Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-17T11:23:29.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of non-wetting drops confined in a Hele-Shaw cell

Published online by Cambridge University Press:  24 April 2018

Ludovic Keiser Open the ORCID record for Ludovic Keiser [Opens in a new window] ,
Khalil Jaafar ,
José Bico  and
Étienne Reyssat
Ludovic Keiser*
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin 75005 Paris, France Sorbonne Université, France Univ. Paris Diderot, France Total S.A., Pôle d’Études et de Recherche de Lacq, BP47 64170 Lacq, France
Khalil Jaafar
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin 75005 Paris, France Sorbonne Université, France Univ. Paris Diderot, France
José Bico
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin 75005 Paris, France Sorbonne Université, France Univ. Paris Diderot, France
Étienne Reyssat*
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin 75005 Paris, France Sorbonne Université, France Univ. Paris Diderot, 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 experimentally investigate the sedimentation of a non-wetting drop confined between two parallel walls. The whole system is immersed in a bath of liquid of low viscosity and a lubricating film may be dynamically formed between the drop and the walls of the cell. Depending on the thickness of the film and on the viscosity ratio between the droplet and the surrounding liquid, viscous dissipation localizes either in the lubrication layer or in the bulk of the drop. The velocity of the droplet is non-trivial as the thickness of the lubricating layer may depend on the interplay between interfacial tension and viscous dissipation. Interestingly, thin films whose nanometric thickness is set by long range intermolecular interactions may lubricate efficiently the motion of highly viscous droplets. We derive asymptotic models that successfully capture the settling velocity of the drop in the different regimes observed experimentally. The effect of partial wetting is finally illustrated by a sharp increase of the velocity of the drops that we attribute to a wetting transition.

JFM classification

Drops and Bubbles: Drops Low-Reynolds-number flows: Hele-Shaw flows Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 845 , 25 June 2018 , pp. 245 - 262
Check for updates
Copyright
© 2018 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
Aussillous, P. & Quéré, D. 2000 Quick deposition of a fluid on the wall of a tube. Phys. Fluids 12, 2367–2371.Google Scholar
Balestra, G., Zhu, L. & Gallaire, F.2017 A viscous droplet in a capillary tube: from Bretherton’s theory to empirical models. arXiv:1711.10447 1–26.Google Scholar
Baroud, C., Gallaire, F. & Dangla, R. 2010 Dynamics of microfluidic droplets. Lab on a Chip 10, 2032–2045.Google Scholar
Bergeron, V. & Radke, C. J. 1992 Equilibrium measurements of oscillatory disjoining pressures in aqueous foam films. Langmuir 8 (19), 3020–3026.CrossRefGoogle Scholar
Bico, J. & Quéré, D. 2002 Self-propelling slugs. J. Fluid Mech. 467, 101–127.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10 (02), 166–188.CrossRefGoogle Scholar
Burgess, D. & Foster, M. R. 1990 Analysis of the boundary conditions for a Hele-Shaw bubble. Phys. Fluids 2 (7), 1105–1117.CrossRefGoogle Scholar
Cantat, I. 2013 Liquid meniscus friction on a wet plate: bubbles, lamellae, and foams. Phys. Fluids 25, 031303.Google Scholar
Chaudhury, K., Acharya, P. V. & Chakraborty, S. 2014 Influence of disjoining pressure on the dynamics of steadily moving long bubbles inside narrow cylindrical capillaries. Phys. Rev. E 89 (5), 1–11.Google Scholar
Cohen-Addad, S. & Höhler, R. 2014 Rheology of foams and highly concentrated emulsions. Curr. Opin. Colloid Interface Sci. 19 (6), 536–548.Google 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
Denkov, N. D., Tcholakova, S., Golemanov, K., Ananthapadmanabhan, K. P. & Lips, A. 2008 Viscous friction in foams and concentrated emulsions under steady shear. Phys. Rev. Lett. 100, 138301.Google Scholar
Derjaguin, B. V. 1993 On the thickness of a layer of liquid remaining on the walls of vessels after their emptying, and the theory of the application of photoemulsion after coating on the cine film. Progr. Surface Sci. 43, 129–133.Google Scholar
Dias, E. O. & Miranda, J. A. 2013 Control of centrifugally driven fingering in a tapered Hele-Shaw cell. Phys. Rev. E 87, 053014.Google Scholar
Eggers, J. 2001 Air entrainment through free-surface cusps. Phys. Rev. Lett. 86, 4290–4293.Google Scholar
Eri, A. & Okumura, K. 2011 Viscous drag friction acting on a fluid drop confined in between two plates. Soft Matt. 7 (12), 5648–5653.Google Scholar
Gauglitz, P. A. & Radke, C. J. 1990 The dynamics of liquid film breakup in constricted cylindrical capillaries. J. Colloid Interface Sci. 134 (1), 14–40.Google Scholar
Hammoud, N. H., Trinh, P. H., Howell, P. D. & Stone, H. A. 2017 Influence of van der waals forces on a bubble moving in a tube. Phys. Rev. Fluids 2, 063601.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.CrossRefGoogle Scholar
Homsy, G. M. 1987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19 (9), 271–311.Google Scholar
Huerre, A., Théodoly, 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, 064501.Google Scholar
Israelachvili, J. 2011 Intermolecular and surface forces. In Intermolecular and Surface Forces, 3rd edn. Elsevier.Google Scholar
Jung, M., Brinkmann, M., Seemann, R., Hiller, T., Sanchez De, M., Lama, L. & Herminghaus, S. 2016 Wettability controls slow immiscible displacement through local interfacial instabilities. Phys. Rev. Fluids 1, 074202.Google Scholar
Keiser, L., Herbaut, R., Bico, J. & Reyssat, É. 2016 Washing wedges: capillary instability in a gradient of confinement. J. Fluid Mech. 790, 619–633.Google Scholar
Klaseboer, E., Gupta, R. & Manica, R. 2014 An extended Bretherton model for long Taylor bubbles at moderate capillary numbers. Phys. Fluids 26, 032107.Google Scholar
Landau, L. & Levich, V. G. 1942 Dragging of a liquid by a moving plate. Acta Physicochim. USSR 17, 42.Google Scholar
Li, Y.-C., Liao, Y.-C., Wen, T.-C. & Wei, H.-H. 2014 Breakdown of the Bretherton law due to wall slippage. J. Fluid Mech. 741, 200–227.Google Scholar
Ling, Y., Fullana, J.-M., Popinet, S. & Josserand, C. 2016 Droplet migration in a Hele–Shaw cell: effect of the lubrication film on the droplet dynamics. Phys. Fluids 28, 062001.CrossRefGoogle Scholar
Lorenceau, E., Restagno, F. & Quéré, D. 2003 Fracture of a viscous liquid. Phys. Rev. Lett. 90, 184501.Google Scholar
Marchand, A., Chan, T. S., Snoeijer, J. H. & Andreotti, B. 2012 Air entrainment by contact lines of a solid plate plunged into a viscous fluid. Phys. Rev. Lett. 108, 204501.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
Pihler-Puzovic, D., Illien, P., Heil, M. & Juel, A. 2012 Suppression of complex fingerlike patterns at the interface between air and a viscous fluid by elastic membranes. Phys. Rev. Lett. 108, 074502.CrossRefGoogle Scholar
Preira, P., Valignat, M.-P., Bico, J. & Théodoly, O. 2013 Single cell rheometry with a microfluidic constriction: quantitative control of friction and fluid leaks between cell and channel walls. Biomicrofluidics 7 (2), 024111.Google Scholar
Princen, H. M. & Kiss, A. D. 1989 Rheology of foams and highly concentrated emulsions. J. Colloid Interface Sci. 128 (1), 176–187.Google Scholar
Reichert, B., Huerre, A., Théodoly, O., Valignat, M.-P., Cantat, I. & Jullien, M.-C. 2018 Topography of the lubrication film under a pancake droplet travelling in a Hele-Shaw cell. J. Fluid Mech., under review.Google Scholar
Reyssat, É. 2014 Drops and bubbles in wedges. J. Fluid Mech. 748, 641–662.Google Scholar
Saffman, P. G. & Taylor, G. I. 1958 Liquid 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
Sauret, A., Boulogne, F., Cappello, J., Dressaire, E. & Stone, H. A. 2015 Damping of liquid sloshing by foams. Phys. Fluids 27, 022103.Google Scholar
Schwartz, L. W., Princen, H. M. & Kiss, A. D. 1986 On the motion of bubbles in capillary tubes. J. Fluid Mech. 172, 259–275.Google Scholar
Seemann, R., Brinkmann, M., Pfohl, T. & Herminghaus, S. 2012 Droplet based microfluidics. Rep. Progr. Phys. 75, 016601.Google Scholar
Seiwert, J., Clanet, C. & Quéré, D. 2011 Coating of a textured solid. J. Fluid Mech. 669, 55–63.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
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269–292.Google Scholar
Snoeijer, J. H., Delon, G., Fermigier, M. & Andreotti, B. 2006 Avoided critical behavior in dynamically forced wetting. Phys. Rev. Lett. 96, 174504.Google Scholar
Taylor, G. I. 1961 Deposition of a viscous fluid on the wall of a tube. J. Fluid Mech. 10, 161–165.Google Scholar
Teletzke, G. F., Davis, H. T. & Scriven, L. E. 1988 Wetting hydrodynamics. Rev. Phys. Appl. 23 (6), 989–1007.Google Scholar
Viola, F., Brun, P.-T., Dollet, B. & Gallaire, F. 2016 Foam on troubled water: capillary induced finite-time arrest of sloshing waves. Phys. Fluids 28, 091701.Google Scholar
Yahashi, M., Kimoto, N. & Okumura, K. 2016 Scaling crossover in thin-film drag dynamics of fluid drops in the Hele-Shaw cell. Sci. Rep. 6, 31395.Google Scholar
Zhao, B., Pahlavan, A. A., Cueto-Felgueroso, L. & Juanes, R. 2018 Forced wetting transition and bubble pinch-off in a capillary tube. Phys. Rev. Lett. 120, 084501.Google Scholar
Zhou, C., Yue, P. & Feng, J. J. 2007 Simulation of neutrophil deformation and transport in capillaries using Newtonian and viscoelastic drop models. Ann. Biomed. Engng 35 (5), 766–780.Google Scholar
Zhu, L. & Gallaire, F. 2016 A pancake droplet translating in a Hele-Shaw cell: lubrication film and flow field. J. Fluid Mech. 798, 955–969.CrossRefGoogle Scholar
Zinchenko, A. Z. & Davis, R. H. 2017 Motion of deformable drops through porous media. Annu. Rev. Fluid Mech. 49, 71–90.Google Scholar