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Wetting of flexible fibre arrays

Nature volume 482, pages 510–513 (2012)Cite this article

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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on the wetting of rigid fibres13,14,15,16,17 or on elastocapillary effects in planar geometries18 and on a fibre brush withdrawn from an infinite bath19.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.

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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.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, 08544, New Jersey, USA

    C. Duprat, A. Y. Beebe & H. A. Stone

  2. CNRS, UMR 7190, Institut Jean le Rond d’Alembert, F-75005 Paris, France,

    S. Protière

  3. UPMC Université Paris 06, UMR 7190, Institut Jean le Rond d’Alembert, F-75005 Paris, France,

    S. Protière

Authors
  1. C. Duprat
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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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