Cluster formation in particle-laden flows is a continuous phase transition

TL;DR

This study reveals that particle clustering in flows undergoes a continuous phase transition, characterized by network measures, with transition timing depending on the Stokes number, providing new insights into flow dynamics.

Contribution

First application of complex networks to analyze spatiotemporal clustering in particle-laden flows, revealing phase transition behavior related to Stokes number.

Findings

Network measures characterize local and global clustering.

Emergence of a giant component indicates a phase transition.

Transition time follows a power law and exponential relation with Stokes number.

Abstract

Studying particle-laden flows is essential to understand diverse physical processes such as rain formation in clouds, pathogen transmission, and pollutant dispersal. Distinct clustering patterns are formed in such flows with particles of different inertia (characterized by Stokes number St). For the first time, we use complex networks to study the spatiotemporal dynamics in such flows. We simulate particles in a 2D Taylor-Green flow and show that the network measures characterize both the local and global clustering properties. As particles cluster into specific patterns from a randomly distributed initial condition, we observe an emergence of a giant component in the derived network through a continuous phase transition. Further, the phase transition time is identified to be related to the Stokes number through a power law for St < 0.25 and an exponential function for St in the range 0.25 to 1. Our findings provide novel insights into the clustering phenomena in particle-laden flows.