When I worked with centrifuges this was also known as a driven cyclone.
In practice a spinning element within a stationary housing forces heavier material (liquid / solids) toward the outer wall and lighter material (air) towards the center.
For zero g operation the separator shown here would require some modification.
The intake, the air outlet and the liquid / solid discharge would all need cutoff valves.
A helix blade attached to the outside of the spinning tube to direct waste material towards the liquid / solid discharge.
The discharge end itself must be the full diameter of the housing as does the cutoff valve and the storage tank opening.
In practice the inner element (tube / helix) must be spun up first relying on the trapped air from the previous cycle to fill the void while driving any entrapped waste to the outer wall.The air blower would be started next to establish a negative pressure on the air outlet.And finally the cutoff valves can be opened.
To achieve any kind of decent separation these devices must spin at very high speed and do require a considerable amount of energy.