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Topography of the lubrication film under a pancake droplet travelling in a Hele-Shaw cell

Published online by Cambridge University Press:  06 July 2018

Benjamin Reichert ,
Axel Huerre ,
Olivier Theodoly ,
Marie-Pierre Valignat ,
Isabelle Cantat  and
Marie-Caroline Jullien Open the ORCID record for Marie-Caroline Jullien [Opens in a new window]
Benjamin Reichert
Affiliation:
Gulliver, UMR CNRS 7083, PSL Research University, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France
Axel Huerre
Affiliation:
Gulliver, UMR CNRS 7083, PSL Research University, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France
Olivier Theodoly
Affiliation:
LAI, INSERM UMR_S 1067, UMR CNRS 7333, Aix-Marseille Université, 13009 Marseille, France
Marie-Pierre Valignat
Affiliation:
LAI, INSERM UMR_S 1067, UMR CNRS 7333, Aix-Marseille Université, 13009 Marseille, France
Isabelle Cantat
Affiliation:
Université de Rennes, CNRS, Institut de Physique de Rennes (IPR), UMR 6251, F-35000 Rennes, France
Marie-Caroline Jullien*
Affiliation:
Gulliver, UMR CNRS 7083, PSL Research University, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France
*
†Email address for correspondence: marie-caroline.jullien@espci.fr
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Abstract

Understanding the dynamics of a droplet pushed by an external fluid in a confined geometry calls for the identification of all the dissipation mechanisms at play in the lubrication film between droplet and cell wall. Experimentally, reflection interference contrast microscopy has proven an efficient tool to measure the thickness of such lubrication films for microfluidic droplets, with a precision of a few nanometres (Huerre et al., Lab on a Chip, vol. 16 (5), 2016, pp. 911–916). The present work takes advantage of the high accuracy of this technique to chart quantitatively the lubrication film between oil droplets and the glass wall of a microfluidic chamber. We find that the lubrication films exhibit a complex three-dimensional shape, which we are able to rationalize using a hydrodynamical model in the lubrication approximation. We show that the complete topography cannot be recovered using a single model boundary condition along the whole interface. Rather, surface tension gradients are negligible at the front of the droplet, whereas they significantly modify the film profile at the rear, where surfactant accumulation induces local thickening of the lubrication film. The presence of ravines on the sides of the droplet is due to three-dimensional effects which can be qualitatively reproduced numerically. To our knowledge, this is the first experimental investigation of such local effects on travelling droplets.

JFM classification

Drops and Bubbles: Drops Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 850 , 10 September 2018 , pp. 708 - 732
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Copyright
© 2018 Cambridge University Press 

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References

Aradian, A., Raphael, E. & De Gennes, P.-G. 2001 Marginal pinching in soap films. Europhys. Lett. 55 (6), 834.Google Scholar
Brenner, H. 2013 Interfacial Transport Processes and Rheology. Elsevier.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.Google Scholar
Burgess, D. & Foster, M. R. 1990 Analysis of the boundary conditions for a Hele-Shaw bubble. Phys. Fluids A 2 (7), 1105–1117.Google Scholar
Cantat, I. 2013 Liquid meniscus friction on a wet wall: bubbles, lamellae and foams. Phys. Fluids 25, 031303.Google Scholar
Cantat, I. & Dollet, B. 2012 Liquid films with high surface modulus moving in tubes: dynamic wetting film and jumpy motion. Soft Matt. 8, 7790.Google Scholar
Champougny, L., Scheid, B., Restagno, F., Vermant, J. & Rio, E. 2015 Surfactant-induced rigidity of interfaces: a unified approach to free and dip-coated films. Soft Matt. 11 (14), 2758–2770.Google Scholar
Cuenot, B., Magnaudet, J. & Spennato, B. 1997 The effects of slightly soluble surfactants on the flow around a spherical bubble. J. Fluid Mech. 339, 25–53.Google Scholar
Delacotte, J., Montel, L., Restagno, F., Scheid, B., Dollet, B., Stone, H. A., Langevin, D. & Rio, E. 2012 Plate coating: influence of concentrated surfactants on the film thickness. Langmuir 28 (8), 3821–3830.Google Scholar
Denkov, N. D., Tcholakova, S., Golemanov, K., Subramanian, V. & Lips, A. 2006 Foam-wall friction: effect of air volume fraction for tangentially immobile bubble surface. Colloids Surf. A 282, 329–347.Google Scholar
Georgieva, D., Schmitt, V., Leal-Calderon, F. & Langevin, D. 2009 On the possible role of surface elasticity in emulsion stability. Langmuir 25 (10), 5565–5573.Google Scholar
Halpern, D. & Secomb, T. W. 1992 The squeezing of red blood cells through parallel-sided channels with near-minimal widths. J. Fluid Mech. 244, 307–322.Google Scholar
Hodges, S. R., Jensen, O. E. & Rallison, J. M. 2004 The motion of a viscous drop trhough a cylindrical tube. J. Fluid Mech. 501, 279.Google Scholar
Huerre, A., Jullien, M.-C., Theodoly, O. & Valignat, M.-P. 2016 Absolute 3D reconstruction of thin films topography in microfluidic channels by interference reflection microscopy. Lab on a Chip 16 (5), 911–916.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
Huerre, A., Valignat, M.-P., Maggs, A. C., Theodoly, O. & Jullien, M.-C. 2017 Laplace pressure based disjoining pressure isotherm in non symmetric conditions. Appl. Phys. Lett. 111 (22), 221601.Google Scholar
Israelachvili, J. N. 2011 Intermolecular and Surface Forces. Academic Press.Google Scholar
de Laplace, P. S.1806 Traité de mécanique céleste: Théorie de l’action capillaire. Suppl. Courcier.Google Scholar
Mysels, K. J. & Cox, M. C. 1962 An experimental test of Frankel’s law of film thickness. J. Colloid Sci. 17 (2), 136–145.Google Scholar
Nagel, M.2014 Modeling droplets flowing in microchannels. PhD thesis, EPFL.Google Scholar
Park, C. W. 1992 Influence of soluble surfactants on the motion of a finite bubble in a capillary tube. Phys. Fluids 4, 2335–2347.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
Quéré, D. & de Ryck, A. 1998 Le mouillage dynamique des fibres. Ann. Phys. 23, 1–151.Google Scholar
Scheid, B., Delacotte, J., Dollet, B., Rio, E., Restagno, F., van Nierop, E. A., Cantat, I., Langevin, D. & Stone, H. A. 2010 The role of surface force rheology in liquid film formation. Europhys. Lett. 90, 24002.Google Scholar
Shen, A. Q., Gleason, B., McKinley, G. H. & Stone, H. A. 2002 Fiber coating with surfactant solutions. Phys. Fluids 14, 4055.Google Scholar
Snoeijer, J. H., Ziegler, J., Andreotti, B., Fermigier, M. & Eggers, J. 2008 Thick films of viscous fluid coating a plate withdrawn from a liquid reservoir. Phys. Rev. Lett. 100 (24), 244502.Google Scholar
Taccoen, N.2015 On the long-term stability of foams: strength of an armored bubble and emergence of global disorder. PhD thesis, Ecole Doctorale de l’Ecole Polytechnique.Google Scholar
Taylor, G. & Saffman, P. G. 1959 A note on the motion of bubbles in a Hele-Shaw cell and porous medium. Q. J. Mech. Appl. Maths 12 (3), 265–279.Google Scholar
Xia, Y. & Whitesides, G. M. 1998 Soft lithography. Annu. Rev. Mater. Sci. 28 (1), 153–184.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.Google Scholar