- 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

Local dissipation limits the dynamics of impacting droplets on smooth and rough substrates

Yuli Wang1,2,*, Gustav Amberg1,3, and Andreas Carlson2,†

  • 1Department of Mechanics, Royal Institute of Technology, 100 44 Stockholm, Sweden
  • 2Department of Mathematics, Mechanics Division, University of Oslo, 0851 Oslo, Norway
  • 3Södertörn University, 14189 Huddinge, Sweden

  • *yuli@mech.kth.se
  • †acarlson@math.uio.no
PDF

Phys. Rev. Fluids 2, 033602 – Published 28 March, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.033602

Abstract

A droplet that impacts onto a solid substrate deforms in a complex dynamics. To extract the principal mechanisms that dominate this dynamics, we deploy numerical simulations based on the phase field method. Direct comparison with experiments suggests that a dissipation local to the contact line limits the droplet spreading dynamics and its scaled maximum spreading radius βmax. By assuming linear response through a drag force at the contact line, our simulations rationalize experimental observations for droplet impact on both smooth and rough substrates, measured through a single contact line friction parameter μf. Moreover, our analysis shows that dissipation at the contact line can limit the dynamics and we describe βmax by the scaling law βmax∼(Reμl/μf)1/2 that is a function of the droplet viscosity (μl) and its Reynolds number (Re).

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (53)

  1. R. Dykhuizen, Review of impact and solidification of molten thermal spray droplets, J. Thermal Spray Technol. 3, 351 (1994).
  2. D. Attinger, Z. Zhao, and D. Poulikakos, An experimental study of molten microdroplet surface deposition and solidification: Transient behavior and wetting angle dynamics, J. Heat Transfer 122, 544 (2000).
  3. S. Fathi, P. Dickens, and F. Fouchal, Regimes of droplet train impact on a moving surface in an additive manufacturing process, J. Mater. Process. Technol. 210, 550 (2010).
  4. V. Bergeron, D. Bonn, J. Y. Martin, and L. Vovelle, Controlling droplet deposition with polymer additives, Nature (London) 405, 772 (2000).
  5. N. Z. Mehdizadeh, S. Chandra, and J. Mostaghimi, Formation of fingers around the edges of a drop hitting a metal plate with high velocity, J. Fluid Mech. 510, 353 (2004).
  6. S. Mandre, M. Mani, and M. P. Brenner, Precursors to Splashing of Liquid Droplets on a Solid Surface, Phys. Rev. Lett. 102, 134502 (2009).
  7. L. Duchemin and C. Josserand, Curvature singularity and film-skating during drop impact, Phys. Fluids 23, 091701 (2011).
  8. J. M. Kolinski, S. M. Rubinstein, S. Mandre, M. P. Brenner, D. A. Weitz, and L. Mahadevan, Skating on a Film of Air: Drops Impacting on a Surface, Phys. Rev. Lett. 108, 074503 (2012).
  9. W. Bouwhuis, R. C. A van der Veen, T. Tran, D. L. Keij, K. G. Winkels, I. R. Peters, D. van der Meer, C. Sun, J. H. Snoeijer, and D. Lohse, Maximal Air Bubble Entrainment at Liquid-Drop Impact, Phys. Rev. Lett. 109, 264501 (2012).
  10. Y. Liu, P. Tan, and L. Xu, Compressible air entrapment in high-speed drop impacts on solid surfaces, J. Fluid Mech. 716, R9 (2013).
  11. C. W. Visser, P. E. Frommhold, S. Wildeman, R. Mettin, D. Lohse, and C. Sun, Dynamics of high-speed micro-drop impact: Numerical simulations and experiments at frame-to-frame times below 100 ns, Soft Matter 11, 1708 (2015).
  12. E. Li and S. T. Thoroddsen, Time-resolved imaging of a compressible air disk under a drop impacting on a solid surface, J. Fluid Mech. 780, 636 (2015).
  13. M. M. Driscoll and S. R. Nagel, Ultrafast Interference Imaging of Air in Splashing Dynamics, Phys. Rev. Lett. 107, 154502 (2011).
  14. K. Yokoi, Numerical studies of droplet splashing on a dry surface: Triggering a splash with the dynamic contact angle, Soft Matter 7, 5120 (2011).
  15. C. W. Visser, Y. Tagawa, C. Sun, and D. Lohse, Microdroplet impact at very high velocity, Soft Matter 8, 10732 (2012).
  16. G. Riboux and J. M. Gordillo, Experiments of Drops Impacting a Smooth Solid Surface: A Model of the Critical Impact Speed for Drop Splashing, Phys. Rev. Lett. 113, 024507 (2014).
  17. L. Xu, W. W. Zhang, and S. R. Nagel, Drop Splashing on a Dry Smooth Surface, Phys. Rev. Lett. 94, 184505 (2005).
  18. A. I. Fedorchenko, A.-B. Wang, and Y.-H. Wang, Effect of capillary and viscous forces on spreading of a liquid drop impinging on a solid surface, Phys. Fluids 17, 093104 (2005).
  19. I. V. Roisman, R. Rioboo, and C. Tropea, Normal impact of a liquid drop on a dry surface: Model for spreading and receding, Proc. Royal Soc. London, Ser. A 458, 1411 (2002).
  20. T. Bennett and D. Poulikakos, Splat-quench solidification: Estimating the maximum spreading of a droplet impacting a solid surface, J. Mater. Sci. 28, 963 (1993).
  21. G. Lagubeau, M. A. Fontelos, C. Josserand, A. Maurel, V. Pagneux, and P. Petitjeans, Spreading dynamics of drop impacts, J. Fluid Mech. 713, 50 (2012).
  22. J. Eggers, M. A. Fontelos, C. Josserand, and S. Zaleski, Drop dynamics after impact on a solid wall: Theory and simulations, Phys. Fluids 22, 062101 (2010).
  23. N. Laan, K. G. de Bruin, D. Bartolo, C. Josserand, and D. Bonn, Maximum Diameter of Impacting Liquid Droplets, Phys. Rev. Appl. 2, 044018 (2014).
  24. B. L. Scheller and D. W. Bousfield, Newtonian drop impact with a solid surface, AIChE J. 41, 1357 (1995).
  25. M. Pasandideh-Fard, Y. Qiao, S. Chandra, and J. Mostaghimi, Capillary effects during droplet impact on a solid surface, Phys. Fluids 8, 650 (1996).
  26. T. Mao, D. Kuhn, and H. Tran, Spread and rebound of liquid droplets upon impact on flat surfaces, AIChE J. 43, 2169 (1997).
  27. S. Chandra and C. Avedisian, On the collision of a droplet with a solid surface, Proc. Royal Soc. London, Ser. A 432, 13 (1991).
  28. D. Vadillo, A. Soucemarianadin, C. Delattre, and D. Roux, Dynamic contact angle effects onto the maximum drop impact spreading on solid surfaces, Phys. Fluids 21, 122002 (2009).
  29. C. Ukiwe and D. Y. Kwok, On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces, Langmuir 21, 666 (2005).
  30. C. Clanet, C. Béguin, D. Richard, and D. Quéré, Maximal deformation of an impacting drop, J. Fluid Mech. 517, 199 (2004).
  31. C. Josserand and S. Thoroddsen, Drop impact on a solid surface, Annu. Rev. Fluid Mech. 48, 365 (2016).
  32. J. Lee, N. Laan, K. de Bruin, G. Skantzaris, N. Shahidzadeh, D. Derome, J. Carmeliet, and D. Bonn, Universal rescaling of drop impact on smooth and rough surfaces, J. Fluid Mech. 786, R4 (2015).
  33. R. Kannan and D. Sivakumar, Drop impact process on a hydrophobic grooved surface, Colloids Surf. A 317, 694 (2008).
  34. V. Vaikuntanathan and D. Sivakumar, Maximum spreading of liquid drops impacting on groove-textured surfaces: Effect of surface texture, Langmuir 32, 2399 (2016).
  35. J. B. Lee, D. Derome, R. Guyer, and J. Carmeliet, Modeling the maximum spreading of liquid droplets impacting wetting and nonwetting surfaces, Langmuir 32, 1299 (2016).
  36. P. Tsai, S. Pacheco, C. Pirat, L. Lefferts, and D. Lohse, Drop impact upon micro- and nanostructured superhydrophobic surfaces, Langmuir 25, 12293 (2009).
  37. R. C. van der Veen, M. H. Hendrix, T. Tran, C. Sun, P. A. Tsai, and D. Lohse, How microstructures affect air film dynamics prior to drop impact, Soft Matter 10, 3703 (2014).
  38. S. Robson and G. R. Willmott, Asymmetries in the spread of drops impacting on hydrophobic micropillar arrays, Soft Matter 12, 4853 (2016).
  39. A. Yarin, Drop impact dynamics: Splashing, spreading, receding, bouncing, Annu. Rev. Fluid Mech. 38, 159 (2006).
  40. A. Carlson, M. Do-Quang, and G. Amberg, Dissipation in rapid dynamic wetting, J. Fluid Mech. 682, 213 (2011).
  41. A. Carlson, G. Bellani, and G. Amberg, Contact line dissipation in short-time dynamic wetting, Europhys. Lett. 97, 44004 (2012).
  42. D. Jacqmin, Calculation of two-phase Navier-Stokes flows using phase-field modeling, J. Comput. Phys. 155, 96 (1999).
  43. J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system, I: Interfacial free energy, J. Chem. Phys. 28, 258 (1958).
  44. D. Jacqmin, Contact-line dynamics of a diffuse fluid interface, J. Fluid Mech. 402, 57 (2000).
  45. P. Yue, C. Zhou, and J. J. Feng, Sharp-interface limit of the Cahn-Hilliard model for moving contact lines, J. Fluid Mech. 645, 279 (2010).
  46. F. Magaletti, F. Picano, M. Chinappi, L. Marino, and C. M. Casciola, The sharp-interface limit of the Cahn-Hilliard/Navier-Stokes model for binary fluids, J. Fluid Mech. 714, 95 (2013).
  47. G. Amberg, R. Tönhardt, and C. Winkler, Finite element simulations using symbolic computing, Math. Comp Simul. 49, 257 (1999).
  48. V. Khatavkar, P. Anderson, P. Duineveld, and H. Meijer, Diffuse-interface modeling of droplet impact, J. Fluid Mech. 581, 97 (2007).
  49. Q. Zhang, T.-Z. Qian, and X.-P. Wang, Phase field simulation of a droplet impacting a solid surface, Phys. Fluids 28, 022103 (2016).
  50. Y. Wang, M. Do-Quang, and G. Amberg, Events and conditions in droplet impact: A phase field prediction, Int. J. Multiphase Flow 87, 54 (2016).
  51. W. Villanueva and G. Amberg, Some generic capillary-driven flows, Int. J. Multiphase Flow 32, 1072 (2006).
  52. A. Carlson, G. Bellani, and G. Amberg, Universality in dynamic wetting dominated by contact-line friction, Phys. Rev. E 85, 045302 (2012).
  53. J. Wang, M. Do-Quang, J. J. Cannon, F. Yue, Y. Suzuki, G. Amberg, and J. Shiomi, Surface structure determines dynamic wetting, Sci. Rep. 5, 8474 (2015).

Outline

Information

Phys. Rev. Fluids 2, 033602– Published 28 March, 2017
  • Received 24 November 2016

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation