For processing matter in a turbulent mass of particulate material, a substantially annular processing region (14; 104; 206) is provided and is preferably in the form of a substantially annular processing chamber having a radially inner wall which includes a waist (38; 122). A flow of fluid and matter to be processed are admitted to the processing region through one or more inlets (28, 46; 108, 124; 214, 220) with the flow of fluid being directed generally circumferentially into the processing region. In the processing region, matter to be processed is embedded in a compact turbulent band of particulate material for processing. Once processing is complete, the processed matter is withdrawn from the processing region, preferably by entrainment in an exhaust flow of the fluid.