The invention provides a method and apparatus for continuously feeding wet gel polymers into a drying step of a dry polymer synthesis operation. A number of pistons are arranged having inner chambers through which monomers and other reagents are fed and polymerized into wet gel polymers. Each piston operates according to a coordinated schedule so that as one piston finishes extruding polymer into the drying step, a second piston has completed polymerizing more polymer and continues to feed more polymer without interruption. The then finished is re-fed more reagents so as to be ready again when needed next. As a result, cost effective continuous feeding can be achieved without the contamination and impurity problems that have plagued previous attempts to accomplish this.