Instability of particulate pipe flow

TL;DR

This paper analyzes the linear stability of particle-laden pipe flow, showing that particle distribution can induce instabilities consistent with experimental observations.

Contribution

It extends previous stability analysis by incorporating inhomogeneous particle distributions, revealing their impact on flow stability.

Findings

Inhomogeneous particle distributions can cause flow instabilities.

The model's predictions align with experimental flow regimes.

Preferential particle positioning influences flow stability.

Abstract

We present linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles two-way coupled to the fluid velocity field via Stokes drag (Saffman 1962). We extend previous analysis in a channel (Klinkenberg et al. 2011) to allow for the initial distribution of particles to be inhomogeneous and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability at experimentally realistic parameters. The results are compared to the experimental work of Matas et al. (2004a) and are shown to be consistent with the reported flow regimes.