Numerical Simulation for Drop Impact on Textured Surfaces

  • Martina BaggioEmail author
  • Bernhard Weigand
Conference paper
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 121)


Superhydrophobic surfaces with small-scale features have recently gained interest, because impacting droplets may bounce-off faster with respect to a flat superhydrophobic surface. For such surfaces the correct numerical prediction of the impact phenomena is very difficult. Our goal is the numerical study of drop impact on such surfaces using Free Surface 3D (FS3D), our in-house code for the simulation of incompressible multi-phase flows. Until recently, FS3D was not able to represent the interaction of a droplet with a complex textured solid surface. In this work, we show how we added this feature to the code by implementing the representation of embedded arbitrary-shaped boundaries using a Cartesian grid. Two approaches were developed; a preliminary simplified approach and an ultimate, more rigorous one. We discuss both implementations and we show a comparison of the two approaches for a test case. The results show that the predictions for impact dynamics of the two approaches slightly differ. Although, the simplified approach shows only small errors in mass conservation, it is fundamentally not conservative. With the introduction of a new approach we were able to improve the conservativeness of our simulations.



We thank the German Science Foundation (DFG) for the financial support of this research within the international research training group Droplet Interaction Technologies, DROPIT, GRK 2016/1.


  1. 1.
    Bird, J.C., Dhiman, R., Kwon, H., Varanasi, K.K.: Reducing the contact time of a bouncing drop. Nature 503, 385–388 (2013)Google Scholar
  2. 2.
    Gauthier, A., Symon, S., Clanet, C., Quéré, D.: Water impacting on superhydrophobic macrotextures. Nat. Commun. 6, 8001 (2015)Google Scholar
  3. 3.
    Regulagadda, K., Bakshi, S., Das, S.K.: Morphology of drop impact on a superhydrophobic surface with macro-structures. Phys. Fluids 29, 082104 (2017)Google Scholar
  4. 4.
    Chantelot, P., Moqaddam, A.M., Gauthier, A., Chikatamaria, S.S., Clanet, C., Karlin, I.V., Quéré, D.: Water ring-bouncing on repellent singularities. Soft. Matter 14(12), 2227–2233 (2018)CrossRefGoogle Scholar
  5. 5.
    Shen, Y., Liu, S., Zhu, C., Tao, J., Chen, Z., Tao, H., Pan, L., Wang, G., Wang, T.: Bouncing dynamics of impact droplets on the convex superhydrophobic surfaces. Appl. Phys. Lett. 110, 221601 (2017)Google Scholar
  6. 6.
    Khojasteh, D., Bordbar, A., Kamali, R., Marengo, M.: Curvature effect on droplet impacting onto hydrophobic and superhydrophobic spheres. Int. J. Comput. Fluid Dyn. 31(6–8), 310–323 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Liu, Y., Andrew, M., Li, J., Yeomans, J.M., Wang, Z.: Symmetry breaking in drop bouncing on curved surfaces. Nat. Commun. 6, 10034 (2015)Google Scholar
  8. 8.
    Liu, X., Zhao, Y., Chen, S., Shen, S., Zhao, X.: Numerical research on the dynamic characteristics of a droplet impacting a hydrophobic tube. Phys. Fluids 29, 062105 (2017)Google Scholar
  9. 9.
    Schlottke, J., Dulger, E., Weigand, B.: A VOF-based 3D numerical investigation of evaporating, deformed droplets. Prog. Comput. Fluid Dyn. Int. J. 9, 426–435 (2009)CrossRefGoogle Scholar
  10. 10.
    Schlottke, J., Straub, W., Beheng, K.D., Gomaa, H., Weigand, B.: Numerical investigation of collision-induced breakup of raindrops. Part I: methodology 12 references and dependencies on collision energy and eccentricity. J. Atmos. Sci. 67, 557–575 (2010)Google Scholar
  11. 11.
    Ertl, M., Weigand, B.: Analysis methods for direct numerical simulations of primary breakup of shear-thinning liquid jets. Atomization Sprays 27(4), 303–317 (2017)CrossRefGoogle Scholar
  12. 12.
    Reitzle, M., Kieffer-Roth, C., Garcke, H., Weigand, B.: A volume-of-fluid method for three-dimensional hexagonal solidification processes. J. Comput. Phys. 339, 356–369 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Reitzle, M., Ruberto, S., Stierle, R., Gross, J., Tanzen, T., Weigand, B.: Direct numerical simulation of sublimating ice particles. Int. J. Thermal Sci. 145, 105953 (2019)Google Scholar
  14. 14.
    Rauschenberger, P., Weigand, B.: Direct numerical simulation of rigid bodies in multiphase flow within an Eulerian framework. J. Comput. Phys. 291, 238–253 (2015)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Popinet, S.: Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190(2), 572–600 (2003)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Eisenschmidt, K., Ertl, M., Gomaa, H., Kieffer-Roth, C., Meister, C., Rauschenberger, P., Reitzle, M., Schlottke, K., Weigand, B.: Direct numerical simulations for multiphase flows: an overview of the multiphase code FS3D. Appl. Math. Comput. 272, 508–517 (2016)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S., Zanetti, G.: Modelling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 113(1), 134–147 (1994)Google Scholar
  18. 18.
    Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225 (1981)CrossRefGoogle Scholar
  19. 19.
    Rider, W.J., Kothe, D.B.: Reconstructing volume tracking. J. Comput. Phys. 141(2), 112–152 (1998)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Rieber, M.: Numerische Modellierung der Dynamik freier Grenzflächen in Zweiphasenströmungen, dissertation, University of Stuttgart (2004)Google Scholar
  21. 21.
    Wesseling, P.: An Introduction to Multigrid Methods. Wiley (1992)Google Scholar
  22. 22.
    Pathak, A., Raessi, M.: A three-dimensional volume-of-fluid method for reconstructing and advecting three-material interfaces forming contact lines. J. Comput. Phys. 307, 550–573 (2016)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Johansen, H., Colella, P.: A Cartesian grid embedded boundary method for Poisson’s equation on irregular domains. J. Comput. Phys. 147(1), 60–85 (1998)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Regulagadda, K., Bakshi, S., Das, S.K.: Triggering of flow asymmetry by anisotropic deflection of lamella during the impact of a drop onto superhydrophobic surfaces. Phys. Fluids 30, 072105 (2018)Google Scholar
  25. 25.
    Richard, D., Clanet, C., Quéré, D.: Contact time of a bouncing drop. Nature 417, 811 (2002)Google Scholar

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Authors and Affiliations

  1. 1.Institute of Aerospace ThermodynamicsUniversity of StuttgartStuttgartGermany

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