Generalized stability theory of polydisperse particle-laden flows. Part1. Channel flow

TL;DR

This paper develops a generalized stability theory for polydisperse particle-laden flows, revealing how particle size distribution and interactions influence flow stability, with implications for various fluid mechanics applications.

Contribution

It introduces a new mathematical framework combining linear stability analysis with a sectional formulation to study polydisperse particle effects on flow stability.

Findings

Polydispersity significantly alters flow stability characteristics.

Large particles tend to stabilize the flow, while small particles can destabilize it.

Flow stability is highly sensitive to particle size distribution and concentration.

Abstract

We present a generalized hydrodynamic stability theory for interacting particles in polydisperse particle-laden flows. The addition of dispersed particulate matter to a clean flow can either stabilize or destabilize the flow, depending on the particles' relaxation time-scale relative to the carrier flow time scales and the particle loading. To study the effects of polydispersity and particle interactions on the hydrodynamic stability of shear flows, we propose a new mathematical framework by combining a linear stability analysis and a discrete Eulerian sectional formulation to describe the flow and the dispersed particulate matter. In this formulation, multiple momentum and transport equations are written for each size-section of the dispersed phase, where interphase and inter-particle mass and momentum transfer are modelled as source terms in the governing equations. A new modal linear stability framework is derived by linearizing the coupled equations. Using this approach, particle-flow interactions, such as polydispersity, droplet vaporization, condensation, and coalescence, may be modelled. The method is validated with linear stability analyses of clean and monodisperse particle-laden flows. We show that the stability characteristics of a channel flow laden with particles drastically change due to polydispersity. While relatively large monodisperse particles tend to stabilize the flow, adding a second size section of a very small mass fraction of low-to-moderate Stokes number particles may significantly increase the growth rates, and for high-Reynolds numbers may destabilize flows that might have been regarded as linearly stable in the monodisperse case. These findings may apply to a vast number of fluid mechanics applications involving particle-laden flows such as atmospheric flows, environmental flows, medical applications, propulsion, and energy systems.