I am unable to find it again but I once heard of a type of air pump that involved a pair of offset archimedes screws inside a cylinder. The point of the device was that as the screws would turn against eachother it encapsulated air into pockets (like how a centrifugal fan would) but then these pockets would compress their contents as the screws turned against eachother. What was this pump called?
If the screws look like a pair of thick and long interlocking archimedes screws, then the device is called a rotary screw compressor. You can think of it as a special case of a roots blower, where the interlocking lobes on the lobe shafts possess a spiral twist.
By making the lobe depth progressively shallower along the length of the screws, the working fluid gets progressively compressed as it makes its way from the inlet end to the outlet end of the screws.
Rotary screw compressors are used where a continuous, high flow rate of compressed air or gas is needed. They are available in typical ratings of five horsepower and larger. For smaller compressors, conventional reciprocating piston types are used instead.
If you instead feed compressed gas into the outlet end of a rotary screw compressor, it acts like a turbine, extracting expansion work from the compressed gas and forcing the screws to rotate.