Abstract: Multi-stage pneumatic conveying apparatus for separating materials and associated systems and methods are described herein. The pneumatic conveying apparatus can include an inner barrel, an outer barrel, a hopper, a screw and a nose cone. The inner barrel can include inner baffles on its outer surface. The outer barrel can accommodate the inner barrel and include outer baffles on its inner surface. The hopper can include an opening in fluid communication with the inner barrel and can receive materials into the inner barrel. The screw conveyor assembly can be within the inner barrel and transport materials toward the outer barrel. The nose cone can include a plurality of nose cone components on its inner surface. The materials can be transported from the outer barrel to the nose cone via air flow from an external source.