### Combinatorial effects of kneading elements on twin-screw compounding

One of the biggest advantages provided by twin-screw extrusion is the high degree of customization that it affords for screw design. Screws are composed of individual screw elements that together make up one screw configuration.^{1} Among the multitude of different elements used, kneading blocks—one of the most commonly employed mixing elements—are made up of stacked discs or paddles of varying thickness that are staggered at an offset angle.

To determine the effect of paddle thickness on the mixing process, we studied two types of kneading blocks. These are made up of discs with either wide or narrow thickness stacked at 45° (the standard stacking angle for double-flighted twin-screw extruders). The wide discs are approximately three times the thickness of the narrow kneading blocks (4.8 vs. 1.6mm). In twin-screw compounding, base polymers are mixed with additives and fillers to introduce material properties that enhance their performance for specific applications. Efficient mixing, which can be decomposed into two parts—distributive and dispersive mixing—is crucial for maximizing these enhancements. Distributive mixing, a function of strain, controls the spread of the minor phase throughout the polymer matrix.^{2} Dispersive mixing, on the other hand, is a function of stress, and breaks down agglomerates that form due to cohesive forces.^{3, 4}

We have developed an inline methodology that enables the characterization of residence stress distribution (RSD), thereby making it possible to measure dispersive-mixing efficiency.^{5–7} Our methodology is centered on polymeric stress beads that rupture and release an encapsulated dye at a specified critical stress, which is determined by wall thickness and particle size. Using this encapsulated dye, we are able to measure a residence time distribution (RTD) representing 100% bead breakup. An estimate of the percent rupture (percentage of broken stress beads) can be determined by dividing the area underneath the RSD curve by the area underneath the RTD curve: see Figure 1.

Figure 1.

Using a design of experiment approach, we employed a central composite design (CCD) grid to gain statistical insight into the percent rupture rate of the polymeric stress beads (see Figure 2). In addition, the CCD grid allows for the creation of a predictive equation for the rupture rate as a function of significant operating parameters on a 95% confidence interval. The general form of the predictive equation can be seen in Equation 1.

where*C*is the intercept (offset of percent breakup),

*A*is the sensitivity associated with the screw speed,

*N*is the screw speed in RPM,

*B*is the sensitivity associated with specific throughput, and

*Q*is the mass flow rate. The percent breakup is a function of only two parameters (screw speed and specific throughput), which determine the axes on our CCD grids. It should be noted that the

*N*and the

*Q*/

*N*variables in the equation do not refer to the conditions of the tests, but rather the coordinates on the CCD grid.

Figure 2.

We compared screw configurations that use a certain mixing section length (made up of 24mm kneading blocks) with a second configuration that had double the mixing section length (48mm). Furthermore, we made a second comparison between hybrid geometries (those with both wide and narrow kneading blocks) to study the effect that the ordering has on the dispersive mixing performance. The percent rupture rate data for the narrow-screw configurations with mixing-section lengths of 48 and 24mm can be seen in Figure 3(a) and (b), respectively. Figure 3(c) shows the rate for the narrow-wide hybrid geometry, in which the narrow kneading blocks are upstream of the wide kneading blocks. For more detailed pictures of the screw configurations, please see Figure 4.

Figure 3.

Figure 4.Table 1.

Screw geometry | Intercept | Screw speed (N) | Specific throughput (Q/N) | Geometry factor | R^{2} |
---|---|---|---|---|---|

Narrow 48 | 65.49 | 2.83 | 2.67 | – | 0.92 |

Wide 48 | 75.56 | 4.33 | 3.17 | – | 0.99 |

Combined | 70.5 | 3.58 | 2.92 | −4.94 (Narrow 48) | 0.96 |

Screw geometry | Intercept | Screw speed (N) | Specific throughput (Q/N) | Geometry factor | R^{2} |
---|---|---|---|---|---|

Narrow 24 | 37.11 | 3.42 | 1.42 | – | 0.96 |

Wide 24 | 41.78 | 3.08 | 2.25 | – | 0.96 |

Combined | 39.5 | 3.25 | 1.75 | −2.72 | 0.96 |

(Narrow 24) | 0.96 |

Screw geometry | Intercept | Screw speed (N) | Specific throughput (Q/N) | Geometry factor | R^{2} |
---|---|---|---|---|---|

Narrow-Wide 48 | 66.44 | 2.42 | 2.92 | – | 0.99 |

Certain trends can be observed in all of the CCD grids. Analysis of Figure 3(a) and (b) shows that the 48mm mixing section causes the breakage of a greater percentage of stress beads than the 24mm section, with 1.7 times greater efficacy overall. Subsequent increases to the length result in a linear relationship between mixing-section length and percentage breakup. Tables 1–3 show the predictive equation results for all CCD grids that we tested. These equations corroborate the near-linear trend that occurs in the CCD grids when the mixing-section length is doubled, as is shown by the increase in the intercept value. Lastly, the narrow-wide geometry shows a greater similarity to the narrow-48mm configuration than to the wide-48mm mixing section. Although research from the RSD perspective on these hybrid geometries is only just beginning, our results indicate that the permutation of the kneading blocks represents a configuration change capable of causing significant differences in dispersive mixing.

The RSD inline methodology that we have developed represents a reliable technique for characterizing the dispersive-mixing performance of screw geometry. In addition to comparing screw geometries, this methodology also analyzes operating conditions at a quantitative statistical level. In future work, we will look to explore more complex geometries, scalability, and material properties.

## Authors

## References

- C. Rauwendaal,
**Twin Screw Extruder**1^{st}ed. ed., pp. 458-460, Hanser, New York, 1986. ch. 10, sec. 2 - I. Manas-Zloczower,
**Mixing and Compounding of Polymers: Theory and Practice**2^{nd}ed. ed., Hanser, Munich, 2009. - A. Scurati, D. L. Feke and I. Manas-Zloczower,
*Analysis of the kinetics of agglomerate erosion in simple shear flows*,**Chem. Eng. Sci.****60**(23), pp. 6564-6573, 2005. - C. Rauwendaal,
*Mixing in extrusion*,**Proc. SPE ANTEC**, pp. 85-99, 2002. - D. Bigio, W. Pappas, H. Brown II, B. Debebe and W. Dunham,
*Residence stress distributions in twin screw extruders*,**Proc. SPE ANTEC**, pp. 1382-1386, 2011. - D. I. Bigio, M. Wetzel, G. M. Fukuda, R. Adnew, J. Kim and B. Bhatia,
*Residence stress distribution study using a robust design of experiment approach*,**Proc. SPE ANTEC**, pp. 1095-1102, 2013. - G. Fukuda, B. Dryer, J. Webb, D. I. Bigio, M. Wetzel and P. Andersen,
*Combinatorial effects of kneading elements on mixing in twin-screw compounding*,**SPE ANTEC**, 2015.

**DOI:** 10.2417/spepro.005941