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Oscillations of confined fibres transported in microchannels

Published online by Cambridge University Press:  27 November 2017

M. Nagel ,
P.-T. Brun ,
H. Berthet ,
A. Lindner ,
F. Gallaire Open the ORCID record for F. Gallaire [Opens in a new window]  and
C. Duprat Open the ORCID record for C. Duprat [Opens in a new window]
M. Nagel
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, Ecole Polytechnique Federale de Lausanne, Lausanne 1015, Switzerland
P.-T. Brun
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, Ecole Polytechnique Federale de Lausanne, Lausanne 1015, Switzerland Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
H. Berthet
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, UMR 7636, ESPCI Paris, PSL Research University, Université Paris Diderot, Université Pierre et Marie Curie, 10, rue Vauquelin, Paris, France
A. Lindner
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, UMR 7636, ESPCI Paris, PSL Research University, Université Paris Diderot, Université Pierre et Marie Curie, 10, rue Vauquelin, Paris, France
F. Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, Ecole Polytechnique Federale de Lausanne, Lausanne 1015, Switzerland
C. Duprat*
Affiliation:
Laboratoire LadHyX, Department of Mechanics, CNRS, Ecole polytechnique, 91128 Palaiseau, France
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the trajectories of rigid fibres as they are transported in a pressure-driven flow, at low Reynolds number, in shallow Hele-Shaw cells. The transverse confinement and the resulting viscous friction on these elongated objects, as well as the lateral confinement (i.e. the presence of lateral walls), lead to complex fibre trajectories that we characterize with a combination of microfluidic experiments and simulations using modified Brinkman equations. We show that the transported fibre behaves as an oscillator for which we obtain and analyse a complete state diagram.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 444 - 470
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Copyright
© 2017 Cambridge University Press 

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References

Berthet, H.2012 Single and collective fiber dynamics in confined microflows. PhD thesis, PMMH, ESPCI Paris, France.Google Scholar
Berthet, H., Fermigier, M. & Lindner, A. 2013 Single fiber transport in a confined channel: microfluidic experiments and numerical study. Phys. Fluids 25 (10), 103601.CrossRefGoogle Scholar
Berthet, H., du Roure, O. & Lindner, A. 2016 Microfluidic fabrication solutions for tailor-designed fiber suspensions. Appl. Sci. 6 (12), 385.Google Scholar
Boos, W. & Thess, A. 1997 Thermocapillary flow in a Hele-Shaw cell. J. Fluid Mech. 352, 305–330.Google Scholar
Bush, J. W. M. 1997 The anomalous wake accompanying bubbles rising in a thin gap: a mechanically forced marangoni flow. J. Fluid Mech. 352, 283–303.Google Scholar
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 791–810.Google Scholar
D’Angelo, M. V., Semin, B., Picard, G., Poitzsch, M. E., Hulin, J. P. & Auradou, H. 2009 Single fiber transport in a fracture slit: influence of the wall roughness and of the fiber flexibility. Trans. Porous Med. 84 (2), 389–408.Google Scholar
Dendukuri, D., Gu, S., Pregibon, D. C., Hatton, T. A. & Doyle, P. S. 2007 Stop-flow lithography in a microfluidic device. Lab on a chip 7 (7), 818–828.Google Scholar
Dendukuri, D. Y., Panda, P., Haghgooie, R., Kim, J. M., Hatton, T. A. & Doyle, P. S. 2008 Modeling of oxygen-inhibited free radical photopolymerization in a PDMS microfluidic device. Macromolecules 41 (22), 8547–8556.Google Scholar
Drescher, K., Shen, Y., Basslera, B. L. & Stone, H. A. 2013 Biofilm streamers cause catastrophic disruption of flow with consequences for environmental and medical systems. Proc. Natl Acad Sci. USA 110, 4345–4350.CrossRefGoogle ScholarPubMed
Duprat, C., Berthet, H., Wexler, J. S., Roure, O. & Lindner, A. 2015 Microfluidic in situ mechanical testing of photopolymerized gels. Lab on a Chip 15, 244–252.Google Scholar
Gallaire, F., Meliga, P., Laure, P. & Baroud, C. N. 2014 Marangoni induced force on a drop in a Hele-Shaw cell. Phys. Fluids 26 (6), 062105.Google Scholar
Halpern, D. & Secomb, T. W. 1991 Viscous motion of disk-shaped particles through parallel-sided channels with near-minimal widths. J. Fluid Mech. 231, 545–560.Google Scholar
Hecht, F. 2012 New development in FreeFEM + +. J. Numer. Math. 20 (3–4), 251–265.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.Google Scholar
Lindner, A. & Shelley, M. 2015 Elastic fibers in flows. In Fluid-Structure Interactions in Low-Reynolds-Number Flows (ed. Duprat, C. & Shore, H. A.), Royal Society of Chemistry.Google Scholar
de Mestre, N. J. & Russel, W. B. 1975 Low-Reynolds-number translation of a slender cylinder near plane wall*. J. Engng Maths 9 (2), 81–91.Google Scholar
Mitchell, W. H. & Spagnolie, S. E. 2015 Sedimentation of spheroidal bodies near walls in viscous fluids: glancing, reversing, tumbling and sliding. J. Fluid Mech. 772, 600–629.Google Scholar
Moses, K. B., Advani, S. G. & Reinhardt, A. 2001 Investigation of fiber motion near solid boundaries in simple shear flow. Rheol. Acta 40 (3), 296–306.Google Scholar
Nagel, M. & Gallaire, F. 2015 Boundary elements method for microfluidic two-phase flows in shallow channels. Comput. Fluids 107, 272–284.Google Scholar
Quennouz, N., Shelley, M., Roure, O. & Lindner, A. 2015 Transport and buckling dynamics of an elastic fibre in a viscous cellular flow. J. Fluid Mech. 769, 387–402.Google Scholar
Russel, W. B., Hinch, E. J., Leal, L. G. & Tieffenbruck, G. 1977 Rods falling near a vertical wall. J. Fluid Mech. 83, 273–287.Google Scholar
Shen, B., Leman, M., Reyssat, M. & Tabeling, P. 2014 Dynamics of a small number of droplets in microfluidic Hele-Shaw cells. Exp. Fluids 55, 1728.Google Scholar
Stockie, J. M. & Green, S. I. 1998 Simulating the motion of flexible pulp fibres using the immersed boundary method. J. Comput. Phys. 147, 147–165.Google Scholar
Stover, C. A. & Cohen, C. 1990 The motion of rodlike particles in the pressure-driven flow between two flat plates. Rheol. Acta 29 (3), 192–203.Google Scholar
Strogatz, S. H. 1994 Nonlinear Dynamics and Chaos. Perseus Books Publishing.Google Scholar
Uspal, W. E., Burak Eral, H. & Doyle, P. S. 2013 Engineering particle trajectories in microfluidic flows using particle shape. Nat. Commun. 4, 2666.Google Scholar
Wexler, J. S., Trinh, P. H., Berthet, H., Quennouz, N., du Roure, O., Huppert, H. E., Lindner, A. & Stone, H. A. 2013 Bending of elastic fibres in viscous flows: the influence of confinement. J. Fluid Mech. 720, 517–544.Google Scholar