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Bending of elastic fibres in viscous flows: the influence of confinement

  • Jason S. Wexler (a1) (a2), Philippe H. Trinh (a3), Helene Berthet (a2), Nawal Quennouz (a2), Olivia du Roure (a2), Herbert E. Huppert (a4) (a5), Anke Lindner (a2) and Howard A. Stone (a1)...
Abstract

We present a mathematical model and corresponding series of microfluidic experiments examining the flow of a viscous fluid past an elastic fibre in a three-dimensional channel. The fibre’s axis lies perpendicular to the direction of flow and its base is clamped to one wall of the channel; the sidewalls of the channel are close to the fibre, confining the flow. Experiments show that there is a linear relationship between deflection and flow rate for highly confined fibres at low flow rates, which inspires an asymptotic treatment of the problem in this regime. The three-dimensional problem is reduced to a two-dimensional model, consisting of Hele-Shaw flow past a barrier, with boundary conditions at the barrier that allow for the effects of flexibility and three-dimensional leakage. The analysis yields insight into the competing effects of flexion and leakage, and an analytical solution is derived for the leading-order pressure field corresponding to a slit that partially blocks a two-dimensional channel. The predictions of our model show favourable agreement with experimental results, allowing measurement of the fibre’s elasticity and the flow rate in the channel.

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Corresponding author
Email addresses for correspondence: jwexler@princeton.edu, anke.lindner@espci.fr, hastone@princeton.edu
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The original version of this article was published with A. Lindner’s name incorrectly spelled. A notice detailing this has been published and the error rectified in the online PDF and HTML copies.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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