Modeling Shear-Thinning Flow in Twin-Screw Extrusion Processes

Abstract

Background/Objective: Hot-melt extrusion has been established as a formulation strategy for various pharmaceutical applications. However, tailoring the screw configuration is a major challenge where 1D modeling is utilized. This usually requires specific screw parameters, which are rarely noted in the literature, especially when dealing with shear-thinning formulations. Methods: Therefore, a custom-made test rig was used to assess the behavior of various conveying and kneading elements using Newtonian silicon oil and shear-thinning silicon rubber. The pressure and the power were measured as a function of volume flow. A model was proposed characterizing the screw element behavior by six individual parameters A1, A2, A3, B1, B2, B3. Results: The experimental results regarding the behavior with respect to Newtonian fluids were in good agreement with the literature and were modeled in accordance with the Pawlowski approach. In terms of shear-thinning fluids, the influence of screw speed on pressure and power was quantified. An evaluation framework was proposed to assess this effect using two additional parameters. Based on a high number of repetitive measurements, a confidence interval for the individual screw parameters was determined that is suitable to highlight the differences between element types. Conclusions: Finally, geometrical screw parameters for Newtonian and shear-thinning flow were assessed and modeled, with three conveying and three kneading elements characterized.

Keywords: A and B parameters; mechanistic modeling; one-dimensional modeling; screw characteristics; shear thinning; twin-screw extruder.

Figure A1

Flow curves for the rheological characterization by dynamic viscosity over shear rate for silicone oil (left, linear y-axis), silicone rubber (center, logarithmic y-axis), and HEC solution (right, logarithmic y-axis).

Figure 1

Schematic of a 1D model for an entire extrusion process. A generic screw configuration with various elements is given at the top and the graphical representation of pressure, power, viscosity, temperature, degree of filling, and residence time is shown below [20].

Figure 2

Schematic of pressure characteristic (left) and power characteristic (right) for Newtonian flow behavior (black lines) and shear-thinning flow (colored lines). Determination of the dimensionless parameters $\left({\mathrm{A}}_1,{\mathrm{A}}_2,{\mathrm{B}}_1,{\mathrm{B}}_2\right)$ is based on the axis intercepts. The process regimes are classified as back conveying (orange), active conveying (green), over conveying (light yellow), and high over conveying (dark yellow). The arrows represent an increase in screw speed $\left(\mathrm{n}\right)$ [6].

Figure 3

Schematic of the extrusion screw test rig for the characterization of pressure and power. Vertically arranged twin screws with probes for speed, torque, temperature, pressure, and mass flow. The volume flow is adjusted by the die diameter.

Figure 4

Common types of screw elements of a twin-screw extruder: conveying elements with a pitch of 20 $\mathrm{m}\mathrm{m}$ (left) and a kneading element with a staggering angle of 30° (right), including relevant geometric parameters like the outer diameters $\left({\mathrm{d}}_{\mathrm{a}}\right)$, inner diameter $\left({\mathrm{d}}_{\mathrm{i}}\right)$, length $\left(\mathrm{l}\right)$, pitch, and staggering angle $\left(\mathsf{\alpha }\right)$.

Figure 5

Measured dimensionless pressure (left) and power (right) characteristics for conveying elements with a pitch of 20 mm (top), 30 mm (center), and 40 mm (bottom) for shear-thinning flow (colored symbols) with silicone rubber and Newtonian flow (gray stars) with silicone oil. The lines represent the model (Equations (9) and (10)). The arrows represent an increase in screw speed $\left(\mathrm{n}\right)$.

Figure 6

Linearized Equation (11) for pressure (left) and linearized Equation (12) for power (right) characteristics for the determination of the characteristic shear parameters as the slope of the origin lines. Exemplary for the conveying element GFA-30.

Figure 7

Measured dimensionless pressure (left) and power (right) characteristics for kneading elements with a staggering angle of 30° (top) or 60° (bottom) for shear-thinning flow (colored symbols) with silicone rubber and Newtonian flow (gray stars) with silicone oil. The lines represent the models (Equations (9) and (10)). The arrows represent an increase in screw speed $\left(\mathrm{n}\right)$.

Figure 8

Mass flow (black lines) and specific dissipated mechanical energy (SDME) (red/orange lines) as a function of screw speed for typical die diameters (2, 3, 4 $\mathrm{m}\mathrm{m}$). Conveying elements (pitches: 20, 30 and 40 $\mathrm{m}\mathrm{m}$) (left) and kneading elements (staggering angles: 30, 60, and 90°) (right). SDME_overrun of KB-90 (orange lines) with overrun throughput of KB-60.