Pump having flexible liner and compounding apparatus having such a pump

A pump has a flexible liner which is expanded and contracted by application of positive and negative fluid pressure for receiving and discharging fluent material. The liner is received in a rigid shell which defines the maximum volume received. In discharging fluent material, a vacuum is applied to one side of the liner, while applying pressure to the other side so the liner is collapsed against the rigid shell. The liner is arranged so as to be the only part of the pump which contacts the fluent material, and is replaceable to effect rapid and easy cleaning of the pump. The liner has multiple pump cells which can expand and contract for moving fluent material through the pump cell. The pump cells can be sized and arranged so that by selection of particular pump cells which receive the fluent material, precise volumes can be metered by the pump.