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Droplet wetting transitions on inclined substrates in the presence of external shear and substrate permeability

Leonardo Espín* and Satish Kumar†

  • Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA

  • *Present address: Mayo Clinic Neural Engineering Laboratory, Rochester, MN 55905, USA.
  • †kumar030@umn.edu
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Phys. Rev. Fluids 2, 014004 – Published 23 January, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.014004

Abstract

Understanding the gravity-driven motion of droplets on inclined substrates in the presence of external shear and substrate permeability is important for applications such as spray coating and filtration. In this paper, we use a lubrication-theory-based model to study how external shear and substrate permeability affect droplet wetting transitions. A nonlinear evolution equation for the droplet height as a function of time and two spatial variables is derived and numerically solved. The contact-line region is described using a precursor film and disjoining pressure. Depending on its direction, external shear can either suppress or drive wetting transitions, but does not appear to significantly change the critical droplet speeds associated with these transitions. Substrate permeability generally suppresses wetting transitions due to liquid absorption and does appear to significantly affect these critical droplet speeds. The strong influence of substrate permeability and external shear on droplet wetting transitions indicates that it will be important to account for these effects when developing accurate models for industrial applications.

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References (38)

  1. T. Podgorski, J. M. Flesselles, and L. Limat, Corners, Cusps, and Pearls in Running Drops, Phys. Rev. Lett. 87, 036102 (2001).
  2. N. Le Grand, A. Daerr, and L. Limat, Shape and motion of drops sliding down an inclined plane, J. Fluid Mech. 541, 293 (2005).
  3. L. W. Schwartz, D. Roux, and J. J. Cooper-White, On the shapes of droplets that are sliding on a vertical wall, Physica D 209, 236 (2005).
  4. G. Ahmed, M. Sellier, M. Jermy, and M. Taylor, Modeling the effects of contact angle hysteresis on the sliding of droplets down inclined surfaces, Eur. J. Mech. B-Fluids 48, 218 (2014).
  5. J. A. Moriarty, L. W. Schwartz, and E. O. Tuck, Unsteady spreading of thin liquid films with small surface tension, Phys. Fluids 3, 733 (1991).
  6. I. S. McKinley, S. K. Wilson, and B. R. Duffy, Spin coating and air-jet blowing of thin viscous drops, Phys. Fluids 11, 30 (1999).
  7. P. Dimitrakopoulos, Deformation of a droplet adhering to a solid surface in shear flow: Onset of interfacial sliding, J. Fluid Mech. 580, 451 (2007).
  8. P. Dimitrakopoulos, Gravitational effects on the deformation of a droplet adhering to a horizontal solid surface in shear flow, Phys. Fluids 19, 122105 (2007).
  9. J. Fan, M. C. T. Wilson, and N. Kapur, Displacement of liquid droplets on a surface by a shearing air flow, J. Colloid Interface Sci. 356, 286 (2011).
  10. A. Hashimoto, M. Sakai, J.-H. Song, N. Yoshida, S. Suzuki, Y. Kameshima, and A. Nakajima, Direct observation of water droplet motion on a hydrophobic self-assembled monolayer surface under airflow, J. Surf. Finish. Soc. Jpn. 59, 907 (2008).
  11. L. Espín and S. Kumar, Droplet spreading and absorption on rough, permeable substrates, J. Fluid Mech. 784, 465 (2015).
  12. L. Espín and S. Kumar, Forced spreading of films and droplets of colloidal suspensions, J. Fluid Mech. 742, 495 (2014).
  13. L. Espín and S. Kumar, Sagging of evaporating droplets of colloidal suspensions on inclined substrates, Langmuir 30, 11966 (2014).
  14. Z. Wang, L. Espín, F. S. Bates, S. Kumar, and C. W. Macosko, Water droplet spreading and imbibition on superhydrophilic poly(butylene terephthalate) melt-blown fiber mats, Chem. Eng. Sci. 146, 104 (2016).
  15. A. Oron, S. H. Davis, and S. G. Bankoff, Long-scale evolution of thin liquid films, Rev. Mod. Phys. 69, 931 (1997).
  16. N. Alleborn and H. Raszillier, Spreading and sorption of a droplet on a porous substrate, Chem. Eng. Sci. 59, 2071 (2004).
  17. R. V. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81, 1131 (2009).
  18. T. P. Witelski and M. Bowen, ADI schemes for higher-order nonlinear diffusion equations, Appl. Numer. Math. 45, 331 (2003).
  19. M. R. Mata and A. L. Bertozzi, A numerical scheme for particle-laden thin film flow in two dimensions, J. Comput. Phys. 230, 6334 (2011).
  20. L. W. Schwartz, Hysteretic effects in droplet motions on heterogeneous substrates: Direct numerical simulation, Langmuir 14, 3440 (1998).
  21. L. W. Schwartz and R. R. Eley, Simulation of droplet motion on low-energy and heterogeneous surfaces, J. Colloid Interface Sci. 202, 173 (1998).
  22. H.-Y. Kim, H. J. Lee, and B. H. Kang, Sliding of liquid drops down an inclined solid surface, J. Colloid Interface Sci. 247, 372 (2002).
  23. R. Krechetnikov, On application of lubrication approximations to nonunidirectional coating flows with clean and surfactant interfaces, Phys. Fluids 22, 092102 (2010).
  24. R. Tadmor, Line energy and the relation between advancing, receding, and young contact angles, Langmuir 20, 7659 (2004).
  25. M. N. Popescu, G. Oshanin, S. Dietrich, and A-M. Cazabat, Precursor films in wetting phenomena, J. Phys. Condens. Matter 24, 243102 (2012).
  26. Y. Y. Koh, Y. C. Lee, P. H. Gaskell, P. K. Jimack, and H. M. Thompson, Droplet migration: Quantitative comparisons with experiment, Eur. Phys. J.-Spec. Top. 166, 117 (2009).
  27. L. W. Schwartz and S. Garoff, Contact angle hysteresis and the shape of the three-phase line, J. Colloid Interface Sci. 106, 422 (1985).
  28. R. Golestanian and E. Raphaël, Roughening transition in a moving contact line, Phys. Rev. E 67, 031603 (2003).
  29. E. S. Benilov and M. S. Benilov, A thin drop sliding down an inclined plate, J. Fluid Mech. 773, 75 (2015).
  30. P. G. Simpkins and E. L. Bales, Water-drop response to sudden accelerations, J. Fluid Mech. 55, 629 (1972).
  31. T. D. Blake and K. J. Ruschak, A maximum speed of wetting, Nature (London) 282, 489 (1979).
  32. V. M. Starov, S. R. Kostvintsev, V. D. Sobolev, M. G. Velarde, and S. A. Zhdanov, Spreading of liquid drops over dry porous layers: Complete wetting case, J. Colloid Interface Sci. 252, 397 (2002).
  33. B. A. Puthenveettil, V. K. Senthilkumar, and E. J. Hopfinger, Motions of droplets on inclined surfaces in the inertial regime, J. Fluid Mech. 726, 26 (2013).
  34. N. Savva and S. Kalliadasis, Droplet motion on inclined heterogeneous substrates, J. Fluid Mech. 725, 462 (2013).
  35. J. H. Snoeijer and B. Andreotti, Moving contact lines: Scales, regimes, and dynamical transitions, Annu. Rev. Fluid Mech. 45, 269 (2013).
  36. E. Vandre, M. S. Carvalho, and S. Kumar, Delaying the onset of dynamic wetting failure through meniscus confinement, J. Fluid Mech. 707, 496 (2012).
  37. E. Vandre, M. S. Carvalho, and S. Kumar, On the mechanism of wetting failure during fluid displacement along a moving substrate, Phys. Fluids 25, 102103 (2013).
  38. E. Vandre, M. S. Carvalho, and S. Kumar, Characteristics of air entrainment during dynamic wetting failure along a planar substrate, J. Fluid Mech. 747, 119 (2014).

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Phys. Rev. Fluids 2, 014004– Published 23 January, 2017
  • Received 20 July 2016

©2017 American Physical Society

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