A Quasi-Analytical Solution for "Carreau-Yasuda-like" Shear-thinning Fluids Flowing in Slightly Tapered Pipes

TL;DR

This paper develops a quasi-analytical solution for Carreau-Yasuda-like shear-thinning fluids flowing in slightly tapered pipes, providing a new analytical approach for complex non-Newtonian fluid flow in industrial applications.

Contribution

It introduces the first quasi-analytical solution for Carreau-Yasuda-like fluids in tapered pipes, combining order-of-magnitude analysis with inertial neglect.

Findings

Derived analytical expressions validated by numerical methods

Applied to extrusion bioprinting process

Enhanced understanding of shear-thinning fluid flow in tapered geometries

Abstract

This paper presents a quasi-analytical framework for "Carreau-Yasuda-like" fluids with a viscosity characterized by two constant plateau at low and high shear rates connected by a shear-thinning branch, and flowing in slightly tapered pipes. This setup is common in research and industrial applications since the last century, by assuming both a Newtonian or a non-Newtonian inelastic behaviour. Nevertheless, an analytical solution for "Carreau-Yasuda-like" fluids is still lacking. The expressions have been derived by using the order-of-magnitude analysis and neglecting the inertial terms in the momentum balance equations. The analytical solutions are employed to an extrusion bioprinting process as an application example, and verified through numerical procedures.