Skip to main content
Log in

Numerical study of energetics and wetting stability of liquid droplets on microtextured surfaces

  • Original Contribution
  • Published:
Colloid and Polymer Science Aims and scope Submit manuscript

Abstract

The suspended wetting state (Cassie-Baxter state) on a microstructured surface tends to collapse to a wetted state (Wenzel state) if the liquid-air interface is perturbed. Multiple metastable Cassie-Baxter (CB) wetting states, separated by an energy barrier from Wenzel state, may also exist. In this study, numerical method is applied to study the wetting properties of liquid droplets on a variety of microtextured surfaces with a particular focus on the stability of the CB wetting state. A dimensionless form of droplet energy is used to compare the relative stabilities of multiple metastable states. The sequence of stable drop configurations with increasing droplet volume on a particular substrate is analyzed for both isotropic and anisotropic cases. Applying dimensional variation, characterized by the pillar spacing and pillar width, on surface microtexture, the key parameter which plays dominant role in the stability of droplet is explored. The solid-fraction that the droplet avails at the drop-base is observed to be the most vital parameter for the droplet stability. Spreading of droplet from one isotropic wetting configuration to an anisotropic configuration is not favorable unless the spreading of the droplet is restricted to be unidirectional.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Cui XS, Li W (2010) On the possibility of superhydrophobic behavior for hydrophilic materials J Colloid Interface Sci 347:156–162

    Article  CAS  Google Scholar 

  2. Patankar NA (2004) Transition between superhydrophobic states on rough surfaces Langmuir 20:7097–7102

    Article  CAS  Google Scholar 

  3. Chen Y, He B, Lee J, Patankar NA (2005) Anisotropy in the wetting of rough surfaces J Colloid Interface Sci 281:458–464

    Article  Google Scholar 

  4. Bhushan B, Jung YC (2011) Natural and biomimetic artificial surfaces for superhydrophobicity, self-cleaning, low adhesion, and drag reduction Prog Mater Sci 56:1–108

    Article  CAS  Google Scholar 

  5. Barkhudarov PM, Shah PB, Watkins EB, Doshi DA, Brinker CJ, Majewski J (2008) Corrosion inhibition using superhydrophobic films Corros Sci 50:897–902

    Article  CAS  Google Scholar 

  6. Lv C, Hao P, Yao Z, Niu F (2015) Departure of condensation droplets on superhydrophobic surfaces Langmuir 31(8):2414–2420

    Article  CAS  Google Scholar 

  7. Wenzel RN (1936) Resistance of solid surfaces to wetting by water Ind Eng Chem 28:988–994

    Article  CAS  Google Scholar 

  8. Cassie ABD, Baxter S (1944) Wettability of porous surfaces Trans Faraday Soc 40:546–551

    Article  CAS  Google Scholar 

  9. Afferrante L, Carbone G (2010) Microstructured superhydrorepellent surfaces: effect of drop pressure on fakir-state stability and apparent contact angles J Phys Condens Matter 22(32):325107

    Article  CAS  Google Scholar 

  10. Barbieri L, Wagner E, Hoffmann P (2007) Water wetting transition parameters of perfluorinated substrates with periodically distributed flat-top microscale obstacles Langmuir 23(4):1723–1734

    Article  CAS  Google Scholar 

  11. Zheng QS, Yu Y, Zhao ZH (2005) Effects of hydraulic pressure on the stability and transition of wetting modes of superhydrophobic surfaces Langmuir 21(26):12207–12212

    Article  CAS  Google Scholar 

  12. Cai T, Jia Z, Yang H, Wang G (2016) Investigation of Cassie-Wenzel wetting transitions on microstructured surfaces Colloid Polym Sci 294(5):833–840

    Article  CAS  Google Scholar 

  13. Guo HY, Li B, Feng XQ (2016) Feng, stability of Cassie-Baxter wetting states on microstructured surfaces Phys Rev E 94(4):042801

    Article  Google Scholar 

  14. Bico J, Marzolin C, Quéré D (1999) Pearl drops Europhys Lett 47(2):220–226

    Article  CAS  Google Scholar 

  15. Callies M, Chen Y, Marty F, Pépin A, Quéré D (2005) Microfabricated textured surfaces for super-hydrophobicity investigations Microelectron Eng 78-79:100–105

    Article  CAS  Google Scholar 

  16. Hans M, Müller F, Grandthyll S, Hüfner S, Mücklich F (2012) Anisotropic wetting of copper alloys by one-step laser micro-patterning Appl Surf Sci 263:416–422

    Article  CAS  Google Scholar 

  17. Bhushan B, Jung YC (2006) Micro and nanoscale characterization of hydrophobic and hydrophilic leaf surface Nanotechnology 17:2758–2772

    Article  CAS  Google Scholar 

  18. Gogolides E, Ellinas K, Tserepi A (2015) Hierarchical micro and nano structured, hydrophilic, superhydrophobic and superoleophobic surfaces incorporated in microfluidics, microarrays and lab on chip microsystems Microelectron Eng 132:135–155

    Article  CAS  Google Scholar 

  19. Tuvshindorj U, Yildirim A, Ozturk FE, Bayindir M (2014) Robust Cassie state of wetting in transparent superhydrophobic coatings ACS Appl Mater Interfaces 6(12):9680–9688

    Article  CAS  Google Scholar 

  20. Dubov AL, Perez-Toralla K, Letailleur A, Barthel E, Teisseire J (2013) Superhydrophobic silica surfaces: fabrication and stability J Micromech Microeng 23:125013

    Article  Google Scholar 

  21. He B, Patankar NA, Lee J (2003) Multiple equilibrium droplet shapes and design criterion for rough hydrophobic surfaces Langmuir 19:4999–5003

    Article  CAS  Google Scholar 

  22. Dubov AL, Mourran A, Moller M, Vinogradova OI (2015) Regimes of wetting transitions on superhydrophobic textures conditioned by energy of receding contact lines Appl Phys Lett 106:241601

    Article  Google Scholar 

  23. Bottiglione F, Mundo RD, Soria L, Carbone G (2015) Wenzel to Cassie transition in superhydrophobic randomly rough surfaces Nanosci Nanotechnol Lett 7:74–78

    Article  Google Scholar 

  24. Zhang X, Zhu W, He G, Zhang P, Zhang Z, Parkin IP (2016) Flexible and mechanically robust superhydrophobic silicone surfaces with stable Cassie–Baxter state J Mater Chem A 4(37):14180–14186

    Article  CAS  Google Scholar 

  25. Long J, Pan L, Fan P, Gong D, Jiang D, Zhang H, Li L, Zhong M (2016) Cassie-state stability of metallic superhydrophobic surfaces with various micro/nanostructures produced by a femtosecond laser Langmuir 32(4):1065–1072

    Article  CAS  Google Scholar 

  26. Whyman G, Bormashenko E (2011) How to make the Cassie wetting state stable? Langmuir 27:8171–8176

    Article  CAS  Google Scholar 

  27. Wang G, Jia Z, Yang H (2016) Stability of a water droplet on micropillared hydrophobic surfaces Colloid Polym Sci 294(5):851–858

    Article  CAS  Google Scholar 

  28. Nosonovsky M (2007) Multiscale roughness and stability of superhydrophobic biomimetic interfaces Langmuir 23:3157–3161

    Article  CAS  Google Scholar 

  29. Zu YQ, Yan YY (2016) Single droplet on micro-square-post surfaces-theoretical model and numerical simulation Sci Rep 6:19281

    Article  CAS  Google Scholar 

  30. Liu T, Li Y, Li X, Sun W (2017) Mechanism study on transition of Cassie droplets to Wenzel state after meniscus touching substrate of pillars J Phys Chem C 121(18):9802–9814

    Article  CAS  Google Scholar 

  31. Gong W, Zu Y, Chen S, Yan Y (2017) Wetting transition energy curves for a droplet on a square-post patterned surface Sci Bull 62(2):136–142

    Article  Google Scholar 

  32. Wang Y, Chen S (2015) Droplets impact on textured surfaces: mesoscopic simulation of spreading dynamics Appl Surf Sci 327:159–167

    Article  CAS  Google Scholar 

  33. Hao J, Wang Z (2016) Modeling Cassie-Baxter state on superhydrophobic surfaces J Dispers Sci Technol 37(8):1208–1213

    Article  Google Scholar 

  34. Zhang W, Zhang R, Jiang C, Wu C (2017) Effect of pillar height on the wettability of micro-textured surface: volume-of-fluid simulations Int J Adhes Adhes 74:64–69

    Article  CAS  Google Scholar 

  35. Pashos G, Kokkoris G, Papathanasiou AG, Boudouvis AG (2016) Wetting transitions on patterned surfaces with diffuse interaction potentials embedded in a Young-Laplace formulation J Chem Phys 144:034105

    Article  CAS  Google Scholar 

  36. Zhao H, Park KC, Law KY (2012) Effect of surface texturing on superoleophobicity, contact angle hysteresis, and robustness Langmuir 28(42):14925–14934

    Article  CAS  Google Scholar 

  37. Chatain D, Lewis D, Baland JP, Carter WC (2006) Numerical analysis of the shapes and energies of droplets on micropatterned substrates Langmuir 22(9):4237–4243

    Article  CAS  Google Scholar 

  38. Gross M, Varnik F, Raabe D, Steinbach I (2010) Small droplets on superhydrophobic substrates Phys Rev E 81:051606

    Article  Google Scholar 

  39. Brakke KA (1992) The surface evolver Exp Math 1(2):141–165

    Article  Google Scholar 

  40. K. A. Brakke 2013, Surface Evolver documentation

  41. Arfken G (1985) Mathematical methods for physicists, Third edn. Academic Press, London,

    Google Scholar 

  42. Promraksa A, Chen LJ (2012) Modeling contact angle hysteresis of a liquid droplet sitting on a cosine wave-like patterned surface J Colloid Interface Sci 384:172–181

    Article  CAS  Google Scholar 

  43. Brandon S, Wachs A, Marmur A (1997) Simulated contact angle hysteresis of a three-dimensional drop on a chemically heterogenous surface: a numerical example J Colloid Interface Sci 191:110–116

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Md. Ashiqur Rahman.

Ethics declarations

Funding

The present study was not funded by any funding agency.

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goswami, A., Rahman, M.A. Numerical study of energetics and wetting stability of liquid droplets on microtextured surfaces. Colloid Polym Sci 295, 1787–1796 (2017). https://doi.org/10.1007/s00396-017-4158-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00396-017-4158-x

Keywords

Navigation