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

Jason S. Wexler, Philippe H. Trinh, Helene Berthet, Nawal Quennouz, Olivia Du Roure, Herbert E. Huppert, Anke Linder, Howard A. Stone

Research output: Contribution to journalArticle

30 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)517-544
Number of pages28
JournalJournal of Fluid Mechanics
Volume720
DOIs
StatePublished - Apr 2013

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • Hele-Shaw flows
  • flow-structure interactions
  • microfluidics

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  • Cite this

    Wexler, J. S., Trinh, P. H., Berthet, H., Quennouz, N., Du Roure, O., Huppert, H. E., Linder, A., & Stone, H. A. (2013). Bending of elastic fibres in viscous flows: The influence of confinement. Journal of Fluid Mechanics, 720, 517-544. https://doi.org/10.1017/jfm.2013.49