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Shell buckling for programmable metafluids


The pursuit of materials with enhanced functionality has led to the emergence of metamaterials—artificially engineered materials whose properties are determined by their structure rather than composition. Traditionally, the building blocks of metamaterials are arranged in fixed positions within a lattice structure1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19. However, recent research has revealed the potential of mixing disconnected building blocks in a fluidic medium20,21,22,23,24,25,26,27. Inspired by these recent advances, here we show that by mixing highly deformable spherical capsules into an incompressible fluid, we can realize a ‘metafluid’ with programmable compressibility, optical behaviour and viscosity. First, we experimentally and numerically demonstrate that the buckling of the shells endows the fluid with a highly nonlinear behaviour. Subsequently, we harness this behaviour to develop smart robotic systems, highly tunable logic gates and optical elements with switchable characteristics. Finally, we demonstrate that the collapse of the shells upon buckling leads to a large increase in the suspension viscosity in the laminar regime. As such, the proposed metafluid provides a promising platform for enhancing the functionality of existing fluidic devices by expanding the capabilities of the fluid itself.

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Fig. 1: Metafluid comprising highly deformable capsules.
Fig. 2: Modelling metafluids.
Fig. 3: Programming metafluids for functionality.
Fig. 4: Harnessing nonlinearity for tunable rheology.

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Data availability

The data that support the findings of this study are openly available in GitHub at


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This research was supported by NSF through the Harvard University Materials Research Science and Engineering Center grant number DMR-2011754, the Fund for Scientific Research-Flanders (FWO) and the European Research Council (ERC starting grant ILUMIS). We thank G. Mckinley and B. Keshavarz and S. Sun for their help with the rheology tests; G. Coupier for the idea of a pressure-driven flow; A. Meeussen, N. Rubin, S. Wei, D. Lim and A. Dorrah for their help with optical experiments; and C. McCann and A. Watkins for comments on the paper.

Author information

Authors and Affiliations



A.D., B.G., B.V.R. and K.B. proposed and developed the research idea. A.D., Y.Y. and A.C. designed and fabricated the centimetre-scale capsules. Y.W. fabricated and characterized the micrometre-scale capsules. A.D. designed and conducted the experiments and optical simulations. B.V.R. conducted the numerical calculations. A.D., B.V.R. and K.B. wrote the paper. K.B., B.G., S.R. and D.W. supervised the research.

Corresponding authors

Correspondence to Benjamin Gorissen or Katia Bertoldi.

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The authors declare no competing interests.

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Peer review information

Nature thanks Thomas Brunet, Corentin Coulais and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary information

Supplementary Information

This file contains Supplementary text, Figs. 1–28, Tables 1 and 2, and References.

Peer Review File

Supplementary Video 1

Pressure–volume curve of a single capsule.

Supplementary Video 2

Pressure–volume curve of the metafluid.

Supplementary Video 3

Smart gripper.

Supplementary Video 4

Interactions with flexible structures.

Supplementary Video 5

Tunable optical properties.

Supplementary Video 6

Pressure-driven flow.

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Djellouli, A., Van Raemdonck, B., Wang, Y. et al. Shell buckling for programmable metafluids. Nature 628, 545–550 (2024).

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