A complex network framework for studying particle-laden flows

Studying particle-laden flows is essential for understanding diverse physical processes such as rain formation in clouds, pathogen transmission, and pollutant dispersal. This work introduces a framework of complex networks to analyze the particle dynamics through a Lagrangian perspective. To illustrate this method, we study the clustering of inertial particles (small heavy particles) in Taylor-Green flow, where the dynamics depend on the particle Stokes number (St). Using complex networks, we can obtain the instantaneous local and global clustering characteristics simultaneously. Furthermore, from the complex networks derived from the particle locations, we observe an emergence of a giant component through a continuous phase transition as particles cluster in the flow field, thus providing novel insight into the spatiotemporal dynamics of particles such as the rate of clustering. Finally, we believe that complex networks have a great potential for analyzing the spatiotemporal dynamics of particle-laden flows.