A new analytical solution for the biharmonic equation was developed for single screw extrusion cross-channel fluid mechanical flow. This analysis led to a quantitative model for residence time distribution when combined with the historic solutions of the drag and pressure flow in the rectangular channel in the single-screw extruder. The focus of the theoretical and experimental investigation here was to examine how closely the new analytical solution correlated with experimental residence time data for a free-helix extruder. This new extrusion device was operated as both a conventional extruder and a more positive displacement device by using only helix rotation as the pump. The Moffatt eddies that occur in the quiescent corners of the rectangular channel with screw rotation were found to have a strong effect on the residence time of the extruder. Because there were no quiescent corners for the free-helix flow there was essentially no residence time tail for this mode of extruder displacement. The theoretical results for a sheet of dye spanning the screw channel width and dye "blobs" were compared with experimental results for both modes of operation. In all cases, the experiments and the theory predictions were essentially consistent.