- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Rivulet cascade from falling liquid films with side contact lines

G. Lavalle*, J. Sebilleau, and D. Legendre

  • Institut de Mécanique des Fluides de Toulouse (IMFT) - Université de Toulouse, CNRS-INPT-UPS, 31400 Toulouse, France

  • *Present address: Mines Saint-Etienne, Université de Lyon, CNRS, UMR 5307 LGF, Centre SPIN, Department PEG, F-42023 Saint-Etienne, France; gianluca.lavalle@imft.fr
PDF

Phys. Rev. Fluids 5, 124001 – Published 2 December, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.124001

Abstract

We investigate the dynamics of films of partially wetting liquids falling down a vertical plane in the presence of air. We focus on the little-studied case where the film is not in contact with lateral walls and thus has two side contact lines. By way of 3D direct numerical simulations, we study the fingering instability and the distribution of rivulets. Our results show that the instability develops as a cascade: two twin rivulets first develop at the free sides, followed by a series of twin rivulets growing closer to the center. This self-sustained fall is caused by the formation of stagnation zones at the front contact line as the liquid behind the ridge escapes toward a newly created rivulet. We also show that the established rivulet distance follows the prediction of linear instability, despite the cascade. The dynamics of the cascade is modified by inertial and film thickness effects, as well as by initial shape perturbations of the contact line. On the contrary, varying the contact angle does not affect the development of the cascade, apart from the average wavelength.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (39)

  1. B. E. Thompson and J. Jang, Aerodynamic efficiency of wings in rain, J. Aircraft 33, 1047 (1996).
  2. M. Spaid and G. Homsy, Stability of Newtonian and viscoelastic dynamic contact lines, Phys. Fluids 8, 460 (1996).
  3. D. Bonn, J. Eggers, J. Indekeu, J. Meunier, and E. Rolley, Wetting and spreading, Rev. Mod. Phys. 81, 739 (2009).
  4. H. Huppert, Flow and instability of a viscous current down a slope, Nature (London) 300, 427 (1982).
  5. N. Silvi and E. Dussan V, The rewetting of an inclined solid surface by a liquid, Phys. Fluids 28, 5 (1985).
  6. J. M. Jerrett and J. R. de Bruyn, Fingering instability of a gravitationally driven contact line, Phys. Fluids A: Fluid Dyn. 4, 234 (1992).
  7. J. R. de Bruyn, Growth of fingers at a driven three-phase contact line, Phys. Rev. A 46, R4500(R) (1992).
  8. M. F. G. Johnson, R. A. Schluter, M. J. Miksis, and S. G. Bankoff, Experimental study of rivulet formation on an inclined plate by fluorescent imaging, J. Fluid Mech. 394, 339 (1999).
  9. L. Kondic and J. Diez, Pattern formation in the flow of thin films down an incline: Constant flux configuration, Phys. Fluids 13, 3168 (2001).
  10. R. Ledesma-Aguilar, A. Hernández-Machado, and I. Pagonabarraga, Dynamics of driven three-dimensional thin films: From hydrophilic to superhydrophobic regimes, Phys. Fluids 20, 072101 (2008).
  11. J. A. Diez and L. Kondic, Contact Line Instabilities of Thin Liquid Films, Phys. Rev. Lett. 86, 632 (2001).
  12. D. Moyle, M.-S. Chen, and G. Homsy, Nonlinear rivulet dynamics during unstable wetting flows, Int. J. Multiph. Flow 25, 1243 (1999).
  13. M. H. Eres, L. W. Schwartz, and R. V. Roy, Fingering phenomena for driven coating films, Phys. Fluids 12, 1278 (2000).
  14. R. Ledesma-Aguilar, R. Nistal, A. Hernández-Machado, and I. Pagonabarraga, Controlled drop emission by wetting properties in driven liquid filaments, Nat. Mater. 10, 367 (2011).
  15. D. Sebastia-Saez, S. Gu, and M. Ramaioli, Effect of the contact angle on the morphology, residence time distribution and mass transfer into liquid rivulets: A CFD study, Chem. Eng. Sci. 176, 356 (2018).
  16. L. Kondic and J. Diez, Instabilities in the flow of thin films on heterogeneous surfaces, Phys. Fluids 16, 3341 (2004).
  17. J. Marshall and S. Wang, Contact-line fingering and rivulet formation in the presence of surface contamination, Comput. Fluids 34, 664 (2005).
  18. D. Slade, S. Veremieiev, Y. Lee, and P. Gaskell, Gravity-driven thin film flow: The influence of topography and surface tension gradient on rivulet formation, Chem. Eng. Process. 68, 7 (2013).
  19. H. Lan, J. L. Wegener, B. F. Armaly, and J. A. Drallmeier, Developing laminar gravity-driven thin liquid film flow down an inclined plane, ASME J. Fluids Eng. 132, 081301 (2010).
  20. B. Thoraval, J. Lallement, P. Berthoumieu, C. Laurent, and P. Gajan, An experimental study on gravity-driven film: Influence of viscosity, wall surface treatment and transitory state, in 10th International Conference on Multiphase Flow (ICMF), 2019, Rio de Janeiro, Brazil.
  21. J. Lallement, Modélisation et simulation numérique d'écoulements de films minces avec effet de mouillage partiel, Ph.D. thesis, ISAE, 2019 .
  22. C. Huh and L. E. Scriven, Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, J. Colloid Interf. Sci. 35, 85 (1971).
  23. O. V. Voinov, Hydrodynamics of wetting, Fluid Dyn. 11, 714 (1976).
  24. R. G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow, J. Fluid Mech. 168, 169 (1986).
  25. J. Magnaudet, M. Rivero, and J. Fabre, Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow, J. Fluid Mech. 284, 97 (1995).
  26. D. Legendre and J. Magnaudet, The lift force on a spherical bubble in a viscous linear shear flow, J. Fluid Mech. 368, 81 (1998).
  27. T. Bonometti and J. Magnaudet, An interface-capturing method for incompressible two-phase flows: Validation and application to bubble dynamics, Int. J. Multiph. Flow 33, 109 (2007).
  28. J.-B. Dupont and D. Legendre, Numerical simulation of static and sliding drop with contact angle hysteresis, J. Comput. Phys. 229, 2453 (2010).
  29. C. Hirt and B. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39, 201 (1981).
  30. J. Brackbill, D. Kothe, and C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100, 335 (1992).
  31. S. T. Zalesak, Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys. 31, 335 (1979).
  32. H. S. H. Mohand, H. Hoang, G. Galliero, and D. Legendre, On the use of a friction model in a volume of fluid solver for the simulation of dynamic contact lines, J. Comput. Phys. 393, 29 (2019).
  33. D. Legendre and M. Maglio, Comparison between numerical models for the simulation of moving contact lines, Comput. Fluids 113, 2 (2015).
  34. W. Nusselt, Der wärmeaustausch am berieselungskühler, VDI-Zeitschrift 67, 206 (1923).
  35. G. Lavalle, J. P. Vila, G. Blanchard, C. Laurent, and F. Charru, A numerical reduced model for thin liquid films sheared by a gas flow, J. Comput. Phys. 301, 119 (2015).
  36. J. Sebilleau, L. Lebon, and L. Limat, Dry patches in a flowing film: Predicting rewetting and the effects of inertia, Phys. Fluids 27, 102106 (2015).
  37. T. Podgorski, J.-M. Flesselles, and L. Limat, Dry arches within flowing films, Phys. Fluids 11, 845 (1999).
  38. S. Troian, E. Herbolzheimer, S. Safran, and J. Joanny, Fingering instabilities of driven spreading films, Europhys. Lett. 10, 25 (1989).
  39. G. Lerisson, P. G. Ledda, G. Balestra, and F. Gallaire, Dripping down the rivulet, Phys. Rev. Fluids 4, 100504 (2019).

Outline

Information

Phys. Rev. Fluids 5, 124001– Published 2 December, 2020
  • Received 18 January 2020
  • Accepted 4 November 2020
Crossmark - Check for updates button

©2020 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation