Boundary Layer for a Non-Newtonian Flow over a Rough Surface

TL;DR

This paper investigates the boundary layer behavior of non-Newtonian shear thinning and thickening fluids over rough surfaces, providing error estimates for wall laws considering small-scale roughness effects.

Contribution

It introduces a mathematical analysis of boundary layer correctors for non-Newtonian flows over rough surfaces, including error estimates in terms of roughness amplitude.

Findings

Derived error estimates for wall laws involving roughness parameter eps

Analyzed boundary layer correctors for shear thinning and thickening fluids

Addressed mathematical challenges from nonlinearity of the flow equations

Abstract

We analyze the effect of a rough surface on shear thinning and shear thickening fluids, modeled by power law stress tensors. The roughness is modeled by a small wavelength and small amplitude oscillation, parametrized by eps. We study the boundary layer corrector near the rough surface, and provide error estimates in terms of eps for the associated wall laws. With regards to previous studies, Mathematical difficulties arise from the nonlinearity of the corrector equations.