Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T09:10:09.773Z Has data issue: false hasContentIssue false
  • English
  • Français

Washing wedges: capillary instability in a gradient of confinement

Published online by Cambridge University Press:  10 February 2016

Ludovic Keiser ,
Rémy Herbaut ,
José Bico  and
Etienne Reyssat
Ludovic Keiser
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636, France ESPCI Paris, 10 rue Vauquelin, 75005 Paris, France PSL Research University Sorbonne Université - UPMC, Univ. Paris 06, France Sorbonne Paris Cité - UDD, Univ. Paris 07, France Total S.A., Pôle d’Études et de Recherche de Lacq, BP47, 64170, Lacq, France
Rémy Herbaut
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636, France ESPCI Paris, 10 rue Vauquelin, 75005 Paris, France PSL Research University Sorbonne Université - UPMC, Univ. Paris 06, France Sorbonne Paris Cité - UDD, Univ. Paris 07, France
José Bico
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636, France ESPCI Paris, 10 rue Vauquelin, 75005 Paris, France PSL Research University Sorbonne Université - UPMC, Univ. Paris 06, France Sorbonne Paris Cité - UDD, Univ. Paris 07, France
Etienne Reyssat*
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636, France ESPCI Paris, 10 rue Vauquelin, 75005 Paris, France PSL Research University Sorbonne Université - UPMC, Univ. Paris 06, France Sorbonne Paris Cité - UDD, Univ. Paris 07, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present experimental results on the extraction of oil trapped in the confined region of a wedge. Upon addition of a more wetting liquid, we observe that oil fingers develop into this extracting liquid. The fingers eventually pinch off and form droplets that are driven away from the apex of the wedge by surface tension along the gradient of confinement. During an experiment, we observe that the size of the expelled oil droplets decreases as the unstable front recedes towards the wedge. We show how this size can be predicted from a linear stability analysis reminiscent of the classical Saffman–Taylor instability. However, the standard balance of capillary and bulk viscous dissipation does not account for the dynamics found in our experiments, leaving as an open question the detailed theoretical description of the instability.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Low-Reynolds-number flows: Low-Reynolds-number flows Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 790 , 10 March 2016 , pp. 619 - 633
Check for updates
Copyright
© 2016 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

Al-Housseiny, T. T., Tsai, P. A. & Stone, H. A. 2012 Control of interfacial instabilities using flow geometry. Nat. Phys. 8 (10), 747–750.Google Scholar
Bain, C. D., Burnett-Hall, G. D. & Montgomerie, R. R. 1994 Rapid motion of liquid drops. Nature 372, 414–415.Google Scholar
Bico, J. & Quéré, D. 2002 Self-propelling slugs. J. Fluid Mech. 467, 101–127.Google Scholar
Bischofberger, I., Ramachandran, R. & Nagel, S. R. 2014 Fingering versus stability in the limit of zero interfacial tension. Nat. Commun. 5, 5265.CrossRefGoogle ScholarPubMed
Bouasse, H. 1924 Capillarité, Phénomènes Superficiels. Delagrave.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10 (November), 166–188.Google Scholar
Brochard, F. 1989 Motion of droplets on solid surfaces induced by chemical or thermal gradients. Langmuir 5 (3), 432–438.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
Bush, J. W. M. & Hu, D. L. 2006 Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38 (1), 339–369.CrossRefGoogle Scholar
Cantat, I. 2013 Liquid meniscus friction on a wet plate: bubbles, lamellae, and foams. Phys. Fluids 25 (3), 031303.CrossRefGoogle Scholar
Chaudhury, M. K. & Whitesides, G. M. 1992 How to make water run uphill. Science 256 (5063), 1539–1541.CrossRefGoogle ScholarPubMed
Chevallier, E., Saint-Jalmes, A., Cantat, I., Lequeux, F. & Monteux, C. 2013 Light induced flows opposing drainage in foams and thin-films using photosurfactants. Soft Matt. 9 (29), 7054–7060.CrossRefGoogle Scholar
Dangla, R., Kayi, S. C. & Baroud, C. N. 2013 Droplet microfluidics driven by gradients of confinement. Proc. Natl Acad. Sci. USA 110 (3), 853–858.Google Scholar
Domingues dos Santos, F. & Ondarçuhu, T. 1995 Free-running droplets. Phys. Rev. Lett. 75 (16), 2972–2975.Google Scholar
de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls and Waves. Springer.CrossRefGoogle Scholar
Greenspan, H. P. 1978 On the motion of a small viscous droplet that wets a surface. J. Fluid Mech. 84, 125–143.CrossRefGoogle Scholar
Hauksbee, F. 1710 An account of an experiment touching the direction of a drop of oil of oranges, between two glass planes, towards any side of them that is nearest press’d together. By Mr. Fr. Hauksbee, F. R. S. Phil. Trans. R. Soc. Lond. 27 (325–336), 395–396.Google Scholar
Hodges, S. R., Jensen, O. E. & Rallison, J. M. 2004 The motion of a viscous drop through a cylindrical tube. J. Fluid Mech. 501, 279–301.Google Scholar
Hosoi, A. E. & Bush, J. W. M. 2001 Evaporative instabilities in climbing films. J. Fluid Mech. 442, 217–239.Google Scholar
Huerre, A., Theodoly, O., Leshansky, A. M., Valignat, M.-P., Cantat, I. & Jullien, M.-C. 2015 Droplets in microchannels: dynamical properties of the lubrication film. Phys. Rev. Lett. 115 (6), 064501.Google Scholar
Ichimura, K., Oh, S.-K. & Nakagawa, M. 2000 Light-driven motion of liquids on a photoresponsive surface. Science 288 (June), 1624–1626.CrossRefGoogle ScholarPubMed
Jackson, S. J., Stevens, D., Giddings, D. & Power, H. 2015 Dynamic-wetting effects in finite-mobility-ratio Hele-Shaw flow. Phys. Rev. E 92, 023021.Google Scholar
Kohira, M. I., Hayashima, Y. & Nagayama, M. 2001 Synchronized self-motion of two camphor boats. Langmuir 17, 7124–7129.Google Scholar
Landau, L. & Levich, V. G. 1942 Dragging of a liquid by a moving plate. Acta Physicochim. USSR 17, 42.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.Google Scholar
Lorenceau, E. & Quéré, D. 2004 Drops on a conical wire. J. Fluid Mech. 510, 29–45.Google Scholar
Maxworthy, T. 1989 Experimental study of interface instability in a Hele-Shaw cell. Phys. Rev. A 39 (11), 5863–5866.CrossRefGoogle Scholar
Mazouchi, A. & Homsy, G. M. 2000 Thermocapillary migration of long bubbles in cylindrical capillary tubes. Phys. Fluids 12 (3), 542–549.Google Scholar
Morrow, N. R. & Mason, G. 2001 Recovery of oil by spontaneous imbibition. Curr. Opin. Colloid Interface Sci. 6, 321–337.Google Scholar
Park, C.-W., Gorell, S. & Homsy, G. M. 1984a Two-phase displacement in Hele-Shaw cells: experiments on viscously driven instabilities. J. Fluid Mech. 141, 257–287.Google Scholar
Park, C.-W., Gorell, S. & Homsy, G. M. 1984b Corrigendum. J. Fluid Mech. 144, 468–469.Google Scholar
Park, C.-W. & Homsy, G. M. 1984 Two-phase displacement in Hele Shaw cells: theory. J. Fluid Mech. 139, 291–308.Google Scholar
Piroird, K., Clanet, C. & Quéré, D. 2011a Capillary extraction. Langmuir 27, 9396–9402.Google Scholar
Piroird, K., Clanet, C. & Quéré, D. 2011b Detergency in a tube. Soft Matt. 7 (16), 7498–7503.CrossRefGoogle Scholar
Prakash, M., Quéré, D. & Bush, J. W. M. 2008 Surface tension transport of prey by feeding shorebirds: the capillary ratchet. Science 320 (5878), 931–934.Google Scholar
Reinelt, D. A. 1987 The effect of thin film variations and transverse curvature on the shape of fingers in a Hele-Shaw cell. Phys. Fluids 30, 2617–2623.Google Scholar
Renvoisé, P., Bush, J. W. M., Prakash, M. & Quéré, D. 2009 Drop propulsion in tapered tubes. Europhys. Lett. 86 (6), 64003.Google Scholar
Reyssat, E. 2014 Drops and bubbles in wedges. J. Fluid Mech. 748, 641–662.Google Scholar
Saffman, P. G. & Taylor, G. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245 (1242), 312–329.Google Scholar
Schwartz, L. 1986 Stability of Hele-Shaw flows: the wetting-layer effect. Phys. Fluids 29 (1986), 3086–3088.Google Scholar
Schwartz, L. W., Princen, H. M. & Kiss, A. D. 1986 On the motion of bubbles in capillary tubes. J. Fluid Mech. 172 (-1), 259–275.Google Scholar
Weislogel, M. M. 1997 Steady spontaneous capillary flow in partially coated tubes. AIChE J. 43 (3), 645–654.CrossRefGoogle Scholar
Ybert, C. & di Meglio, J.-M. 2000 Ascending air bubbles in solutions of surface-active molecules: influence of desorption kinetics. Eur. Phys. J. E 3, 143–148.Google Scholar

Keiser et al. supplementary movie

See pdf file

Download Keiser et al. supplementary movie(Video)
Video 5.5 MB
Supplementary material: PDF

Keiser et al. supplementary caption

Caption for movie

Download Keiser et al. supplementary caption(PDF)
PDF 97.8 KB