Oscillations in a flexible channel flow of a generalized Newtonian fluid

TL;DR

This paper investigates oscillatory behaviors in the flow of generalized Newtonian fluids through a flexible channel, revealing how fluid rheology and membrane stress influence flow stability and complexity.

Contribution

It introduces a combined analytical and numerical approach to study flow oscillations in a flexible channel with non-Newtonian fluids, highlighting the effects of rheology and membrane tension.

Findings

Flow oscillations depend on fluid rheology and membrane stress.

Shear-thinning fluids can exhibit oscillatory or chaotic flow.

Flow behavior varies significantly with Reynolds number and membrane tension.

Abstract

We study the flow of a generalized Newtonian fluid, characterized by a power-law model, through a channel consisting of a wall with a flexible membrane under longitudinal tension. It is assumed that at steady state the flow through the channel admits a constant flux unidirectional flow profile, while for the unsteady case, we employ the long wave approximation and use a set of reduced equations to describe the variation of the shape of the membrane (assumed to be massless and elastic) and the variation of the fluid-flux. By means of asymptotic expansion, multiscale analysis and full numerical solutions of the pertinent governing equations, we show that depending upon the Reynolds number and the membrane stress, the flow behaviour for a shear-thinning, shear-thickening and Newtonian fluid may be markedly different, being oscillatory for one while chaotic for the other. The results presented herein hold practical relevance for several biologically relevant processes involving transport of rheologically complex biofluids through flexible domains.