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Revisited Cassie's law to incorporate microstructural capillary effects

C. M. Mackenzie Dover and K. Sefiane*

  • School of Engineering, The University of Edinburgh, King's Buildings, Robert Stevenson Road, Edinburgh EH9 3FB, United Kingdom

  • *K.Sefiane@ed.ac.uk
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Phys. Rev. Fluids 4, 081601(R) – Published 7 August, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.081601

Abstract

The equilibrium contact angle and the receding contact angle of water droplets suspended on surfaces comprising arrays of equidistant, uniformly sized square micropillars has been measured with goniometry. Surfaces with distinct pillar size and spacing were fabricated via photolithography and deep reactive-ion etching prior to hydrophobization via the molecular vapor deposition of perflourodecyltrichlorosilane (FDTS). The surfaces exhibited superhydrophobic properties and the measured equilibrium contact angle was compared with the prediction of the Cassie equation based on the measured contact angle on a flat FDTS surface and the surface morphology. A poor agreement between the experimental data and the data predicted by the Cassie equation was found when the spacing between structures was less than the width of the pillars. For more closely spaced structures, the deviation between the measured and predicted values increased. In this roughness region, the measured angle is unchanged by the spacing but the receding angle continues to be dependent on the surface structure. A microscopic examination of the interface between the surface and the droplet revealed that the liquid-gas portion of the contact line was distorted at the pillar edges. The extent of the distortion could not be accurately quantified but it was shown that if the capillary region was assumed to be semicircular and extending half of the width of a pillar in to the liquid-gas region of the contact line, that the contact angle could be predicted well. Moreover, a good prediction of the experimental data of a prior study of droplets on closely spaced circular polydimethylsiloxane micropillar arrays is presented.

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References (41)

  1. C. Choi, D. I. Yu, and M. Kim, Surface wettability effect on flow pattern and pressure drop in adiabatic two-phase flows in rectangular microchannels with T-junction mixer, Exp. Therm. Fluid. Sci. 35, 1086 (2011).
  2. K. Osari, N. Unno, J. Taniguchi, K. Macinaga, T. Ohsaki, and N. Sakai, Evaluation of filling behavior on UV nanoimprint lithography using release coating, Microelectron. Eng. 87, 918 (2010).
  3. P. Calvert, Inkjet printing for materials and devices, Chem. Mater. 13, 3299 (2001).
  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. M. Schena, D. Shalon, R. W. Davis, and P. O. Brown, Quantitative monitoring of gene expression patterns with a complementary DNA microarray, Science 270, 467 (1995).
  6. V. Dugas, J. Broutin, and E. Souteyrand, Droplet evaporation study applied to DNA chip manufacturing, Langmuir 21, 9130 (2005).
  7. W. Jai and H. H. Qiu, Experimental investigation of droplet dynamics and heat transfer in spray cooling, Exp. Therm. Fluid. Sci. 27, 829 (2003).
  8. S. Tawfick, M. De Volder, D. Copic, S. J. Park, C. R. Oliver, E. S. Polsen, M. J. Roberts, and A. J. Hart, Engineering of micro- and nanostructured surfaces with anisotropic geometries and properties, Adv. Mater. 24, 1628 (2012).
  9. C. Mackenzie-Dover, G. Duursma, K. Sefiane, J. Christy, and J. Terry, Effect of micropillar spacing and temperature of substrate on contact angle dynamics, Heat Transfer Eng. 40, 794 (2018).
  10. Y. H. Yeong, A. Milonis, E. Loth, and I. S. Bayer, Microscopic receding contact line dynamics on pillar and irregular superhydrophobic surfaces, Sci. Rep. 5, 8384 (2015).
  11. Y. Q. Zu and Y. Y. Yan, Single droplet on micro square-post patterned surfaces-theoretical model and numerical simulation, Sci. Rep. 6, 19281 (2016).
  12. C. W. Yao, T. P. Garvin, J. L. Alvarado, A. M. Jacobi, B. G. Jones, and C. P. Marsh, Droplet contact angle behaviour on a hybrid surface with hydrophobic and hydrophillic properties, Appl. Phys. Lett. 101, 111605 (2012).
  13. N. J. Shirtcliffe, G. Mchale, S. Atherton, and M. I. Newton, An introduction to superhydrophobicity, Adv. Colloid Interface Sci. 161, 124 (2010).
  14. G. McHale, N. J. Shirtcliffe, and M. I. Newton, Super-hydrophobic and super-wetting surfaces: Analytical potenial? Analyst 129, 284 (2004).
  15. R. N. Wenzel, Resistance of solid surfaces to wetting by water, Ind. Eng. Chem. 28, 988 (1936).
  16. A. B. D. Cassie and S. Baxter, Wettability of porous surfaces, Trans. Faraday Soc. 40, 546 (1944).
  17. K. Y. Law, Definitions for hydrophilicity, hydrophobicity, and superhydrophobicity: Getting the basics right, J. Phys. Chem. Lett. 5, 686 (2014).
  18. L. Gao and T. J. McCarthy, Teflon is hydrophilic. Comments and definitions of hydrophobic, shear versus tensile hydrophobicity, and wettability characterisation, Langmuir 24, 9183 (2008).
  19. N. A. Patankar, Hysteresis with regard to Cassie and Wenzel states on superhydrophobic surfaces, Langmuir, 26, 7498 (2010).
  20. B. Bhurat and Y. C. Jung, Natural and biomimetic artificial surfaces for superhydrophobicity, self-cleaning, low adhesion, and drag reduction, Prog. Mater. Sci. 56, 1 (2011).
  21. J. Kim and C.-J. Kim, Nanostructured surfaces for dramatic reduction of flow resistance in droplet-based microfluidics, in Proceedings of the 15th IEEE International Conference on Micro Electro Mechanical Systems, Las Vegas, 2002 (unpublished), p. 479.
  22. L. Afferante and G. Carbone, The effect of drop volume and micropillar shape on the apparent contact angle of ordered microstructured surfaces, Soft Matter 10, 3906 (2014).
  23. B. Zhang, X. Chen, J. Dobnikar, Z. Wang, and X. Zhang, Spontaneous Wenzel to Cassie dewetting transition on structured surfaces, Phys. Rev. Fluids 1, 073904 (2016).
  24. Q. Zheng, C. Lv, P. Hao, and J. Sheridan, Small is beautiful, and dry, Sci. China Phys. Mech. 53, 2245 (2010).
  25. B. Bhushan, M. Nosovsky, and Y. C. Jung, Towards optimization of patterned superhydrophobic surfaces, J. R. Soc. Interface 4, 643 (2007).
  26. G. Wang, Z. Jai, and H. Yang, Stability of a water droplet on micropillared hydrophobic surfaces, Colloid Polym. Sci. 294, 851 (2016).
  27. H. Y. Erbil and C. Elif Cansoy, Range of applicability of the Wenzel and Cassie-Baxter equations for superhydrophobic surfaces, Langmuir 25, 14135 (2009).
  28. C. W. Extrand, Contact angles and hysteresis on surfaces with chemically heterogeneous islands, Langmuir 19, 3793 (2003).
  29. M. Iwamatsu, Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces, J. Colloid Interface Sci. 297, 772 (2006).
  30. G. McHale, Cassie and Wenzel: Were they really so wrong?, Langmuir 23, 8200 (2007).
  31. L. Gao and T. J. McCarthy, How Wenzel and Cassie were wrong, Langmuir 23, 3762 (2007).
  32. T. Lui, Y. Li, X. Li, and W. Sun, Mechanism study on transition of Cassie droplets to Wenzel state after meniscus touching substrate of pillars, J. Phys. Chem. C 121, 9802 (2017).
  33. A. J. B. Milne and A. Amirfazli, The Cassie equation: How it is meant to be used, Adv. Colloid Interface Sci. 170, 48 (2012).
  34. Q. Zheng and C. Lu, Size effects of surface roughness to superhydrophobicity, Procedia IUTAM 10, 462 (2014).
  35. X. Song, J. Zhai, Y. Wang, and L. Jaing, Fabrication of superhydrophobic surfaces by self-assembly and their water-adhesion properties, J. Phys. Chem. B 109, 4048 (2005).
  36. N. A. Malvadkar, M. J. Hancock, K. Sekeroglu, W. J. Dressick, and M. C. Demirel, An engineered anisotropic nanofilm with unidirectional wetting properties, Nat. Mater. 12, 1023 (2010).
  37. S. Boduroglu, M. Cetinkaya, W. J. Dressick, A. Singh, and M. C. Demirel, Controlling the wettability and adhesion of nanostructured poly-(p-xylylene) films, Langmuir 23, 11391 (2007).
  38. J. Davies, S. Haq, T. Hawke, and J. P. Sargent, A practical approach to the development of a synthetic Gecko tape, Int. J. Adhes. Adhes. 29, 380 (2009).
  39. X. Wang and R. A. Weiss, A facile method for preparing sticky, hydrophobic polymer surfaces, Langmuir 28, 3298 (2012).
  40. W. Choi, A. Tuteja, J. M. Mabry, R. E. Cohen, and G. H. McKinley, A modified Cassie-Baxter relationship to explain contact angle hysteresis and anisotropy on non-wetting textured surfaces, J. Colloid Interface Sci. 339, 208 (2009).
  41. A. Paxson and K. V. Varasani, Self-similarity of contact line depinning from textured surfaces, Nat. Commun. 4, 1492 (2013).

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Phys. Rev. Fluids 4, 081601(R)– Published 7 August, 2019
  • Received 20 March 2019
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