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Droplet motion on chemically heterogeneous substrates with mass transfer. I. Two-dimensional dynamics

Danny Groves

Nikos Savva*

  • School of Mathematics, Cardiff University, Cardiff CF24 4AG, Wales, United Kingdom

  • Computation-Based Science and Technology Research Center, The Cyprus Institute, Nicosia 2121, Cyprus

  • *Corresponding author: n.savva@cyi.ac.cy
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Phys. Rev. Fluids 6, 123601 – Published 9 December, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.123601

Abstract

We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer, and capillarity. The resulting long-wave evolution equation for the droplet thickness is treated analytically via the method of matched asymptotic expansions in the limit of slow mass transfer rates, quasistatic dynamics, and vanishingly small slip lengths to deduce a lower-dimensional system of integrodifferential equations for the two moving fronts. We demonstrate that the predictions of the deduced system agree excellently with simulations of the full model for a number of representative cases within the domain of applicability of the analysis. Specifically, we focus on situations where the mass of the drop changes periodically, to highlight a number of interesting features of the dynamics, which include stick-slip, hysteresislike effects, as well as the possibility for the droplet to alternate between the constant-radius and constant-angle stages which have been previously reported in related works. These features of the dynamics are further scrutinized by investigating how the bifurcation structure of droplet equilibria evolves as the mass of the droplet varies.

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Droplet motion on chemically heterogeneous substrates with mass transfer. II. Three-dimensional dynamics

Nikos Savva and Danny Groves
Phys. Rev. Fluids 6, 123602 (2021)

Article Text

References (67)

  1. H.-Y. Kim, S. Jeon, M. Song, and K. Kim, Numerical simulations of water droplet dynamics in hydrogen fuel cell gas channel, J. Power Sources 246, 679 (2014).
  2. M. J. Cheah, I. G. Kevrekidis, and J. B. Benziger, Water slug formation and motion in gas flow channels: The effects of geometry, surface wettability, and gravity, Langmuir 29, 9918 (2013).
  3. V. Dugas, J. Broutin, and E. Souteyrand, Droplet evaporation study applied to DNA chip manufacturing, Langmuir 21, 9130 (2005).
  4. J. Park and J. Moon, Control of colloidal particle deposit patterns within picoliter droplets ejected by ink-jet printing, Langmuir 22, 3506 (2006).
  5. P. Calvert, Inkjet printing for materials and devices, Chem. Mater. 13, 3299 (2001).
  6. A. D. Eales, N. Dartnell, S. Goddard, and A. F. Routh, The impact of trough geometry on film shape: A theoretical study of droplets containing polymer, for P-OLED display applications, J. Colloid. Interf. Sci. 458, 53 (2015).
  7. J. H. Snoeijer and B. Andreotti, Moving contact lines: Scales, regimes, and dynamical transitions, Annu. Rev. Fluid Mech. 45, 269 (2013).
  8. D. Bonn, J. Eggers, J. Indekeu, J. Meunier, and E. Rolley, Wetting and spreading, Rev. Mod. Phys. 81, 739 (2009).
  9. T. Cubaud and M. Fermigier, Advancing contact lines on chemically patterned surfaces, J. Colloid. Interf. Sci. 269, 171 (2004).
  10. E. Rio, A. Daerr, F. Lequeux, and L. Limat, Moving contact lines of a colloidal suspension in the presence of drying, Langmuir 22, 3186 (2006).
  11. J. Y. Chung, J. P. Youngblood, and C. M. Stafford, Anisotropic wetting on tunable micro-wrinkled surfaces, Soft Matter 3, 1163 (2007).
  12. H. Kusumaatmaja and J. M. Yeomans, Modeling contact angle hysteresis on chemically patterned and superhydrophobic surfaces, Langmuir 23, 6019 (2007).
  13. H. B. Eral, D. J. C. M. 't Mannetje, and J. M. Oh, Contact angle hysteresis: A review of fundamentals and applications, Colloid. Polym. Sci. 291, 247 (2012).
  14. S. Brandon and A. Marmur, Simulation of contact angle hysteresis on chemically heterogeneous surfaces, J. Colloid. Interf. Sci. 183, 351 (1996).
  15. W. Barthlott and C. Neinhuis, Purity of the sacred lotus, or escape from contamination in biological surfaces, Planta 202, 1 (1997).
  16. I. P. Parkin and R. G. Palgrave, Self-cleaning coatings, J. Mater. Chem. 15, 1689 (2005).
  17. A. Ghosh, S. Beaini, B. J. Zhang, R. Ganguly, and C. M. Megaridis, Enhancing dropwise condensation through bioinspired wettability patterning, Langmuir 30, 13103 (2014).
  18. A. Lee, M.-W. Moon, H. Lim, W.-D. Kim, and H.-Y. Kim, Water harvest via dewing, Langmuir 28, 10183 (2012).
  19. T. Pravinraj and R. Patrikar, A droplet actuation technique for a lab-on-chip device using partial wetting surface without external force, Sens. Actuators, A 285, 482 (2019).
  20. H. Zhou, M. Zhang, C. Li, C. Gao, and Y. Zheng, Excellent fog-droplets collector via integrative janus membrane and conical spine with micro/nanostructures, Small 14, 1801335 (2018).
  21. S. Baek, H. S. Moon, W. Kim, S. Jeon, and K. Yong, Effect of liquid droplet surface tension on impact dynamics over hierarchical nanostructure surfaces, Nanoscale 10, 17842 (2018).
  22. O. Bliznyuk, E. Vereshchagina, E. S. Kooij, and B. Poelsema, Scaling of anisotropic droplet shapes on chemically stripe-patterned surfaces, Phys. Rev. E 79, 041601 (2009).
  23. H. P. Jansen, K. Sotthewes, C. Ganser, C. Teichert, H. J. W. Zandvliet, and E. S. Kooij, Tuning kinetics to control droplet shapes on chemically striped patterned surfaces, Langmuir 28, 13137 (2012).
  24. H. P. Jansen, K. Sotthewes, C. Ganser, H. J. W. Zandvliet, C. Teichert, and E. S. Kooij, Shape of picoliter droplets on chemically striped patterned substrates, Langmuir 30, 11574 (2014).
  25. R. David and A. W. Neumann, Anisotropic drop shapes on chemically striped surfaces, Colloids Surf. A: Physicochem. Eng. Asp. 393, 32 (2012).
  26. L. Zou, H. Wang, X. Zhu, Y. Ding, R. Chen, and Q. Liao, Droplet splitting on chemically striped surface, Colloids Surf. A: Physicochem. Eng. Asp. 537, 139 (2018).
  27. C. Lam, R. Wu, D. Li, M. Hair, and A. Neumann, Study of the advancing and receding contact angles: Liquid sorption as a cause of contact angle hysteresis, Adv. Collloid. Interfac. 96, 169 (2002).
  28. D. Arora, A. P. Deshpande, and S. Chakravarthy, Experimental investigation of fluid drop spreading on heterogeneous and anisotropic porous media, J. Colloid. Interf. Sci. 293, 496 (2006).
  29. C. Aydemir, Time-dependent behavior of a sessile water droplet on various papers, Int. J. Polym. Mater. 59, 387 (2010).
  30. L. Espín and S. Kumar, Droplet spreading and absorption on rough, permeable substrates, J. Fluid Mech. 784, 465 (2015).
  31. D. Brutin and V. Starov, Recent advances in droplet wetting and evaporation, Chem. Soc. Rev. 47, 558 (2018).
  32. H. Y. Erbil, Evaporation of pure liquid sessile and spherical suspended drops: A review, Adv. Collloid. Interfac. 170, 67 (2012).
  33. T. Pham and S. Kumar, Imbibition and evaporation of droplets of colloidal suspensions on permeable substrates, Phys. Rev. Fluids 4, 034004 (2019).
  34. V. Charitatos, T. Pham, and S. Kumar, Droplet evaporation on inclined substrates, Phys. Rev. Fluids 6, 084001 (2021).
  35. D. Brutin, Droplet Wetting and Evaporation: From Pure to Complex Fluids (Academic, New York, 2015).
  36. J. M. Stauber, S. K. Wilson, B. R. Duffy, and K. Sefiane, Evaporation of droplets on strongly hydrophobic substrates, Langmuir 31, 3653 (2015).
  37. J. M. Stauber, S. K. Wilson, B. R. Duffy, and K. Sefiane, On the lifetimes of evaporating droplets with related initial and receding contact angles, Phys. Fluids 27, 122101 (2015).
  38. A. Amini and G. M. Homsy, Evaporation of liquid droplets on solid substrates. I. Flat substrate with pinned or moving contact line, Phys. Rev. Fluids 2, 043603 (2017).
  39. A. Amini and G. M. Homsy, Evaporation of liquid droplets on solid substrates. II. Periodic substrates with moving contact lines, Phys. Rev. Fluids 2, 043604 (2017).
  40. T. Pham and S. Kumar, Drying of droplets of colloidal suspensions on rough substrates, Langmuir 33, 10061 (2017).
  41. H. Y. Erbil, G. McHale, and M. I. Newton, Drop evaporation on solid surfaces: Constant contact angle mode, Langmuir 18, 2636 (2002).
  42. S. Armstrong, G. McHale, R. Ledesma-Aguilar, and G. G. Wells, Pinning-free evaporation of sessile droplets of water from solid surfaces, Langmuir 35, 2989 (2019).
  43. G. G. Wells, É. Ruiz-Gutiérrez, Y. L. Lirzin, A. Nourry, B. V. Orme, M. Pradas, and R. Ledesma-Aguilar, Snap evaporation of droplets on smooth topographies, Nat. Commun. 9, 1380 (2018).
  44. K. B. Kiradjiev, C. J. W. Breward, and I. M. Griffiths, Surface-tension- and injection-driven spreading of a thin viscous film, J. Fluid Mech. 861, 765 (2018).
  45. J. M. Oliver, J. P. Whiteley, M. A. Saxton, D. Vella, V. S. Zubkov, and J. R. King, On contact-line dynamics with mass transfer, Eur. J. Appl. Math. 26, 671 (2015).
  46. H. P. Greenspan, On the motion of a small viscous droplet that wets a surface, J. Fluid Mech. 84, 125 (1978).
  47. L. M. Hocking, The spreading of a thin drop by gravity and capillarity, Q. J. Mech. Appl. Math. 36, 55 (1983).
  48. A. A. Lacey, The motion with slip of a thin viscous droplet over a solid surface, Stud. Appl. Math. 67, 217 (1982).
  49. N. Savva and D. Groves, Droplet motion on chemically heterogeneous substrates with mass transfer. II. Three-dimensional dynamics, Phys. Rev. Fluids 6, 123602 (2021).
  50. M. Pradas, N. Savva, J. B. Benziger, I. G. Kevrekidis, and S. Kalliadasis, Dynamics of fattening and thinning 2D sessile droplets, Langmuir 32, 4736 (2016).
  51. M. A. Saxton, J. P. Whiteley, D. Vella, and J. M. Oliver, On thin evaporating drops: When is the d2-law valid? J. Fluid Mech. 792, 134 (2016).
  52. M. A. Saxton, D. Vella, J. P. Whiteley, and J. M. Oliver, Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop, J. Eng. Math. 106, 47 (2017).
  53. N. Savva, A. Rednikov, and P. Colinet, Asymptotic analysis of the evaporation dynamics of partially wetting droplets, J. Fluid Mech. 824, 574 (2017).
  54. E. Ruckenstein and C. Dunn, Slip velocity during wetting of solids, J. Colloid. Interf. Sci. 59, 135 (1977).
  55. H. K. Moffatt, Viscous and resistive eddies near a sharp corner, J. Fluid Mech. 18, 1 (1964).
  56. C. Huh and L. Scriven, Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, J. Colloid. Interf. Sci. 35, 85 (1971).
  57. N. Savva and S. Kalliadasis, Two-dimensional droplet spreading over topographical substrates, Phys. Fluids 21, 092102 (2009).
  58. R. Vellingiri, N. Savva, and S. Kalliadasis, Droplet spreading on chemically heterogeneous substrates, Phys. Rev. E 84, 036305 (2011).
  59. D. N. Sibley, A. Nold, and S. Kalliadasis, The asymptotics of the moving contact line: Cracking an old nut, J. Fluid Mech. 764, 445 (2015).
  60. J. Eggers, Existence of receding and advancing contact lines, Phys. Fluids 17, 082106 (2005).
  61. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1972), Sec. 25.4.
  62. https://github.com/n-savva/2d_mass_transfer.
  63. L. W. Schwartz, Hysteretic effects in droplet motions on heterogeneous substrates: Direct numerical simulation, Langmuir 14, 3440 (1998).
  64. N. Savva and S. Kalliadasis, Droplet motion on inclined heterogeneous substrates, J. Fluid Mech. 725, 462 (2013).
  65. E. L. Allgower and K. Georg, Numerical Continuation Methods (Springer-Verlag, Berlin, 1990).
  66. N. Savva, S. Kalliadasis, and G. A. Pavliotis, Two-Dimensional Droplet Spreading Over Random Topographical Substrates, Phys. Rev. Lett. 104, 084501 (2010).
  67. N. Savva, D. Groves, and S. Kalliadasis, Droplet dynamics on chemically heterogeneous substrates, J. Fluid Mech. 859, 321 (2018).

Outline

Information

Phys. Rev. Fluids 6, 123601– Published 9 December, 2021
  • Received 15 July 2020
  • Accepted 27 October 2021
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