Abstract: A screw extruder (10) having a barrel (18) which has a bore (26) defining an inner surface (44) and one or more extruder screws (28), positioned within the bore (26). The extruder screw or screws (28) include a central shaft (34) and one or more screw flights (30). The extruder screw or screws (28) farther including one or more dispersive mixing elements (204), (234), (308), (406), (508), (558), which interact with the inner surface of the barrel (44) to form one or more progressively narrowing passages (46) through which material is forced into multiple regions of high elongational and shear stress (480, (120), (214), (310), (410), (510), (564).A second preferred embodiment is a screw extruder (10) having a barrel (18) having a bore (26) defining an inner surface (44) and one or more extruder screws (600), (701), positioned within the bore (26).