Ooh nice:
from the perspective of an inertial frame the case is stationary but the platform and screw are rotating - this is actually a
third configuration. We have now listed:
1. Traditional: "bulk material" and platform and case in the same inertial frame, screw rotating.
2. "New": bulk material, platform, and screw in the same inertial frame, case rotating.
3. "Reelya's crazy newness": case in an inertial frame, the bulk material and platform and screw in the same rotating frame.
I think there are these other two configurations to round it all out:
4. Case, bulk material/platform, and screw all in different rotating frames.
5. Case and screw rotating, bulk material and platform inertial.
Actually number 5 is the same behavior as the traditional. Which is interesting. Which leads me to believe: technically if you have a rotating case with scoops, you don't
need the internal screw at all (although for solid materials it helps a lot). In fact, rotating case with inlet scoops and no screw is a just low performance turbopump.
EDIT: If the case is rotating relative to the bulk material, the scoops create a ram pressure effect due to the relative motion. This pressure is the force that drives the material up the pipe. In this configuration, the "pressure" of the material against the screw is a reaction, it is not the "driving" force - this can be shown by a free body diagram.
EDIT: IMAGES!!! If you "unroll" the screw, you get a wedge.
Traditional screw pump: the wedge moves, creating its own ram pressure to raise the material:
"New" screw pump: the wedge doesn't move, so something has to push the material up the wedge.
When the case is spinning, the "push" for this comes from the ram pressure of the scoop moving.
What these diagrams can't show is that the scoop version can only make pressure in the "wedge" direction by first making pressure in the tangential direction (into or out of the page for these drawings). This tangential motion requires a radial pressure gradient to keep those particles moving in a circle; this pressure gradient is NOT present in the traditional screw, because the motion of the wedge is always in the "wedge" direction - it doesn't need tangential motion.
This is a fun digression