A recently published approach for modeling the cross flow in an extruder channel using a new solution to the biharmonic equation is utilized in a study of chaotic mixing in a free helix single screw extruder. This novel extruder was designed and constructed with the screw flight, also referred to as the helix, detached from the screw core. Each of the screw elements could be rotated independently to obtain chaotic motion in the screw channel. Using the new extruder, experimental evidence for the increased mixing of a dye, for both a Dirac and droplet input, with a chaotic flow field relative to the traditional residence time distribution is presented. These experimental results are compared using the new biharmonic equation-based model. Because of the ability to periodically rotate only the flight/helix, the chaotic mixing results are minimally confounded by the existence of Moffat eddies.