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Part of the book series: Environmental Science and Engineering ((ENVENG))

Abstract

We consider numerical simulations of drops sliding on an inclined solid surface. The simulations are performed using our in house research code JADIM based on the Volume of Fluid formulation of the mass and momentum equations. Special algorithms have been developed for the simulation of the hysteresis of the contact line as well as for the description of moving contact lines. The onset of motion is analyzed and the effect of the contact line hysteresis is studied. The critical angle of inclination, as well as the corresponding drop shape, are discussed and compared with previous experiments. The sliding velocity for a constant angle of inclination is also considered and compared with experiments. The different shapes observed in experiments (rounded, corner, cusp, or pearling drop) are recovered depending on both the fluid properties and the angle of inclination. The drop sliding velocity is then considered for larger values of the hysteresis.

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References

  • Afkhami S, Zaleski S, Bussmann M (2009) A mesh-dependent model for applying dynamic contact angles to VOF simulations. J Comput Phys 228:5370–5389

    Article  Google Scholar 

  • Bikerman JJ (1950) Sliding of drops from surfaces of different roughnesses. J Colloid Interface Sci 5:349–359

    Google Scholar 

  • Blake TD (2006) The physics of moving wetting lines. J Colloid Interface Sci 299:1–13

    Article  Google Scholar 

  • Bonn D, Eggers J, Indekeu J, Meunier J, Rolley E (2009) Wetting and spreading. Rev Mod Phys 81:739–805

    Article  Google Scholar 

  • Bonometti T, Magnaudet J (2007) An interface capturing method for incompressible two-phase flows. Validation and application to bubble dynamics. Int J Multiph Flow 33:109–133

    Article  Google Scholar 

  • Brackbill J, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100:335–354

    Article  Google Scholar 

  • Cox RG (1986) The dynamics of the spreading of liquids on solid surfaces. Part 1: Viscous flow. J Fluid Mech 168:169–194

    Article  Google Scholar 

  • Dimitrakopoulos P, Higdon JJL (1999) On the gravitational displacement of three dimensional fluid droplets from inclined solid surfaces. J Fluid Mech 295:181–209

    Article  Google Scholar 

  • Dupont JB, Legendre D (2010) Numerical simulations of static and sliding drop with contact angle hysteresis. J Comput Phys 229:2453–2478

    Article  Google Scholar 

  • Dussan EB (1976) The moving contact line: the slip boundary condition. J Fluid Mech 77:665–684

    Article  Google Scholar 

  • Dussan EB (1985) On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. Part 2. Small drops and bubbles having contact angle of arbitrary size. J Fluid Mech 151:1–20

    Article  Google Scholar 

  • Dussan EBV, Ramé E, Garoff S (1991) On identifying the appropriate boundary conditions at moving contact lines: an experimental investigation. J Fluid Mech 230:97–116

    Article  Google Scholar 

  • Extrand CW (1995) Liquid drops on an inclined plane: the relation between contact angles, drop shape, and retentive force. J Colloid Interface Sci 170:515–521

    Article  Google Scholar 

  • Fang C, Hidrovo C, Wang F, Eaton J, Goodson K (2008) 3-D numerical simulation of contact angle hysteresis for microscale two phase flow. Int. J. Multiph. Flow 34:690–705

    Article  Google Scholar 

  • Furmidge CGL (1962) I. The sliding of liquid drops on solid surfaces and a theory for spray retention. J Colloid Sci 17:309–324

    Article  Google Scholar 

  • Huh C, Scriven LE (1971) Hydrodynamic model of the steady movement of a solid/liquid/fluid contact line. J Colloid Interface Sci 35:85–101

    Article  Google Scholar 

  • Lafaurie B, Nardone C, Scardovelli R, Zaleski S, Zanetti G (1994) Modelling merging and fragmentation in multiphase flows with surfer. J Comput Phys 113:134–147

    Article  Google Scholar 

  • Lauga E, Brenner MP, Stone HA (2007) Microfluidics: the no-slip boundary condition. In: Tropea C et al (ed) Handbook of experimental fluid dynamics, Chap. 19. Springer, NY, pp 1219–1240

    Google Scholar 

  • Le Grand N, Daerr A, Limat L (2005) Shape and motion of drops sliding down an inclined plate. J Fluid Mech 541:293–315

    Article  Google Scholar 

  • Legendre D, Maglio M (2013) Numerical simulation of spreading drops. Colloids and Surf A 432:29–37

    Google Scholar 

  • Maglio M (2012) Numerical simulation of spreading, sliding and coalescing drops on surfaces. PhD thesis, Institut National Polytechnique de Toulouse, France

    Google Scholar 

  • Marsh JA, Garoff S, Dussan EB (1983) Dynamic contact angles and hydrodynamics near a moving contact line. Phys Rev Lett 70:2778–2782

    Article  Google Scholar 

  • Milinazzo F, Shinbrot M (1988) A numerical study of a drop on a vertical wall. J Colloid Interface Sci 121:254–264

    Article  Google Scholar 

  • Ngan CG, Dussan EB (1989) On the dynamics of liquid spreading on solid surfaces. J Fluid Mech 209:191–226

    Article  Google Scholar 

  • Podgorski MT (2000) Ruissellement en conditions de mouillage partiel. PhD thesis, Université Paris 6, France

    Google Scholar 

  • Popinet S, Zaleski S (1999) A front-tracking algorithm for accurate representation of surface tension. Int J Numer Meth Fluids 30:775–793

    Article  Google Scholar 

  • Renardy M, Renardy Y, Li J (2001) Numerical simulation of moving contact line problems using a volume-of-Fluid method. J Comput Phys 94:243–263

    Article  Google Scholar 

  • Rio E (2005) Gouttes, Flaques et Arches sèches: Des lignes de contact en présence d’un ècoulement. PhD thesis, Université Paris 6, France

    Google Scholar 

  • Rotemberg Y, Boruvka L, Neumann W (1984) The shape of nonaxisymmetric drops on inclined planar surfaces. J Colloid Interface Sci 102:424–434

    Article  Google Scholar 

  • Scardovelli R, Zaleski S (1999) Direct numerical simulation of free surface and interfacial flow. Annu Rev Fluid Mech 31:567–603

    Article  Google Scholar 

  • Sethian J (1999) Level set methods and fast marching methods. Cambridge University Press, Cambridge

    Google Scholar 

  • Shen C, Ruth DW (1998) Experimental and numerical investigations of the interface profile close to a moving contact line. Phys Fluids 10:789–799

    Article  Google Scholar 

  • Spelt PDM (2005) A level-set approach for simulations of flows with multiple moving contact lines with hysteresis. J Comput Phys 207:389–404

    Article  Google Scholar 

  • Sussman M, Fatemi E, Smereka P, Osher S (1998) A level set approach for computing solutions in incompressible two-phase flows. J Comput Phys 27:663–680

    Google Scholar 

  • Voinov OV (1976) Hydrodynamics of wetting. Fluid Dyn 11:714–721

    Google Scholar 

  • Winkels KG, Weijs JH, Eddi A, Snoeijer JH (2012) Initial spreading of low-viscosity drops on partially wetting surfaces. Phys Rev E 85:055301(R)

    Google Scholar 

  • Yokoi K, Vadillo D, Hinch J, Hutchings I (2009) Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface. Phys Fluids 21:072102

    Article  Google Scholar 

  • Zalesak S (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31:335–362

    Article  Google Scholar 

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Correspondence to Dominique Legendre .

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Maglio, M., Legendre, D. (2014). Numerical Simulation of Sliding Drops on an Inclined Solid Surface. In: Sigalotti, L., Klapp, J., Sira, E. (eds) Computational and Experimental Fluid Mechanics with Applications to Physics, Engineering and the Environment. Environmental Science and Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-00191-3_3

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