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Dynamic wetting failure in surfactant solutions

Published online by Cambridge University Press:  19 January 2016

Chen-Yu Liu ,
Eric Vandre ,
Marcio S. Carvalho  and
Satish Kumar
Chen-Yu Liu
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
Eric Vandre
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
Marcio S. Carvalho*
Affiliation:
Department of Mechanical Engineering, Pontificia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ 22451-900, Brazil
Satish Kumar*
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The influence of insoluble surfactants on dynamic wetting failure during displacement of Newtonian fluids in a rectangular channel is studied in this work. A hydrodynamic model for steady Stokes flows of dilute surfactant solutions is developed and evaluated using three approaches: (i) a one-dimensional (1D) lubrication-type approach, (ii) a novel hybrid of a 1D description of the receding phase and a 2D description of the advancing phase, and (iii) an asymptotic theory of Cox (J. Fluid Mech., vol. 168, 1986b, pp. 195–220). Steady-state solution families in the form of macroscopic contact angles as a function of the capillary number are determined and limit points are identified. When air is the receding fluid, Marangoni stresses are found to increase the receding-phase pressure gradients near the contact line by thinning the air film without significantly changing the capillary-pressure gradients there. As a consequence, the limit points shift to lower capillary numbers and the onset of wetting failure is promoted. The model predictions are then used to interpret decades-old experimental observations concerning the influence of surfactants on air entrainment (Burley & Kennedy, Chem. Engng Sci., vol. 31, 1976, pp. 901–911). In addition to being a computationally efficient alternative for the rectangular geometries considered here, the hybrid modelling approach developed in this paper could also be applied to more complicated geometries where a thin air layer is present near a contact line.

JFM classification

Materials Processing Flows: Coating Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 285 - 309
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Copyright
© 2016 Cambridge University Press 

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References

Anyfantakis, M., Fell, D., Butt, H.-J. & Auernhammer, G. K. 2012 Time-dependent dynamic receding contact angles studied during the flow of dilute aqueous surfactant solutions through fluorinated microtubes. Chem. Lett. 41 (10), 1232–1234.CrossRefGoogle Scholar
Baret, J.-C. 2012 Surfactants in droplet-based microfluidics. Lab on a Chip 12 (3), 422–433.CrossRefGoogle ScholarPubMed
Blake, T. D. 2006 The physics of moving wetting lines. J. Colloid Interface Sci. 299, 1–13.CrossRefGoogle ScholarPubMed
Burley, R. & Kennedy, B. S. 1976 An experimental study of air entrainment at a solid/liquid/gas interface. Chem. Engng Sci. 31, 901–911.CrossRefGoogle Scholar
Chan, T. S., Srivastava, S., Marchand, A., Andreotti, B., Biferale, L., Toschi, F. & Snoeijer, J. H. 2013 Hydrodynamics of air entrainment by moving contact lines. Phys. Fluids 25 (7), 074105.CrossRefGoogle Scholar
Christodoulou, K. N., Kistler, S. F. & Schunk, P. R. 1997 Advances in computational methods for free-surface flows. In Liquid Film Coating (ed. Kistler, S. & Schweizer, P. M.), pp. 297–367. Chapman & Hall.CrossRefGoogle Scholar
Cox, R. G. 1986a The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169–194.CrossRefGoogle Scholar
Cox, R. G. 1986b The dynamics of the spreading of liquids on a solid surface. Part 2. Surfactants. J. Fluid Mech. 168, 195–220.CrossRefGoogle Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81 (3), 1131–1198.CrossRefGoogle Scholar
Deryagin, B. M. & Levi, S. M. 1964 Film Coating Theory: Physical Chemistry of Coating. The Focal Press.Google Scholar
Dussan, V. E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77 (4), 665–684.CrossRefGoogle Scholar
Eggers, J. 2005 Existence of receding and advancing contact lines. Phys. Fluids 17 (8), 082106.CrossRefGoogle Scholar
Fell, D., Auernhammer, G. K., Bonaccurso, E., Liu, C., Sokuler, R. & Butt, H.-J. 2011 Influence of surfactant concentration and background salt on forced dynamic wetting and dewetting. Langmuir 27 (6), 2112–2117.CrossRefGoogle ScholarPubMed
Fell, D., Pawanrat, N., Bonaccurso, E., Butt, H.-J. & Auernhammer, G. K. 2012 Influence of surfactant transport suppression on dynamic contact angle hysteresis. Colloid Polym. Sci. 291 (2), 361–366.CrossRefGoogle Scholar
Gao, P. & Lu, X.-Y. 2013 On the wetting dynamics in a Couette flow. J. Fluid Mech. 724, R1.CrossRefGoogle Scholar
Hocking, L. M. 1976 A moving fluid interface on a rough surface. J. Fluid Mech. 76 (4), 801–817.CrossRefGoogle Scholar
Hood, P. 1976 Frontal solution program for unsymmetric matrices. Intl J. Numer. Meth. Engng 10, 379–399.CrossRefGoogle Scholar
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35 (1), 85–101.CrossRefGoogle Scholar
Jacqmin, D. 2004 Onset of wetting failure in liquid–liquid systems. J. Fluid Mech. 517, 209–228.CrossRefGoogle Scholar
Jensen, O. E. & Grotberg, J. B. 1992 Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture. J. Fluid Mech. 240, 259–288.Google Scholar
Kistler, S. F. 1993 Hydrodynamics of wetting. In Wettability (ed. Berg, J. C.), pp. 311–429. Marcel Dekker, Inc.Google Scholar
Kumar, S. & Matar, O. K. 2004 On the Faraday instability in a surfactant-covered liquid. Phys. Fluids 16 (1), 39–46.CrossRefGoogle Scholar
Langevin, D. 2014 Rheology of adsorbed surfactant monolayers at fluid surfaces. Annu. Rev. Fluid Mech. 46, 47–65.CrossRefGoogle Scholar
Lavalle, G., Vila, J.-P., Blanchard, G., Laurent, C. & Charru, F. 2015 A numerical reduced model for thin liquid films sheared by a gas flow. J. Comput. Phys. 301, 119–140.CrossRefGoogle Scholar
Ledesma-Aguilar, R., Hernandez-Machado, A. & Pagonabarraga, I. 2013 Theory of wetting-induced fluid entrainment by advancing contact lines on dry surfaces. Phys. Rev. Lett. 110 (26), 264502.CrossRefGoogle ScholarPubMed
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 (20), 204501.CrossRefGoogle ScholarPubMed
Marston, J. O., Hawkins, V., Decent, S. P. & Simmons, M. J. H. 2009 Influence of surfactant upon air entrainment hysteresis in curtain coating. Exp. Fluids 46, 549–558.CrossRefGoogle Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 031–980.CrossRefGoogle Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 2007 Numerical Recipes: the Art of Scientific Computing, 3rd edn. Cambridge University Press.Google Scholar
Rame, E. 2001 The spreading of surfactant-laden liquids with surfactant transfer through the contact line. J. Fluid Mech. 440, 205–234.CrossRefGoogle Scholar
Sbragaglia, M., Sugiyama, K. & Biferale, L. 2008 Wetting failure and contact line dynamics in a Couette flow. J. Fluid Mech. 614, 471–493.CrossRefGoogle Scholar
Schunk, P. R. & Scriven, L. E. 1997 Surfactant effects in coating processes. In Liquid Film Coating (ed. Kistler, S. F. & Schweizer, P. M.), pp. 495–536. Chapman & Hall.CrossRefGoogle Scholar
Scriven, L. E. & Sternling, C. V. 1960 The Marangoni effects. Nature 187, 186–188.Google Scholar
Shah, D. O. & Schechter, R. S.(Eds) 2012 Improved Oil Recovery by Surfactant and Polymer Flooding. Elsevier.Google Scholar
Shen, A. Q., Gleason, B., McKinley, G. H. & Stone, H. A. 2002 Fiber coating with surfactant solutions. Phys. Fluids 14 (11), 4055.CrossRefGoogle Scholar
Sibley, D. N., Nold, A. & Kalliadasis, S. 2015 The asymptotics of the moving contact line: cracking an old nut. J. Fluid Mech. 764, 445–462.CrossRefGoogle Scholar
Smith, M. K. & Neitzel, G. P. 2006 Multiscale modelling in the numerical computation of isothermal non-wetting. J. Fluid Mech. 554, 67–83.Google Scholar
Snoeijer, J. H. 2006 Free-surface flows with large slopes: beyond lubrication theory. Phys. Fluids 18 (2), 021701.CrossRefGoogle Scholar
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269–292.CrossRefGoogle Scholar
Stay, M. S. & Barocas, V. H. 2003 Coupled lubrication and Stokes flow finite elements. Intl J. Numer. Meth. Fluids 43, 129–146.Google Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381–411.CrossRefGoogle Scholar
Sui, Y., Ding, H. & Spelt, P. D. 2014 Numerical simulations of flows with moving contact lines. Annu. Rev. Fluid Mech. 46, 97–119.CrossRefGoogle Scholar
Sui, Y. & Spelt, P. D. 2013 Validation and modification of asymptotic analysis of slow and rapid droplet spreading by numerical simulation. J. Fluid Mech. 715, 283–313.Google Scholar
Tricot, Y.-M. 1997 Surfactants: static and dynamic surface tension. In Liquid Film Coating (ed. Kistler, S. & Schweizer, P. M.), pp. 99–136. Chapman & Hall.CrossRefGoogle Scholar
Tsai, B., Carvalho, M. S. & Kumar, S. 2010 Leveling of thin films of colloidal suspensions. J. Colloid Interface Sci. 343 (1), 306–313.Google Scholar
Vandre, E., Carvalho, M. S. & Kumar, S. 2012 Delaying the onset of dynamic wetting failure through meniscus confinement. J. Fluid Mech. 707, 496–520.CrossRefGoogle Scholar
Vandre, E., Carvalho, M. S. & Kumar, S. 2013 On the mechanism of wetting failure during fluid displacement along a moving substrate. Phys. Fluids 25 (10), 102103.CrossRefGoogle Scholar
Vandre, E., Carvalho, M. S. & Kumar, S. 2014 Characteristics of air entrainment during dynamic wetting failure along a planar substrate. J. Fluid Mech. 747, 119–140.CrossRefGoogle Scholar
Vandre, E. A.2013. Onset of dynamic wetting failure: the mechanics of high-speed fluid displacement. PhD thesis, University of Minnesota.Google Scholar
Weinstein, S. J. & Ruschak, K. J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36, 29–53.CrossRefGoogle Scholar