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Experimental investigation of three-dimensional motion characteristics of centimeter-sized particles settling in still water
Phys. Rev. Fluids 11, 064301 – Published 8 June, 2026
DOI: https://doi.org/10.1103/ydfl-52yk
Abstract
This study experimentally investigates the three-dimensional settling process of centimeter-sized spherical particles in still water using convergent binocular vision technology. The results reveal that the number of settling particles significantly influences the settling behavior when particles are released side by side. Individual particles initially settle along nearly straight paths before randomly deflecting and returning after reaching maximum deviation points. In contrast, twin particles settle synchronously in an almost mirror-image manner, with random deflection largely suppressed—a phenomenon referred to as the mutual support phenomenon (MSP) is this study. The outermost two particles in triplet and quadruplet configurations also exhibit a typical MSP during the settling process. However, the middle particle in the triplet configuration behaves similarly to an individual particle, while the middle two particles in the quadruplet configuration display more complicated settling trajectories due to asymmetric influences from neighboring particles. Additionally, particle image velocimetry measurements are conducted in specific cases to explore the possible mechanisms underlying the random deflection of individual particles and the MSP observed in twin particles.
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References (37)
- J. L. Deng, X. M. Wang, H. Y. Wang, H. D. Cao, and J. X. Xia, Quantitative description of size and mass distribution of polymetallic nodules in northwest Pacific Ocean basin, Minerals 14, 1230 (2004).
- T. Kuhn and C. Rühlemann, Exploration of polymetallic nodules and resource assessment: A case study from the German contract area in the Clarion-Clipperton zone of the tropical northeast Pacific, Minerals 11, 618 (2021).
- R. Kurose and S. Komori, Drag and lift forces on a rotating sphere in a linear shear flow, J. Fluid Mech. 384, 183 (1999).
- P. P. Brown and D. F. Lawler, Sphere drag and settling velocity revisited, J. Environ. Eng. 129, 222 (2003).
- Q. Zhou and N. S. Cheng, Experimental investigation of single particle settling in turbulence generated by oscillating grid, Chem. Eng. J. 149, 289 (2009).
- G. H. Good, P. J. Ireland, G. P. Bewley, E. Bodenschatz, L. R. Collins, and Z. Warhaft, Settling regimes of inertial particles in isotropic turbulence, J. Fluid Mech. 759, R3 (2014).
- S. Shahi and E. Kuru, Experimental investigation of the settling velocity of spherical particles in power-law fluids using particle image shadowgraph technique, Int. J. Miner. Process. 153, 60 (2016).
- J. Feng, H. H. Hu, and D. D. Joseph, Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation, J. Fluid Mech. 261, 95 (1994).
- G. Gheissary and B. H. A. A. van den Brule, Unexpected phenomena observed in particle settling in non-Newtonian media, J. Non-Newton. Fluid Mech. 67, 1 (1996).
- M. Jenny, J. Dušek, and G. Bouchet, Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid, J. Fluid Mech. 508, 201 (2004).
- C. H. J. Veldhuis and A. Biesheuvel, An experimental study of the regimes of motion of spheres falling or ascending freely in a Newtonian fluid, Int. J. Multiphase Flow 33, 1074 (2007).
- M. Horowitz and C. H. K. Williamson, The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres, J. Fluid Mech. 651, 251 (2010).
- A. F. Fortes, D. D. Joseph, and T. S. Lundgren, Nonlinear mechanics of fluidization of beds of spherical particles, J. Fluid Mech. 177, 467 (1987).
- A. Doostmohammadi and A. M. Ardekani, Interaction between a pair of particles settling in a stratified fluid, Phys. Rev. E 88, 023029 (2013).
- S. M. Dash and T. S. Lee, Two spheres sedimentation dynamics in a viscous liquid column, Comput. Fluids 123, 218 (2015).
- C. C. Liao, W. W. Hsiao, T. Y. Lin, and C. A. Lin, Simulations of two sedimenting-interacting spheres with different sizes and initial configurations using immersed boundary method, Comput. Mech. 55, 1191 (2015).
- L. H. Tsai, C. C. Chang, T. W. Pan, and R. Glowinski, Numerical study of the wall effect on particle sedimentation, Int. J. Comput. Fluid Dyn. 32, 158 (2018).
- D. D. Joseph, Y. J. Liu, M. Poletto, and J. Feng, Aggregation and dispersion of spheres falling in viscoelastic liquids, J. Non-Newton. Fluid Mech. 54, 45 (1994).
- J. Wu and R. Manasseh, Dynamics of dual-particles settling under gravity, Int. J. Multiph. Flow. 24, 1343 (1998).
- C. Cao, S. Chen, J. Li, Z. Liu, L. Zha, S. Bao, and C. Zheng, Simulating the interactions of two freely settling spherical particles in Newtonian fluid using lattice-Boltzmann method, Appl. Math. Comput. 250, 533 (2015).
- D. Nie and J. Lin, Simulation of sedimentation of two spheres with different densities in a square tube, J. Fluid Mech. 896, A12 (2020).
- C. R. Chu, T. R. Wu, Y. F. Tu, S. K. Hu, and C. L. Chiu, Interaction of two free-falling spheres in water, Phys. Fluids 32, 033304 (2020).
- J. Liu, P. Zhang, Y. Xiao, Z. Wang, S. Yuan, and H. Tang, Interaction between dual spherical particles during settling in fluid, Phys. Fluids 33, 013312 (2021).
- C. L. Chiu, C. M. Fan, and C. R. Chu, Numerical analysis of two spheres falling side by side, Phys. Fluids 34, 072112 (2022).
- Y. Xiao, J. Liu, P. Zhang, J. Zhou, D. Liang, Z. Wang, T. Zhang, S. Yuan, and H. Tang, Experimental study of the settling of twin spherical particles released side by side: The impact of particle size, fluid viscosity, initial spacing, and particle density, Int. J. Sediment Res. 38, 83 (2023).
- R. Di Felice, The sedimentation velocity of dilute suspensions of nearly monosized spheres, Int. J. Multiphase Flow 25, 559 (1999).
- W. B. Daniel, R. E. Ecke, G. Subramanian, and D. L. Koch, Clusters of sedimenting high-Reynolds-number particles, J. Fluid Mech. 625, 371 (2009).
- Y. J. Chou, S. H. Gu, and Y. C. Shao, An Euler-Lagrange model for simulating fine particle suspension in liquid flows, J. Comput. Phys. 299, 955 (2015).
- S. Shahi and E. Kuru, An experimental investigation of settling velocity of natural sands in water using particle image shadowgraph, Powder Technol. 281, 184 (2015).
- N. Zhang, W. Zhu, H. He, Y. Lv, and S. Wang, Experimental study on settling velocity of soil particles in dredged slurry, Mar. Geores. Geotechnol. 35, 747 (2017).
- A. J. Petersen, L. Baker, and F. Coletti, Experimental study of inertial particles clustering and settling in homogeneous turbulence, J. Fluid Mech. 864, 925 (2019).
- N. A. Patankar, P. Singh, D. D. Joseph, R. Glowinski, and T. W. Pan, A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow 26, 1509 (2000).
- Z. G. Feng and E. E. Michaelides, The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems, J. Comput. Phys. 195, 602 (2004).
- A. E. Yacoubi, S. Xu, and Z. J. Wang, Computational study of the interaction of freely moving particles at intermediate Reynolds numbers, J. Fluid Mech. 705, 134 (2012).
- D. Nie, J. Lin, and M. Zheng, Direct numerical simulation of multiple particles sedimentation at an intermediate Reynolds number, Commun. Comput. Phys. 16, 675 (2014).
- L. Sun, R. Zhang, Z. W. Zhou, J. F. Yin, and D. D. Meringolo, Influences of particle-particle and particle-wall interactions on the settling behaviors of the centimeter-sized spherical particles, Eur. J. Mech. B. Fluids 115, 204387 (2026).
- Z. Y. Zhang, A flexible new technique for camera calibration, IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330 (2000).
