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Aerodynamic interactions of drops on parallel fibres

Nature Physics volume 19, pages 1667–1672 (2023)Cite this article

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Abstract

The wetting behaviour of drops on rigid and elastic fibres is important in many applications including textiles, fog collection, systems with absorbent fibres, and in natural settings such as spiderwebs. Yet, little is known about the behaviour of fibre-attached drops when exposed to a background air flow. Additionally, control of drop motion and coalescence with neighbouring drops remains a challenge. Here we show that in the presence of a uniform air flow, drops wetting parallel fibres can interact aerodynamically, both with their downstream and upstream neighbours. These interactions can lead to a variety of behaviours, including alignment, repulsion and coalescence. Using particle-image velocimetry, we visualize the wake patterns and explain the alignment and coalescence behaviours based on the interactions between the wakes and drops. We obtain a diagram of the different interaction regimes, depending on the distance between the fibres. Finally, we apply this knowledge to realize controlled drop coalescence.

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Fig. 1: Drops on parallel fibres align when exposed to air flow perpendicular to the fibres.
Fig. 2: Drops can influence their downstream neighbours.
Fig. 3: Fixed drops can influence their upstream motile neighbours.
Fig. 4: Controlling collective drop motion with air flow.

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Data availability

An extended version of the videos and datasets used to support this study is available at Zenodo (https://doi.org/10.5281/zenodo.8003261).

Code availability

The MATLAB scripts used to support this study are available at Zenodo (https://doi.org/10.5281/zenodo.8003261).

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Acknowledgements

We acknowledge L. Martinelli for designing and printing fairings for the angle brackets, P. Kaneelil for rendering the zither in SolidWorks and D. Hoffman for help with wind tunnel upgrades. We thank ExxonMobil for partial support of the research via a grant to the Andlinger Center for Energy and the Environment at Princeton University. L.D. and M.A.E. were supported by the Metropolis Initiative at Princeton University.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ, USA

    Jessica L. Wilson, Amir A. Pahlavan, Martin A. Erinin, Camille Duprat, Luc Deike & Howard A. Stone

  2. Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, USA

    Amir A. Pahlavan

  3. LadHyX, CNRS, Ecole polytechnique, Institut polytechnique de Paris, Palaiseau, France

    Camille Duprat

  4. High Meadows Environmental Institute, Princeton University, Princeton, NJ, USA

    Luc Deike

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  1. Jessica L. Wilson
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Contributions

J.L.W., A.A.P. and H.A.S. conceived of the project. J.L.W. and A.A.P. designed the overall study. J.L.W. built the experimental apparatus and performed the experiments. M.A.E. assisted J.L.W. with PIV experiments. J.L.W., A.A.P., M.A.E., L.D. and C.D. analysed the data. J.L.W. wrote the manuscript with the help of A.A.P., M.A.E., C.D., L.D. and H.A.S. All authors reviewed the manuscript.

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Correspondence to Howard A. Stone.

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The authors declare no competing interests.

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Nature Physics thanks Wilko Rohlfs and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–10, Discussion and Tables 1 and 2.

Supplementary Video 1

Multiple drops on multiple fibres align in the presence of a uniform air flow (U ≈ 2.4 m s−1). The drops are approximately 1.4 mm in diameter and the fibres are 2b = 127 μm in diameter. Fibres are spaced 2.7 D apart.

Supplementary Video 2

A motile drop aligns with a fixed drop on the front fibre in the presence of a uniform air flow (U ≈ 2.4 m s−1). The drops are approximately 1.4 mm in diameter and the fibres are 2b = 127 μm in diameter. Fibres are spaced 14.5 D apart.

Supplementary Video 3

A motile drop aligns with a fixed drop on the front fibre in the presence of a uniform air flow (U ≈ 2.4 m s−1). The drops are approximately 1.4 mm in diameter and the fibres are 2b = 127 μm in diameter. Fibres are spaced 2.7 D apart.

Supplementary Video 4

A motile drop is repelled by a fixed drop on the front fibre in the presence of a uniform air flow (U ≈ 2.4 m s−1). The drops are approximately 1.4 mm in diameter, and the fibres are 2b = 127 μm in diameter. Fibres are spaced 1.6 D apart.

Supplementary Video 5

A motile drop aligns with a fixed drop on the back fibre in the presence of a uniform air flow (U ≈ 2.4 m s−1). The drops are approximately 1.4 mm in diameter, and the fibres are 2b = 127 μm in diameter. Fibres are spaced 2.7 D apart.

Supplementary Video 6

A motile drop takes no notice of a fixed drop on the back fibre in the presence of a uniform air flow (U ≈ 2.4 m s−1). The drops are approximately 1.4 mm in diameter, and the fibres are 2b = 127 μm in diameter. Fibres are spaced 4.9 D apart.

Supplementary Video 7

At intermediate fibre spacings, a motile drop on the front fibre can exhibit a variety of behaviours in the presence of a fixed drop on the back fibre. Here the motile drop turns around in the vicinity of the fixed drop. The drops are approximately 1.4 mm in diameter and the fibres are 2b = 127 μm in diameter. Fibres are spaced 4.4 D apart.

Supplementary Video 8

A fixed drop on the front fibre can induce coalescence of drops on the back fibre in the presence of a uniform air flow (U ≈ 2.9 m s−1). The fibres are 2b = 511 μm in diameter. Fibres are spaced 2.1 D apart.

Supplementary Video 9

Without a fixed drop on the front fibre, coalescence of drops on the back fibre does not occur. U ≈ 2.9 m s−1. The fibres are 2b = 511 μm in diameter. Fibres are spaced 2.1 D apart.

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Wilson, J.L., Pahlavan, A.A., Erinin, M.A. et al. Aerodynamic interactions of drops on parallel fibres. Nat. Phys. 19, 1667–1672 (2023). https://doi.org/10.1038/s41567-023-02159-4

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