  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.
