Mathematical modelling of a thin-film flow obeying Carreau's law without high-rate viscosity

TL;DR

This paper develops an asymptotic model for thin-film quasi-Newtonian flows obeying Carreau's law, extending Reynolds law to account for non-Newtonian viscosity effects in very thin domains.

Contribution

It introduces a new asymptotic analysis framework for non-Newtonian thin-film flows with Carreau law viscosity, without high-rate viscosity effects.

Findings

Derived an extended Reynolds law for Carreau fluids in thin domains

Provided insights into non-Newtonian effects on thin-film flow behavior

Established a mathematical framework for future non-Newtonian flow studies

Abstract

In this paper, we derive an extension of the Reynolds law for quasi-Newtonian fluid flows through a thin domain with thickness $0<\varepsilon\ll 1$ with viscosity obeying the Carreau law without high-rate viscosity, by applying asymptotic analysis with respect to $\varepsilon$. This provides a framework for understanding how the non-Newtonian effects and the thickness of the domain (which is significantly smaller than the other dimensions) influence its flow behavior.