Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T15:11:06.319Z Has data issue: false hasContentIssue false
  • English
  • Français

Contact Angles of Sessile Droplets Deposited on Rough and FlatSurfaces in the Presence of External Fields

Published online by Cambridge University Press:  09 July 2012

E. Bormashenko
E. Bormashenko*
Affiliation:
Ariel University Center of Samaria, Applied Physics Department, Department of Chemistry and Biotechnology Engineering, POB 3, Ariel, 40700, Israel
*
∗ Corresponding author. E-mail: edward@ariel.ac.il
Get access

Abstract

The paper proposes a general framework allowing the analysis of wetting problems in thesituation when interfacial tensions depend on external fields. An equation predictingapparent contact angles of sessile droplets deposited on rough surfaces in the presence ofexternal fields is derived. The problem of wetting is discussed in the framework of thevariational approach. Derivation of a general equation generalizing the Cassie and Wenzelapproaches is presented. The effects related to the line tension which are important fornano-structured surfaces are considered.

Keywords

electrowettingdependence of interfacial tensions on external fields Cassie and Wenzel modelsline tensionexcess free energy variationtransversality conditions
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 4: Modelling phenomena on micro- and nanoscale , 2012 , pp. 1 - 5
Copyright
© EDP Sciences, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Pollack, M., Fair, R., Shenderov, A.. Electrowetting-based actuation of liquid droplets for microfluidic applications. Appl. Phys. Lett., 77 (2000), 1725–1726. CrossRefGoogle Scholar
Hayes, R., Feenstra, B.. Video-speed electronic paper based on electrowetting. Nature, 425 (2003), 383–385. CrossRefGoogle ScholarPubMed
Mugele, Fr., Baret, J.-Ch.. Electrowetting : from basics to applications. J. Phys. : Condens. Matter, 17 (2005), R705-R774. Google Scholar
Krupenkin, T., Taylor, J., Schneider, T., Yang, S., From Rolling Ball to Complete Wetting : The Dynamic Tuning of Liquids on Nanostructured Surfaces. Langmuir, 20 (2004), 3824–3827. CrossRefGoogle ScholarPubMed
Nguyen, N.-Tr., Zhu, G., Chua, Y.-Ch., Phan, V.-Ng., Tan, S.-H.. Magnetowetting and Sliding Motion of a Sessile Ferrofluid Droplet in the Presence of a Permanent Magnet. Langmuir, 26 (2010), 12553–12559. CrossRefGoogle ScholarPubMed
Zhou, Q., Ristenpart, W., Stroeve, P.. Magnetically Induced Decrease in Droplet Contact Angle on Nanostructured Surfaces. Langmuir 27, (2011), 11747–11751. CrossRefGoogle ScholarPubMed
Liggieri, L., Sanfeld, A., Steinchenbad, A.. Effects of magnetic and electric fields on surface tension of liquids. Physica A, 206 (1994), 299–331. CrossRefGoogle Scholar
Banpurkar, A., Nichols, K., Mugele, Fr.. Electrowetting-Based Microdrop Tensiometer. Langmuir, 24 (2008), 10549–10551. CrossRefGoogle ScholarPubMed
Shapiro, B., Moon, H., Garrell, R., Kim, CJ.. Equilibrium behavior of sessile drops under surface tension, applied external fields, and material variations. J. Applied Physics, 93 (2003), 5794–5811 CrossRefGoogle Scholar
P. de Gennes, F. Brochard-Wyart, D. Quere. Capillarity and Wetting Phenomena. Springer, Berlin, 2003.
Cassie, A., Baxter, S.. Wettablity of porous surfaces. Trans. Faraday Soc., 40 (1944), 546–551. CrossRefGoogle Scholar
Cassie, A.. Contact angles. Discuss. Faraday Soc., 3 (1948), 11–16. CrossRefGoogle Scholar
Wenzel, R.. Resistance of solid surfaces to wetting by water. Ind. Eng. Chem., 28 (1936), 988–994. CrossRefGoogle Scholar
Marmur, A.. Wetting on hydrophobic rough surfaces : to be heterogeneous or not to be? Langmuir, 19 (2003), 8343–8348. CrossRefGoogle Scholar
Nosonovsky, M.. On the Range of Applicability of the Wenzel and Cassie Equations. Langmuir, 23 (2007), 9919–9920. CrossRefGoogle ScholarPubMed
Miwa, M., Nakajima, A., Fujishima, A., Hashimoto, K., Watanabe, T.. Effects of the Surface Roughness on Sliding Angles of Water Droplets on Superhydrophobic Surfaces. Langmuir, 16 (2000), 5754. CrossRefGoogle Scholar
Larsen, S., Taboryski, R.. A Cassie-like law using triple phase boundary line fractions for faceted droplets on chemically heterogeneous surfaces. Langmuir, 25 (2009), 1282–1284. CrossRefGoogle ScholarPubMed
Bhushan, B., Nosonovsky, M.. The rose petal effect and the modes of superhydrophobicity. Philosophical Trans. Royal Soc. A, 368 (2010), 4713–4728. CrossRefGoogle ScholarPubMed
Wong, T.-S., Ho, Ch.-M.. Dependence of Macroscopic Wetting on Nanoscopic Surface Textures. Langmuir, 25 (2009), 12851–12854. CrossRefGoogle ScholarPubMed
Aronov, D., Molotskii, M., Rosenman, G.. Electron-induced wettability modification. Physical Review B 76 (2007), 035437. CrossRefGoogle Scholar
I. Gelfand, S. Fomin. Calculus of Variations. Dover, New York, 2000.
Marmur, A.. Line tension effect on contact angles : Axisymmetric and cylindrical systems with rough or heterogeneous solid surfaces. Colloids Surf. A, 136 (1998), 81–88. CrossRefGoogle Scholar
Starov, V., Velarde, M.. Surface forces and wetting phenomena. J. Phys. Condens. Matter., 21 (2009), 464121. CrossRefGoogle ScholarPubMed
Bormashenko, E.. Young, Boruvka-Neumann, Wenzel and Cassie-Baxter equations as the transversality conditions for the variational problem of wetting. Colloids and Surfaces A, 345 (2009), 163–165. CrossRefGoogle Scholar
Bormashenko, E.. Wetting of Flat and Rough Curved Surfaces. J. Phys. Chem. C, 113 (2009), 17275–17277. CrossRefGoogle Scholar
Bormashenko, E.. A Variational Approach to Wetting of Composite Surfaces : Is Wetting of Composite Surfaces a One-Dimensional or Two-Dimensional Phenomenon? Langmuir, 25 (2009), 10451–10454. CrossRefGoogle ScholarPubMed
Bormashenko, E.. General equation describing wetting of rough surfaces. Journal of Colloid and Interface Science, 360 (2011), 317–319. CrossRefGoogle ScholarPubMed
Amirfazli, A., Neumann, A.. Status of three-phase line tension. Advances in Colloid and Interface Science, 110 (2004), 121–141. CrossRefGoogle ScholarPubMed