Chaotic mixing in a free‐helix extruder using a new solution to the biharmonic equation

Abstract

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 proposed mechanism for solid bed encapsulation: Based on comparing three dimensional andone‐dimensionalscrew melting models

“…[30] The reasons for the limitation of the conventional barrel analysis when compared to the general predictions of the screwrotation analysis were recently discussed in detail. [31] For the tradition barrel rotation analysis, referring to Figure 1, the flow rate analysis is restricted to the z direction channel flow:…”

“…These transformed (moving) reference frame concepts are utilized in the following development: the boundary conditions at the barrel of the flight-helix, V b , which is the velocity of the flighthelix next to the barrel." [31] "An outline of a new single screw melting concept was previewed in 2009 for the typical conventional melting process. [32] This screw rotation model predicted that the solid bed melted due to dissipation and heat transfer in all four melt films surrounding the melting solid bed, as illustrated in Figure 9.…”

“…[ 30 ] The reasons for the limitation of the conventional barrel analysis when compared to the general predictions of the screw‐rotation analysis were recently discussed in detail. [ 31 ] For the tradition barrel rotation analysis, referring to Figure 1, the flow rate analysis is restricted to the z direction channel flow: At constant rotation rate, as H increases V b and thus V bz , the barrel z direction velocity, must be decreased to keep the shear rate consistent relative to the screw core velocity, V sc ( H ). At the limit when H is large enough to force the screw radius to 0, Q will be 0.…”

“…A recent numerical analysis of screw channel flow and Moffatt eddies found that by keeping the barrel interface velocity independent of the channel depth, the results were consistent with those found using Equation (7). These transformed (moving) reference frame concepts are utilized in the following development: the boundary conditions at the barrel of the flight‐helix, V b , which is the velocity of the flight‐helix next to the barrel.” [ 31 ]…”