Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-10T14:32:40.419Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  25 March 2015

N. Quennouz ,
M. Shelley ,
O. du Roure  and
A. Lindner
N. Quennouz
Affiliation:
Physique et Mécanique des Milieux Hétérogènes UMR7636 ESPCI-CNRS-Université Pierre et Marie Curie-Université Paris Diderot-10 rue Vauquelin F-75005 Paris, France
M. Shelley*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
O. du Roure*
Affiliation:
Physique et Mécanique des Milieux Hétérogènes UMR7636 ESPCI-CNRS-Université Pierre et Marie Curie-Université Paris Diderot-10 rue Vauquelin F-75005 Paris, France
A. Lindner
Affiliation:
Physique et Mécanique des Milieux Hétérogènes UMR7636 ESPCI-CNRS-Université Pierre et Marie Curie-Université Paris Diderot-10 rue Vauquelin F-75005 Paris, France
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Slender-body theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 769 , 25 April 2015 , pp. 387 - 402
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Attia, R., Pregibon, D. C., Doyle, P. S., Viovy, J.-L. & Bartolo, D. 2009 Soft microflow sensors. Lab on a Chip 9 (9), 1213–1218.Google Scholar
Becker, L. & Shelley, M. 2001 The instability of elastic filaments in shear flow yields first normal stress differences. Phys. Rev. Lett. 87, 198301.Google Scholar
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, 246–256.Google Scholar
Gray, J. 2001 Cell Movements: From Molecules to Motility. Garland.Google Scholar
Johnson, R. E. 1980 An improved slender-body theory for Stokes flow. J. Fluid Mech. 99, 411–431.Google Scholar
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.CrossRefGoogle ScholarPubMed
Keller, J. & Rubinow, S. 1976 Slender-body theory for slow viscous flow. J. Fluid Mech. 75, 705–714.Google Scholar
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.Google Scholar
Manikantan, H. & Saintillan, D. 2013 Subdiffusive transport of fluctuating elastic filaments in cellular flows. Phys. Fluids 25, 073603.Google Scholar
Quennouz, N.2013 Deformation and transport of an elastic filament in a viscous cellular flow. PhD thesis, UPMC, Paris, France.Google Scholar
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), 1392–1399.CrossRefGoogle ScholarPubMed
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), 1293–1299.Google Scholar
Tornberg, A.-K. & Shelley, M. 2004 Simulating the dynamics and interactions of elastic filaments in Stokes flows. J. Comput. Phys. 196, 8–40.Google Scholar
Wandersman, E., Quennouz, N., Fermigier, M., Lindner, A. & du Roure, O. 2010 Buckled in translation. Soft Matt. 6, 5715–5719.Google Scholar
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, 517–544.Google Scholar
Young, Y.-N. & Shelley, M. 2007 A stretch–coil transition and transport of fibers in cellular flows. Phys. Rev. Lett. 99, 058303.Google Scholar
Zirnsak, M. A., Hur, D. U. & Boger, D. V. 1994 Normal stresses in fibre suspensions. J. Non-Newtonian Fluid Mech. 54, 153–193.Google Scholar