Kinematics of Clustering

TL;DR

This paper investigates how inertial particles in fluid flow can cluster due to flow instabilities, deriving criteria for clustering and a universal curve for clustering rates based on experimental and theoretical analysis.

Contribution

It introduces a new instability boundary expression and a universal clustering rate curve for inertial particles in laminar flow.

Findings

Particles cluster when flow Reynolds number exceeds a critical value.

Derived an expression for the instability boundary.

Established a universal curve for clustering rate.

Abstract

The dynamical system for inertial particles in fluid flow has both attracting and repelling regions, the interplay of which can localize particles. In laminar flow experiments we find that particles, initially moving throughout the fluid domain, can undergo an instability and cluster into subdomains of the fluid when the flow Reynolds number exceeds a critical value that depends on particle and fluid inertia. We derive an expression for the instability boundary and for a universal curve that describes the clustering rate for all particles.