The invention provides systems, methods, and articles useful in the production of foams, and, in particular microcellular foams. The systems include a restriction element that reduces the backflow of polymer melt in an extruder while polymeric material is injected into a mold or ejected from a die. The restriction element is positioned upstream of a blowing agent injection port to maintain the solution of polymer and blowing agent in the extruder above a minimum pressure throughout an injection or ejection cycle, and preferably above the critical pressure required for the maintenance of a single-phase solution of polymer and blowing agent. The systems can be used in injection molding, blow molding, or in any other processing techniques that include injection or ejection cycles. In some embodiments, the systems utilize reciprocating screws for injection or ejection. In other embodiments, the systems include an accumulator connected to an outlet of the extruder, in which a plunger moves to inject polymeric material into a mold or eject polymeric material from a die.