Non-Newtonian rheology in a capillary tube with varying radius

TL;DR

This paper investigates the complex non-linear flow behavior of yield stress fluids in capillary tubes with varying radius, focusing on the yield pressure drop and flow rate under different bubble injection scenarios.

Contribution

It introduces a detailed analysis of yield pressure drop statistics and mean flow rates for non-Newtonian fluids in variable-radius capillaries with bubble injection.

Findings

Flow is absent below a finite yield pressure drop.

Singular behavior occurs above the yield pressure.

Mean flow rates depend on bubble injection patterns.

Abstract

The flow through a capillary tube with non-constant radius and where bubbles of yield stress fluid are injected is strongly non-linear. In particular below a finite yield pressure drop, $P_y$, flow is absent, while a singular behaviour is expected above it. In this paper we compute the yield pressure drop statistics and the mean flow rate in two cases: (i) when a single bubble is injected, (ii) when many bubbles are randomly injected in the fluid.