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

2025/08/06 by Anguiano, María, Suárez-Grau, Francisco J.
#35B27 #35Q35 #76A05 #76A20 #76M50 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.04617

Abstract

In this paper, we derive an extension of the Reynolds law for quasi-Newtonian fluid flows through a thin domain with thickness 0<ε≪ 1 with viscosity obeying the Carreau law without high-rate viscosity, by applying asymptotic analysis with respect to ε. 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.

Citations

• Effective models for generalized Newtonian fluids through a thin porous medium following the Carreau law
• Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary
• Analyse numerique des ecoulements quasi-Newtoniens dont la viscosite obeit a la loi puissance ou la loi de carreau

Related

• Two-dimensional Carreau law for a quasi-newtonian fluid flow through a thin domain with a slightly rough boundary
• Modeling Carreau fluid flows through a very thin porous medium
• Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary
• Effective models for generalized Newtonian fluids through a thin porous medium following the Carreau law
• A thin-film equation for a viscoelastic fluid, and its application to the Landau-Levich problem