Clustering and surface distributions of buoyant particles in open-channel flows

TL;DR

This work addresses how buoyant particles cluster at air–water interfaces under open-channel turbulence and how their surface distributions form. It develops a force-based framework that balances capillary attraction against flow-induced drag, introducing the clustering Weber number $We_ ext{cl}$ to unify clustering behavior across particle types, with $We_ ext{cl} = F_D/F_ ext{cap}$. Through controlled flume experiments using two buoyant particle sizes, the authors show that clustering strength tracks $We_ ext{cl}$ (strong clusters for $We_ ext{cl}\lesssim 0.1$ and weak clusters beyond $We_ ext{cl} \gtrsim 1$) and that surface patterns are governed by channel-scale secondary currents, with intermediate aspect ratios producing persistent accumulation bands that align with analytical predictions for lateral transport $L_w$. The dual finding—$We_ ext{cl}$ controlling micro-scale aggregation and secondary currents dictating macro-scale distribution—provides a predictive framework linking interfacial physics to open-channel flow structure, with potential applications to predicting floating-particle accumulation in rivers and key industrial settings.

Abstract

This study investigates the clustering behaviour and surface distributions of buoyant particles at the air-water interface in open-channel turbulent flow, focusing on the interplay between capillary attraction, hydrodynamic drag, and flow-driven lateral transport. Using controlled laboratory flume experiments, we systematically examine clustering dynamics for two particle types differing in size and density. To interpret the observed behaviour, we extend capillary-based clustering frameworks to open-channel flows by introducing a dimensionless clustering Weber number (We_cl) that captures the balance between the flow-induced disruptive force and capillary attraction, providing a compact description of the observed clustering behaviour. In addition, we demonstrate that secondary currents play a central role in surface particle transport, producing systematic lateral accumulation that depends on channel aspect ratio. Together, these findings extend capillary-driven clustering theory to open-channel turbulence and reveal secondary currents as a key mechanism controlling particle surface distributions.

Figures (5)

• Figure 1: Clustering regimes in the $We_\mathrm{cl}-\phi$ space for open-channel flows, re-defined from Shin2024DenseInterface.
• Figure 2: Particle clustering in open-channel flows with water depth $H$; $x, y,z =$ streamwise, spanwise, and vertical coordinate: (a) The interaction between two identical spheres influenced by both capillary ($F_\mathrm{cap}$) and drag forces ($F_D$); here, $l$ is the inter-particle distance and $\theta$ is the contact angle; (b) Schematic of secondary currents induced by the corner between the sidewall and bed. Streamlines represent the mean cross-stream circulation. $L_w$ denotes the width over which secondary currents develop from the sidewall toward the channel centre.
• Figure 3: Experimental setup and cluster detection: (a) Flume at the Hydraulic Laboratory, UNSW Canberra. Panels (b) and (c) show $D_{30}$ particles under flow conditions $Fr = 0.11$ and $Fr = 0.34$, respectively. The clustering percentage $\chi_{\mathrm{cl}}$, as defined in $\S$\ref{['Results']}, is $\chi_{\mathrm{cl}} = 0.97$ (b) and $\chi_{\mathrm{cl}} = 0.85$ (c). Detected clusters are pseudo-coloured for clarity.
• Figure 4: Clustering behaviour of buoyant particles: (a) Weber number $We_\mathrm{cl}$ as a function of the fraction of clustered particles $\chi_{\mathrm{cl}}$ for $D_{30}$ and $D_{7}$ particles; the solid curve is an empirical fit to the combined dataset; (b) Weber number $We_\mathrm{cl}$ as a function of particle diameter $D_p$ and density ratio $\rho_p/\rho_f$ for $q= 0.11$ m$^2/s$ and $Fr = 0.34$; the contact angle is taken as $\theta = 95^\circ$.
• Figure 5: Surface distributions of buoyant plastics: (a) Ensemble-averaged surface count of buoyant particles ($D_7$) for an intermediate channel aspect ratio $B/H = 4.3$; colours indicate the number of particle detections per surface grid cell, with red regions corresponding to persistent accumulation zones; (b) Comparison between calculated and measured $L_w$, normalized by the respective water depth $H$.