Wetting of flexible fibre arrays

Abstract

Fibrous media are functional and versatile materials, as demonstrated by their ubiquity both in natural systems such as feathers1,2,3,4 and adhesive pads5 and in engineered systems from nanotextured surfaces6 to textile products7, where they offer benefits in filtration, insulation, wetting and colouring. The elasticity and high aspect ratios of the fibres allow deformation under capillary forces, which cause mechanical damage8, matting5,9 self-assembly10,11 or colour changes12, with many industrial and ecological consequences. Attempts to understand these systems have mostly focused on the wetting of rigid fibres13,14,15,16,17 or on elastocapillary effects in planar geometries18 and on a fibre brush withdrawn from an infinite bath19. Here we consider the frequently encountered case of a liquid drop deposited on a flexible fibre array and show that flexibility, fibre geometry and drop volume are the crucial parameters that are necessary to understand the various observations referred to above. We identify the conditions required for a drop to remain compact with minimal spreading or to cause a pair of elastic fibres to coalesce. We find that there is a critical volume of liquid, and, hence, a critical drop size, above which this coalescence does not occur. We also identify a drop size that maximizes liquid capture. For both wetting and deformation of the substrates, we present rules that are deduced from the geometric and material properties of the fibres and the volume of the drop. These ideas are applicable to a wide range of fibrous materials, as we illustrate with examples for feathers, beetle tarsi, sprays and microfabricated systems.

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Figure 1: Shape transitions of a drop sitting on two parallel fibres.
Figure 2: The three different final states of a drop between two flexible fibres.
Figure 3: Influence of the initial drop volume on the final state.
Figure 4: Aerosol size and fibre matrix properties needed to collect, trap or displace a known volume of liquid.

References

  1. 1

    Rijke, A. M. & Jesser, W. A. The feather structure of dippers: water repellency and resistance to water penetration. Wilson J. Ornithol. 122, 563–568 (2010)

    Article  Google Scholar 

  2. 2

    Rijke, B. Y. A. M. The water repellency and feather structure of cormorants, Phalacrocoracidae. J. Exp. Biol. 48, 185–189 (1968)

    Google Scholar 

  3. 3

    Dawson, C., Vincent, J., Jeronimidis, G., Rice, G. & Forshaw, P. Heat transfer through penguin feathers. J. Theor. Biol. 199, 291–295 (1999)

    CAS  Article  Google Scholar 

  4. 4

    Zi, J. et al. Coloration strategies in peacock feathers. Proc. Natl Acad. Sci. USA 100, 12576–12578 (2003)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Eisner, T. & Aneshansley, D. J. Defense by foot adhesion in a beetle (Hemisphaerota cyanea). Proc. Natl Acad. Sci. USA 97, 6568–6573 (2000)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Liu, K. & Jiang, L. Bio-inspired design of multiscale structures for function integration. Nano Today 6, 155–175 (2011)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Eadie, L. & Ghosh, T. K. Biomimicry in textiles: past, present and potential. An overview. J. R. Soc. Interface 6, 761–775 (2011)

    Article  Google Scholar 

  8. 8

    Kamo, J., Hiram, T. & Kamada, K. Solvent-induced morphological change of microporous hollow fiber membranes. J. Membr. Sci. 70, 217–224 (1992)

    CAS  Article  Google Scholar 

  9. 9

    O’Hara, P. D. & Morandin, L. A. Effects of sheens associated with offshore oil and gas development on the feather microstructure of pelagic seabirds. Mar. Pollut. Bull. 60, 672–678 (2010)

    Article  Google Scholar 

  10. 10

    Pokroy, B., Kang, S. H., Mahadevan, L. & Aizenberg, J. Self-organization of a mesoscale bristle into ordered, hierarchical helical assemblies. Science 323, 237–240 (2009)

    CAS  Article  Google Scholar 

  11. 11

    Chandra, D. & Yang, S. Stability of high-aspect-ratio micropillar arrays against adhesive and capillary forces. Acc. Chem. Res. 43, 1080–1091 (2010)

    CAS  Article  Google Scholar 

  12. 12

    Chandra, D., Yang, S., Soshinsky, A., a & Gambogi, R. J. Biomimetic ultrathin whitening by capillary-force-induced random clustering of hydrogel micropillar arrays. ACS Appl. Mater. Interfaces 1, 1698–1704 (2009)

    CAS  Article  Google Scholar 

  13. 13

    Princen, H. Capillary phenomena in assemblies of parallel cylinders III. Liquid columns between horizontal parallel cylinders. J. Colloid Interface Sci. 34, 171–184 (1970)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Wu, X.-F., Bedarkar, A. & Vaynberg, K. A. Droplets wetting on filament rails: surface energy and morphology transition. J. Colloid Interface Sci. 341, 326–332 (2010)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Bedarkar, A., Wu, X.-f. & Vaynberg, A. Wetting of liquid droplets on two parallel filaments. Appl. Surf. Sci. 256, 7260–7264 (2010)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Minor, F. W., Schwartz, M., Wulkow, E., a & Buckles, L. C. Part III: The behavior of liquids on single textile fibers. Text. Res. J. 29, 940–949 (1959)

    CAS  Article  Google Scholar 

  17. 17

    Keis, K., Kornev, K. G., Kamath, Y. K. & Neimark, A. V. in Nanoengineered Nanofibrous Materials (eds Guceri, S., Gogotsi, Y. G & Kuznetsov, V. ) 173–180 (Kluwer, 2004)

    Google Scholar 

  18. 18

    Kwon, H.-M., Kim, H.-Y., Puëll, J. R. M. & Mahadevan, L. Equilibrium of an elastically confined liquid drop. J. Appl. Phys. 103, 093519 (2008)

    ADS  Article  Google Scholar 

  19. 19

    Roman, B. & Bico, J. Elasto-capillarity: deforming an elastic structure with a liquid droplet. J. Phys. Condens. Matter 22, 493101 (2010)

    CAS  Article  Google Scholar 

  20. 20

    Hubbe, M. A. Bonding between cellulosic fibers in the absence and presence of dry-strength agents - a review. BioResources 1, 281–318 (2006)

    Google Scholar 

  21. 21

    Prakash, M., Quéré, D. & Bush, J. W. M. Surface tension transport of prey by feeding shorebirds: the capillary ratchet. Science 320, 931–934 (2008)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Py, C., Bastien, R., Bico, J., Roman, B. & Boudaoud, A. 3D aggregation of wet fibers. Europhys. Lett. 77, 44005 (2007)

    ADS  Article  Google Scholar 

  23. 23

    Hartung, R. Energy metabolism in oil-covered ducks. J. Wildl. Mgmt 31, 798–804 (1967)

    Article  Google Scholar 

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Acknowledgements

C.D. and H.A.S. acknowledge Unilever and the NFS for financial support. S.P. acknowledges financial support from the Emergence(s) Program of the City of Paris and CNRS and thanks Princeton University for its hospitality. We thank A. Lips and P. Warren for comments.

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Authors

Contributions

C.D. and S.P. designed the experiments; A.Y.B., C.D. and S.P. carried out the experiments; C.D., S.P. and H.A.S. discussed and interpreted the results; C.D. and H.A.S. developed the models; and C.D., S.P. and H.A.S. wrote the manuscript.

Corresponding author

Correspondence to H. A. Stone.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-7 with legends, Supplementary Table 1 and legends for Supplementary Movies 1-3. (PDF 4892 kb)

Supplementary Movie 1

This movie shows the evolution of a drop of volume V = 2 μL on a rail formed by two fibres of length L =3 cm and separated by a distance d0 = 0.76 mm, viewed simultaneously from the side and the top. (MOV 10616 kb)

Supplementary Movie 2

This movie shows the evolution of a drop of volume V = 2 μL on a rail formed by two fibres of length L =4 cm and separated by a distance d0 = 0.76 mm, viewed simultaneously from the side and the top. (MOV 11876 kb)

Supplementary Movie 3

This movie shows the evolution of a drop of volume V = 2 μL on a rail formed by two fibres of length L =3.5 cm and separated by a distance d0 = 0.76 mm, viewed simultaneously from the side and the top. (MOV 9718 kb)

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Duprat, C., Protière, S., Beebe, A. et al. Wetting of flexible fibre arrays. Nature 482, 510–513 (2012). https://doi.org/10.1038/nature10779

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