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

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.

💡 Research Summary

The paper investigates how buoyant particles cluster and distribute on the free surface of an open‑channel turbulent flow. Using a recirculating laboratory flume (9.1 m long, 0.6 m wide, 0.7 m deep), the authors released two types of spherical plastic particles—large PETG beads (30 mm diameter, 570 kg m⁻³) and small PP beads (7 mm diameter, 880 kg m⁻³)—under a range of discharge rates, covering a broad span of Reynolds and Froude numbers. High‑speed top‑view video was recorded 6 m downstream of the inlet, and a custom computer‑vision pipeline based on YOLOv8 was employed to detect individual particles and identify clusters (defined as at least two particles in contact).

The central theoretical contribution is the introduction of a dimensionless “clustering Weber number” (We_cl) that quantifies the competition between hydrodynamic drag and inter‑particle capillary attraction. The capillary force is expressed as F_cap = σ D_p f_cap, where σ is water surface tension, D_p the particle diameter, and f_cap a function of inter‑particle distance, contact angle, and Bond number. Drag is approximated as F_D ≈ ρ_w u_² D_p f_drag, with u_ the bed‑shear velocity derived from the measured mean velocity profile using a log‑law. The ratio We_cl = F_D/F_cap reduces to a form that depends only on fluid properties, u_*, σ, and the dimensionless factors f_drag and f_cap, thereby collapsing particle size, density, and wetting characteristics into a single parameter.

Experimental results show a clear monotonic decline of the clustered‑particle fraction χ_cl = (N_total − N_free)/N_total with increasing We_cl. When We_cl ≤ 0.1, χ_cl approaches unity, indicating that virtually all particles belong to compact clusters. As We_cl approaches 1, χ_cl drops sharply, and for We_cl > 1 the system is dominated by hydrodynamic breakup, with less than 60 % of particles remaining in clusters. Remarkably, data from both particle sets collapse onto a single χ_cl–We_cl curve, confirming that the Weber number captures the essential physics regardless of particle size or density.

A secondary focus of the study is the role of large‑scale secondary currents (Prandtl’s second‑kind flows) that arise from the interaction of the sidewalls and the channel bed. These mean cross‑stream circulations were visualized in the experiments and found to drive particles laterally toward the sidewalls, producing asymmetric surface concentration patterns. The authors quantify the lateral extent of the secondary flow (L_w) and demonstrate that, even when We_cl predicts strong clustering, the spatial organization of clusters is governed by the secondary circulation rather than by capillary forces alone.

The paper’s contributions can be summarized as follows: (1) a robust, dimensionless Weber number that predicts the onset of cluster breakup in open‑channel turbulence; (2) a systematic analysis of how particle diameter and density affect We_cl through projected area (drag) and Bond number/weight factor (capillarity); (3) experimental evidence that secondary currents dominate the large‑scale distribution of surface particles, creating preferential accumulation zones independent of the local force balance.

These findings have practical implications for environmental engineering (e.g., predicting the accumulation zones of floating plastic debris in rivers and estuaries), industrial processes involving interfacial particle transport, and the broader field of multiphase flow where surface tension and turbulence interact. By providing a unified scaling framework and highlighting the importance of channel‑scale secondary flows, the work extends capillary‑driven clustering theory from quiescent or quasi‑2‑D layers to realistic three‑dimensional open‑channel turbulence.