Fractional constitutive equation (FACE) for non-Newtonian fluid flow: Theoretical description

TL;DR

This paper introduces a fractional constitutive equation (FACE) for modeling non-Newtonian fluid flow, capturing complex behaviors and unifying previous models through fractional order adjustments, with promising preliminary validation.

Contribution

It proposes a novel fractional-order model (FACE) that generalizes existing non-Newtonian flow models and provides analytical tools for complex flow analysis.

Findings

FACE model encompasses previous models as special cases

Preliminary tests show FACE captures shear stress growth accurately

Analytical tools extend standard models for nonlocal velocity effects

Abstract

Non-Newtonian fluid flow might be driven by spatially nonlocal velocity, the dynamics of which can be described by promising fractional derivative models. This short communication proposes a space FrActional-order Constitutive Equation (FACE) that links viscous shear stress with the velocity gradient, and then interprets physical properties of non-Newtonian fluids for steady pipe flow. Results show that the generalized FACE model contains previous non-Newtonian fluid flow models as end-members by simply adjusting the order of the fractional index, and a preliminary test shows that the FACE model conveniently captures the observed growth of shear stress for various velocity gradients. Further analysis of the velocity profile, frictional head loss, and Reynolds number using the FACE model also leads to analytical tools and criterion that can significantly extend standard models in quantifying the complex dynamics of non-Newtonian fluid flow with a wide range of spatially nonlocal velocities.