Skip to main content Accesibility Help

Dynamic wetting failure in surfactant solutions

  • Chen-Yu Liu (a1), Eric Vandre (a1), Marcio S. Carvalho (a2) and Satish Kumar (a1)

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.

Corresponding author
Email addresses for correspondence:,
Hide All
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), 12321234.
Baret, J.-C. 2012 Surfactants in droplet-based microfluidics. Lab on a Chip 12 (3), 422433.
Blake, T. D. 2006 The physics of moving wetting lines. J. Colloid Interface Sci. 299, 113.
Burley, R. & Kennedy, B. S. 1976 An experimental study of air entrainment at a solid/liquid/gas interface. Chem. Engng Sci. 31, 901911.
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.
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. 297367. Chapman & Hall.
Cox, R. G. 1986a The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169194.
Cox, R. G. 1986b The dynamics of the spreading of liquids on a solid surface. Part 2. Surfactants. J. Fluid Mech. 168, 195220.
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81 (3), 11311198.
Deryagin, B. M. & Levi, S. M. 1964 Film Coating Theory: Physical Chemistry of Coating. The Focal Press.
Dussan, V. E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77 (4), 665684.
Eggers, J. 2005 Existence of receding and advancing contact lines. Phys. Fluids 17 (8), 082106.
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), 21122117.
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), 361366.
Gao, P. & Lu, X.-Y. 2013 On the wetting dynamics in a Couette flow. J. Fluid Mech. 724, R1.
Hocking, L. M. 1976 A moving fluid interface on a rough surface. J. Fluid Mech. 76 (4), 801817.
Hood, P. 1976 Frontal solution program for unsymmetric matrices. Intl J. Numer. Meth. Engng 10, 379399.
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35 (1), 85101.
Jacqmin, D. 2004 Onset of wetting failure in liquid–liquid systems. J. Fluid Mech. 517, 209228.
Jensen, O. E. & Grotberg, J. B. 1992 Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture. J. Fluid Mech. 240, 259288.
Kistler, S. F. 1993 Hydrodynamics of wetting. In Wettability (ed. Berg, J. C.), pp. 311429. Marcel Dekker, Inc.
Kumar, S. & Matar, O. K. 2004 On the Faraday instability in a surfactant-covered liquid. Phys. Fluids 16 (1), 3946.
Langevin, D. 2014 Rheology of adsorbed surfactant monolayers at fluid surfaces. Annu. Rev. Fluid Mech. 46, 4765.
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, 119140.
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.
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.
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, 549558.
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 031980.
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.
Rame, E. 2001 The spreading of surfactant-laden liquids with surfactant transfer through the contact line. J. Fluid Mech. 440, 205234.
Sbragaglia, M., Sugiyama, K. & Biferale, L. 2008 Wetting failure and contact line dynamics in a Couette flow. J. Fluid Mech. 614, 471493.
Schunk, P. R. & Scriven, L. E. 1997 Surfactant effects in coating processes. In Liquid Film Coating (ed. Kistler, S. F. & Schweizer, P. M.), pp. 495536. Chapman & Hall.
Scriven, L. E. & Sternling, C. V. 1960 The Marangoni effects. Nature 187, 186188.
Shah, D. O. & Schechter, R. S.(Eds) 2012 Improved Oil Recovery by Surfactant and Polymer Flooding. Elsevier.
Shen, A. Q., Gleason, B., McKinley, G. H. & Stone, H. A. 2002 Fiber coating with surfactant solutions. Phys. Fluids 14 (11), 4055.
Sibley, D. N., Nold, A. & Kalliadasis, S. 2015 The asymptotics of the moving contact line: cracking an old nut. J. Fluid Mech. 764, 445462.
Smith, M. K. & Neitzel, G. P. 2006 Multiscale modelling in the numerical computation of isothermal non-wetting. J. Fluid Mech. 554, 6783.
Snoeijer, J. H. 2006 Free-surface flows with large slopes: beyond lubrication theory. Phys. Fluids 18 (2), 021701.
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269292.
Stay, M. S. & Barocas, V. H. 2003 Coupled lubrication and Stokes flow finite elements. Intl J. Numer. Meth. Fluids 43, 129146.
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, 381411.
Sui, Y., Ding, H. & Spelt, P. D. 2014 Numerical simulations of flows with moving contact lines. Annu. Rev. Fluid Mech. 46, 97119.
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, 283313.
Tricot, Y.-M. 1997 Surfactants: static and dynamic surface tension. In Liquid Film Coating (ed. Kistler, S. & Schweizer, P. M.), pp. 99136. Chapman & Hall.
Tsai, B., Carvalho, M. S. & Kumar, S. 2010 Leveling of thin films of colloidal suspensions. J. Colloid Interface Sci. 343 (1), 306313.
Vandre, E., Carvalho, M. S. & Kumar, S. 2012 Delaying the onset of dynamic wetting failure through meniscus confinement. J. Fluid Mech. 707, 496520.
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.
Vandre, E., Carvalho, M. S. & Kumar, S. 2014 Characteristics of air entrainment during dynamic wetting failure along a planar substrate. J. Fluid Mech. 747, 119140.
Vandre, E. A.2013. Onset of dynamic wetting failure: the mechanics of high-speed fluid displacement. PhD thesis, University of Minnesota.
Weinstein, S. J. & Ruschak, K. J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36, 2953.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed