Semi-analytical models for non-Newtonian fluids in tapered and cylindrical ducts, applied to the extrusion-based additive manufacturing

In this paper, mathematical models aiming at describing the fluid flow of non-Newtonian fluids inside ducts with both convergent and cylindrical sections have been formulated. The theory has been implemented for the description of industrially interesting fluids such as moisture-cured silicones and thermoplastics, which are well described by the Carreau and Cross-Williams-Landel-Ferry (Cross-WLF) rheological models, respectively. The viscous flow in a die has been considered, comparing the results with Computational Fluid Dynamics (CFD) solutions extracted through the Finite Element Method (FEM) software Comsol Multiphysics. The agreement with numerical data is very good, showing the potential for next experimental applications in predicting some very important and useful quantities, such as the extrusion force, which is critical for a wide range of 3D printing processes. The novelty relies in the general applicability of the theoretical models to viscous flows, no matter what its rheological behaviour is.