Skip to main content

Transport and buckling dynamics of an elastic fibre in a viscous cellular flow

  • N. Quennouz (a1), M. Shelley (a2), O. du Roure (a1) and A. Lindner (a1)

We study, using both experiment and theory, the coupling of transport and shape dynamics for elastomeric fibres moving through an inhomogeneous flow. The cellular flow, created electromagnetically in our experiment, comprises many identical cells of counter-rotating vortices, with a global flow geometry characterized by a backbone of stable and unstable manifolds connecting hyperbolic stagnation points. Our mathematical model is based upon slender-body theory for the Stokes equations, with the fibres modelled as inextensible elastica. Above a certain threshold of the control parameter, the elasto-viscous number, transport of fibres is mediated by their episodic buckling by compressive stagnation point flows, lending an effectively chaotic component to their dynamics. We use simulations of the model to construct phase diagrams of the fibre state (buckled or not) near stagnation points in terms of two variables that arise in characterizing the transport dynamics. We show that this reduced statistical description quantitatively captures our experimental observations. By carefully reproducing the experimental protocols and time scales of observation within our numerical simulations, we also quantitatively explain features of the measured buckling probability curve as a function of the effective flow forcing. Finally, we show within both experiment and simulation the existence of short and long time scales in the evolution of fibre conformation.

Corresponding author
Email addresses for correspondence:,
Hide All
Attia, R., Pregibon, D. C., Doyle, P. S., Viovy, J.-L. & Bartolo, D. 2009 Soft microflow sensors. Lab on a Chip 9 (9), 12131218.
Becker, L. & Shelley, M. 2001 The instability of elastic filaments in shear flow yields first normal stress differences. Phys. Rev. Lett. 87, 198301.
Goto, S., Nagazono, H. & Kato, H. 1986 The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions. II. Capillary flow. Rheol. Acta 25, 246256.
Gray, J. 2001 Cell Movements: From Molecules to Motility. Garland.
Johnson, R. E. 1980 An improved slender-body theory for Stokes flow. J. Fluid Mech. 99, 411431.
Kantsler, V. & Goldstein, R. E. 2012 Fluctuations, dynamics, and the stretch–coil transition of single actin filaments in extensional flows. Phys. Rev. Lett. 108 (3), 038103.
Keller, J. & Rubinow, S. 1976 Slender-body theory for slow viscous flow. J. Fluid Mech. 75, 705714.
Lindner, A. & Shelley, M. 2014 Elastic fibers in flows. In Fluid–Structure Interactions at Low Reynolds Numbers (ed. Duprat, C. & Stone, H. A.), Royal Society of Chemistry.
Manikantan, H. & Saintillan, D. 2013 Subdiffusive transport of fluctuating elastic filaments in cellular flows. Phys. Fluids 25, 073603.
Quennouz, N.2013 Deformation and transport of an elastic filament in a viscous cellular flow. PhD thesis, UPMC, Paris, France.
Rusconi, R., Lecuyer, S., Autrusson, N., Guglielmini, L. & Stone, H. A. 2011 Secondary flow as a mechanism for the formation of biofilm streamers. Biophys. J. 100 (6), 13921399.
Rusconi, R., Lecuyer, S., Guglielmini, L. & Stone, H. A. 2010 Laminar flow around corners triggers the formation of biofilm streamers. J. R. Soc. Interface 7 (50), 12931299.
Tornberg, A.-K. & Shelley, M. 2004 Simulating the dynamics and interactions of elastic filaments in Stokes flows. J. Comput. Phys. 196, 840.
Wandersman, E., Quennouz, N., Fermigier, M., Lindner, A. & du Roure, O. 2010 Buckled in translation. Soft Matt. 6, 57155719.
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. J. Fluid Mech. 720, 517544.
Young, Y.-N. & Shelley, M. 2007 A stretch–coil transition and transport of fibers in cellular flows. Phys. Rev. Lett. 99, 058303.
Zirnsak, M. A., Hur, D. U. & Boger, D. V. 1994 Normal stresses in fibre suspensions. J. Non-Newtonian Fluid Mech. 54, 153193.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 9
Total number of PDF views: 99 *
Loading metrics...

Abstract views

Total abstract views: 281 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th March 2018. This data will be updated every 24 hours.