Flow of a shear-thinning fluid in a rectangular duct

TL;DR

This paper presents an accurate numerical solution for steady laminar shear-thinning fluid flow in rectangular ducts, revealing how rheology and geometry independently influence flow characteristics and enabling universal scaling laws.

Contribution

The study provides the first detailed numerical analysis of Carreau fluid flow in rectangular ducts, deriving universal formulas for pressure gradient and friction factor considering rheological and geometric effects.

Findings

Pressure gradient correlates with Carreau number following rheological curves.

Fluid rheology and duct aspect ratio independently affect flow characteristics.

Universal scaling laws for pressure gradient and friction factor are established.

Abstract

We address the problem of steady laminar flow of a shear-thinning fluid in rectangular ducts, which is encountered in many systems, in particular, in microfluidic and biomedical devices. However, an exact solution for the flow of non-Newtonian fluids that considers a realistic shear-thinning rheological behavior is not available in the literature. In this study, an accurate solution for the case of Carreau fluid is obtained and investigated numerically. The numerical solution allows us to analyze the effects of the fluid rheology and the aspect ratio of the rectangular duct on the velocity field and pressure gradient that drives the flow. The relationship between the pressure gradient and the Carreau number is found to follow the rheological curve of the shear-thinning fluid. The analysis shows that the fluid rheology and the aspect ratio have independent contributions to the integral flow characteristics. Moreover, separate consideration of these contributions allows us to arrive at universal scaling and general formulae for the pressure gradient and friction factor for various rheological parameters of the fluid and aspect ratios of rectangular ducts.