoplastic or teflon diaphragm and suitable valves on either side of the diaphragm
A double diaphragm is a positive displacement pump which utilises two flexible diaphragms that reciprocate backwards and forwards, creating a short-term chamber, which both draws in and expels liquid through the pump. … The two diaphragms that are connected by a shaft through the Air Diaphragm Pump center section where the air valve is situated.
Though this will depend upon the pump and application, a positive displacement pump, is normally a self-priming pump. … For example, air operated diaphragm pumps self-prime 
by creating a pressure differential in the diaphragm chamber. This draws in surroundings and pulls the fluid into the suction port.