Nonlinear flow response of soft hair beds

Abstract

We are ‘hairy’ on the inside: beds of passive fibres anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. These hairs are soft enough to deform in response to stresses from fluid flows. Yet fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem that is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear-driven Stokes flows. We characterize this system with a theoretical model that accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers towards the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter that controls nonlinear behaviour. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps.

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Figure 1: Physical model of deformable hair beds coupled to low-Reynolds-number fluid flows.
Figure 2: Reconfiguration of beds of straight hairs.
Figure 3: The reconfiguration regime of straight hairs is characterized by a negative Vogel exponent.
Figure 4: Angled hairs break reflection symmetry, both in geometry as well as in drag response.
Figure 5: The reconfiguration regime of angled hairs is characterized by a Vogel exponent that can attain positive values when flow is against the grain.

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Acknowledgements

We thank A. Nasto, A. Helal, A. Gopinath, K. Hood and B. Keshavarz for insightful discussions; K. Broderick for fabrication assistance; F. Frankel for photography of hairs; and S. Lin for tensiometry experiment. A.E.H. acknowledges support from the Defense Advanced Research Projects Agency and US Army Research Office under grant numbers DARPA W31P4Q-13-1-0013 and ARO W911NF-15-1-0166. J.A. acknowledges support the US Army Research Office under grant number W911NF-14-1-0396.

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J.A., J.C. and A.E.H. conceived the project. J.A. performed experiments. J.A., J.C. and E.d.L. contributed to theoretical models. All authors contributed to the paper.

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Correspondence to A. E. Hosoi.

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Alvarado, J., Comtet, J., de Langre, E. et al. Nonlinear flow response of soft hair beds. Nature Phys 13, 1014–1019 (2017). https://doi.org/10.1038/nphys4225

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