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

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

33 Citations (Scopus)

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
Pages (from-to)517-544
Number of pages28
JournalJournal of Fluid Mechanics
Volume720
DOIs
Publication statusPublished - Apr 2013

Keywords

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

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    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