The classical theory of high-speed flow1 predicts that a moving rigid object experiences a drag proportional to the square of its speed. However, this reasoning does not apply if the object in the flow is flexible, because its shape then becomes a function of its speed—for example, the rolling up of broad tree leaves in a stiff wind2. The reconfiguration of bodies by fluid forces is common in nature, and can result in a substantial drag reduction that is beneficial for many organisms3,4. Experimental studies of such flow–structure interactions5 generally lack a theoretical interpretation that unifies the body and flow mechanics. Here we use a flexible fibre immersed in a flowing soap film to measure the drag reduction that arises from bending of the fibre by the flow. Using a model that couples hydrodynamics to bending, we predict a reduced drag growth compared to the classical theory. The fibre undergoes a bending transition, producing shapes that are self-similar; for such configurations, the drag scales with the length of self-similarity, rather than the fibre profile width. These predictions are supported by our experimental data.
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We thank F. Vollmer, S. Childress, A. Libchaber and P. Palffy-Muhoray for conversations, and Y.-Q. Xia who assisted in a preliminary experimental study of the fibre/flow system. M.S. thanks A. Goriely, who originally suggested this as an interesting problem. This work was supported by the National Science Foundation and the Department of Energy.
The authors declare that they have no competing financial interests.
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Alben, S., Shelley, M. & Zhang, J. Drag reduction through self-similar bending of a flexible body. Nature 420, 479–481 (2002). https://doi.org/10.1038/nature01232
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