polymers Communication Average Shear Rates in the Screw Elements of a Corotating Twin-Screw Extruder Bruno Vergnes   Citation: Vergnes, B. Average Shear Rates in the Screw Elements of a Corotating Twin-Screw Extruder. Polymers 2021, 13, 304. https:// doi.org/10.3390/polym13020304 Received: 5 January 2021 Accepted: 18 January 2021 Published: 19 January 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). CEMEF, MINES ParisTech, PSL Research University, UMR CNRS 7635, 06904 Sophia Antipolis, France; bruno.vergnes@mines-paristech.fr Abstract: The rapid estimation of the average shear rate encountered by the material as it flows along the screw elements of a corotating twin-screw extruder is a key point for many applications. In this paper, two methods of evaluation are presented that allow the calculation of the average shear rate as a function of the screw geometry, feed rate, and screw speed. A comparison is made between the approximate and exact methods. It is shown that it is crucial to take into account the shear component due to the pressure flow, especially in the left-handed screw elements. Keywords: twin-screw extruder; screw element; average shear rate 1. Introduction Twin-screw extrusion is a widely used technique with many applications in the field of polymer processing, especially for mixing and compounding applications [1,2]. From an engineering point of view, it is important to be able to rapidly obtain an accurate estimate of the shear rates encountered during flow along the screw elements. Indeed, this allows the correct estimation of significant parameters of the process, such as viscosity, strain, or dissipated power. In the filled sections of the extruder, the flow results from the shear due to the rotation of the screws and the local pressure gradient. If one considers only the screw elements of a corotating intermeshing twin-screw extruder (right-handed or left-handed, a right-handed element has a flight angle such as the screw rotation pushes the material downstream. In contrast, a left-handed element has a flight angle such has the screw rotation pushes the material upstream), the flow conditions are very similar to those in the metering zone of a single-screw extruder [3]. In this case, the average shear rate . γ is usually expressed as [4–8]: . γ = 2π NR 60 h (1) where N is the rotation speed (expressed in rpm), R is the screw radius, and h is the channel depth. This expression means that only the shear flow is considered and the pressure flow is neglected. This assumption is often valid in single-screw extrusion, where pressure gradients are usually low. However, this is no longer the case in twin-screw extrusion, especially in left-handed elements, where values of a few hundred MPa/m are common. It is therefore necessary to include a pressure term in the calculation of the average shear rate. To our knowledge, the literature is rather limited on this subject and only a few papers are available. For example, Mohamed et al. [9] proposed the following expression for a corotating twin-screw extruder: . γ = β 1 N β 2 Q β 3 (2) where Q is the mass flow rate and β 1 , β 2 , and β 3 are constants depending on the screw configuration. If the term Q β 3 allows to consider the effect of pressure, the constants must be determined experimentally, which limits the usefulness of the formulation. Another Polymers 2021, 13, 304. https://doi.org/10.3390/polym13020304 https://www.mdpi.com/journal/polymers