Poiseuille flow for a simplified pseudoplastic rheology

TL;DR

This paper analyzes steady and transient Poiseuille flow in cylindrical and planar geometries using a simplified pseudoplastic rheology model with shear thinning behavior, providing analytical solutions and numerical comparisons.

Contribution

It introduces analytical steady state solutions and numerical transient analysis for pseudoplastic flow with constant viscosity plateaus, enhancing understanding of shear thinning effects.

Findings

Velocity profiles are quasi-plug like with boundary layer shear thinning.

Steady state is reached after the momentum diffusion timescale.

Transient development matches steady state theory in the long-term limit.

Abstract

Poiseuille flow in cylindrical and planar geometries with a simplified, pseudoplastic (shear thinning) rheology characterized by constant viscosity plateaus above and below a transition strain rate is considered. Analytical, steady state solutions for velocity profile and volume flux are formulated. Transient flow development is addressed numerically and compared to the theory in the steady state limit. Stationary flow is approached after the momentum diffusion timescale based on the spatially dominant kinematic viscosity. For large viscosity ratio and shear thinning region confined near the domain boundary, velocity distributions are quasi-plug like with large boundary to interior strain rate ratio.