The Flow of Newtonian and power law fluids in elastic tubes

TL;DR

This paper derives analytical formulas for the flow of Newtonian and power law fluids in elastic tubes, validating them through asymptotic analysis and comparison with Navier-Stokes-based models.

Contribution

It introduces new analytical expressions for non-Newtonian fluid flow in elastic tubes using a lubrication approximation, expanding existing models.

Findings

Derived formulas match qualitative flow trends.

Quantitative convergence to limiting cases.

Comparison confirms consistency with Navier-Stokes models.

Abstract

We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially-dependent characteristic shape for the given rheology and cross sectional size. Two pressure-area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting cases. The Newtonian formulae are compared to similar formulae derived previously from a one-dimensional version of the Navier-Stokes equations.