No abstract

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.

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. The flight‐helix had straight sides that more closely emulated rectangular channel theory than the nominal sloped sides of a conventional single screw channel. 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. Comparing the experimental chaotic mixing with theoretical calculations was facilitated by a recently published technique for accurately placing the dye in the extruder channel. Because of the ability to periodically rotate only the flight/helix, the chaotic mixing results are minimally confounded by the existence of Moffatt eddies.

A series of screws were evaluated with regard to their ability to convey two Newtonian fluids with nominal viscosity of 1000 Pa* s at room temperature. Screws with helix angles of 7, 17, 30 and 45 degrees were constructed with a diameter of 50 mm. Screws at several of the angles also had three flight depths. The extruder-screw pump was constructed so that both the screw and barrel could be rotated independently. We will present the data for the screw rotation of 11 screws. The results strongly suggest that the pumping, volumetric output per revolution, of the screw and the barrel are the same regardless of the screw flight height which had a maximum value of about 0.8 thus leaving the core at only 0.2 the barrel diameter. Since pressure back flow is a function of the first power of the flight with and the cube of the flight height, the measured outputs had to be corrected for this in order to calculate the actual screw forwarding ability.

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.