Static stability of collapsible tube conveying non-Newtonian fluid

TL;DR

This paper investigates the static stability of a collapsible tube conveying non-Newtonian fluid using a quasi one-dimensional model, analyzing how fluid rheology affects stability through numerical methods.

Contribution

It introduces an analytical condition for instability in a non-Newtonian fluid conveying system and explores the influence of fluid rheology on stability.

Findings

Nonuniqueness of the boundary value problem indicates static instability.

The analytical instability condition defines a surface in parameter space.

Fluid rheology significantly influences the stability of the collapsible tube.

Abstract

The global static stability of a Starling Resistor conveying non-Newtonian fluid is considered. The Starling Resistor consists of two rigid circular tubes and axisymmetric collapsible tube mounted between them. Upstream and downstream pressures are the boundary condition as well as external to the collapsible tube pressure. Quasi one-dimensional model has been proposed and a boundary value problem in terms of nondimensional parameters obtained. Nonuniqueness of the boundary value problem is regarded as static instability. The analytical condition of instability which defines a surface in parameter space has been studied numerically. The influence of fluid rheology on stability of collapsible tube is established.