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Evaporation of Sessile Water Droplets in Presence of ContactAngle Hysteresis

Published online by Cambridge University Press:  09 July 2012

S. Semenov ,
V.M. Starov ,
R.G. Rubio ,
H. Agogo  and
M.G. Velarde
S. Semenov
Affiliation:
Dept. of Chemical Engineering, Loughborough University, LE11 3TU Loughborough, UK
V.M. Starov*
Affiliation:
Dept. of Chemical Engineering, Loughborough University, LE11 3TU Loughborough, UK
R.G. Rubio
Affiliation:
Dept. of Quimica Fisica I, Universidad Complutense, 28040 Madrid, Spain
H. Agogo
Affiliation:
Dept. of Quimica Fisica I, Universidad Complutense, 28040 Madrid, Spain
M.G. Velarde
Affiliation:
Instituto Pluridisciplinar, Universidad Complutense, 28040 Madrid, Spain
*
∗ Corresponding author. E-mail: [email protected]
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Abstract

In this paper we present a theory describing the diffusion limited evaporation of sessilewater droplets in presence of contact angle hysteresis. Theory describes two stages ofevaporation process: (I) evaporation with a constant radius of the droplet base; and (II)evaporation with constant contact angle. During stage (I) the contact angle decreases fromstatic advancing contact angle to static receding contact angle, during stage (II) thecontact angle remains equal to the static receding contact angle. Universal dependencesare deduced for both evaporation stages. Obtained universal curves are validated againstavailable in the literature experimental data.

Keywords

evaporationsessile dropletscontact angle hysteresis
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 4: Modelling phenomena on micro- and nanoscale , 2012 , pp. 82 - 98
Copyright
© EDP Sciences, 2012

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References

Agrawal, D.C., Menon, V.J.. Surface tension and evaporation : an empirical relation for water. Physical Review A, 46 (1992), 2166-2169. CrossRefGoogle Scholar
Ajaev, V.S.. Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech. 528 (2005), 279-296. CrossRefGoogle Scholar
D. Bensimon, A. Bensimon, F. Heslot. Process for aligning macromolecules by passage of a meniscus and applications. Patent No. : US 7754425 B2, (2010).
R., Bhardwaj, X., Fang, Attinger, D.. Pattern formation during the evaporation of a colloidal nanoliter drop : a numerical and experimental study. New J. Phys. 11 (2009), 075020.
Bourges-Monnier, C., Shanahan, M.E.R.. Influence of evaporation on contact angle. Langmuir 11 (1995), 2820-2829. CrossRefGoogle Scholar
Campbell, P.G., Weiss, L.E.. Tissue engineering with the aid of inkjet printers. Expert Opin. Biol. Ther. 7 (2007), 1123-1127. CrossRefGoogle ScholarPubMed
Chen, C.-T., Tseng, F.-G., Chieng, C.-C.. Evaporation evolution of volatile liquid droplets in nanoliter wells. Sens. and Actuators A 130-131 (2006), 12-19. CrossRefGoogle Scholar
W.-L. Cheng, F.-Y. Han, Q.-N. Liu, R. Zhao, H.-L. Fan. Experimental and theoretical investigation of surface temperature non-uniformity of spray cooling. Energy (2010), doi :10.1016/j.energy.2010.10.044.
Craster, R.V., Matar, O.K., Sefiane, K.. Pinning, retraction, and terracing of evaporating droplets containing nanoparticles. Langmuir 25 (2009), 3601-3609. CrossRefGoogle ScholarPubMed
David, S., Sefiane, K., Tadrist, L.. Experimental investigation of the effect of thermal properties of the substrate in the wetting and evaporation of sessile drops. Colloids Surf. A : Physicochem. Eng. Aspects 298 (2007), 108-114. CrossRefGoogle Scholar
Deegan, R.D.. Pattern formation in drying drops. Phys. Rev. E 61 (2000), 475-485. CrossRefGoogle ScholarPubMed
Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Nagel, S.R., Witten, T.A.. Contact line deposits in an evaporating drop. Phys. Rev. E 62 (2000), 756-765. CrossRefGoogle Scholar
Dugas, V., Broutin, J., Souteyrand, E.. Droplet evaporation study applied to DNA chip manufacturing. Langmuir 21 (2005), 9130-9136. CrossRefGoogle ScholarPubMed
G.J., Dunn, S.K., Wilson, B.R., Duffy, S., David, Sefiane, K.. A mathematical model for the evaporation of a thin sessile liquid droplet : comparison between experiment and theory. Colloids Surf. A : Physicochem. Eng. Aspects 323 (2008), 50-55. Google Scholar
Dunn, G.J., Wilson, S.K., Duffy, B.R., David, S., Sefiane, K.. The strong influence of substrate conductivity on droplet evaporation. J. Fluid Mech. 623 (2009), 329-351. CrossRefGoogle Scholar
Fuller, S.B., Wilhelm, E.J., Jacobson, J.M.. Ink-jet printed nanoparticle microelectromechanical systems. J. MEMS 11 (2002), 54-60. CrossRefGoogle Scholar
Galvin, K.P.. A conceptually simple derivation of the Kelvin equation. Chem. Eng. Sci. 60 (2005), 4659-4660. CrossRefGoogle Scholar
de Gans, B.-J., Duineveld, P.C., Schubert, U.S.. Inkjet printing of polymers : state of the art and future developments. Adv. Mater. 16 (2004), 203-213. CrossRefGoogle Scholar
Girard, F., Antoni, M., Sefiane, K.. On the effect of Marangoni flow on evaporation rates of heated water drops. Langmuir 24 (2008), 9207-9210. CrossRefGoogle ScholarPubMed
Girard, F., Antoni, M., Faure, S., Steinchen, A.. Evaporation and Marangoni driven convection in small heated water droplets. Langmuir 22 (2006), 11085-11091. CrossRefGoogle ScholarPubMed
F., Girard, M., Antoni, S., Faure, Steinchen, A.. Numerical study of the evaporating dynamics of a sessile water droplet. Microgr. Sci. Technol. XVIII-3/4 (2006), 42-46. Google Scholar
Girard, F., Antoni, M., Faure, S., Steinchen, A.. Influence of heating temperature and relative humidity in the evaporation of pinned droplets. Colloids Surf. A 323 (2008), 36-49. CrossRefGoogle Scholar
Girard, F., Antoni, M.. Influence of substrate heating on the evaporation dynamics of pinned water droplets. Langmuir 24 (2008), 11342-11345. CrossRefGoogle ScholarPubMed
Guena, G., Poulard, C., Voue, M., Coninck, J.D., Cazabat, A.M.. Evaporation of sessile liquid droplets. Colloids Surf. A 291 (2006), 191-196. CrossRefGoogle Scholar
Hu, H., Larson, R.G.. Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B 106 (2002), 1334-1344. CrossRefGoogle Scholar
Hu, H., Larson, R.G.. Analysis of the microfluid flow in an evaporating sessile droplet. Langmuir, 21 (2005), 3963-3971. CrossRefGoogle Scholar
Hu, H., Larson, R.G.. Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir, 21 (2005), 3972-3980. CrossRefGoogle Scholar
Y.M. Hung, Q. Seng. Effects of geometric design on thermal performance of star-groove micro-heat pipes. Int. J. Heat Mass Transfer (2010), doi :10.1016/j.ijheatmasstransfer.2010.09.070.
Ingrosso, C., Kim, J.Y., Binetti, E., Fakhfouri, V., Striccoli, M., Agostiano, A., Curri, M.L., Brugger, J.. Drop-on-demand inkjet printing of highly luminescent CdS and CdSe@ZnS nanocrystal based nanocomposites. Microelectr. Eng. 86 (2009), 1124-1126. CrossRefGoogle Scholar
Karlsson, S., Rasmuson, A., Björn, I.N., Schantz, S.. Characterization and mathematical modelling of single fluidised particle coating. Powder Technol. 207 (2011), 245-256. CrossRefGoogle Scholar
H., Kim, Kim, J.. Evaporation characteristics of a hydrophilic surface with micro-scale and/or nano-scale structures fabricated by sandblasting and aluminum anodization. J. Micromech. Microeng. 20 (2010), 045008 Google Scholar
J.H., Kim, Wei-Xian, Shi, Larson, R.G.. Methods of stretching DNA molecules using flow fields. Langmuir 23 (2007), 755-764. Google Scholar
S.H., Ko, J., Chung, N., Hotz, K.H., Nam, Grigoropoulos, C.P.. Metal nanoparticle direct inkjet printing for low-temperature 3D micro metal structure fabrication. J. Micromech. Microeng. 20 (2010), 125010. Google Scholar
Du, Peng, Li, Luhai, Zhao, Wen, Leng, Xian, Xuwei, Hu. Study on the printing performance of coated paper inkjet ink. Adv. Mater. Res. 174 (2011), 358-361. CrossRefGoogle Scholar
Picknett, R.G., Bexon, R.. The evaporation of sessile or pendant drops in still air. J. Colloid Interface Sci. 61 (1977), 336-350. CrossRefGoogle Scholar
A.Ye., Rednikov, Colinet, P.. Truncated versus extended microfilms at a vapor-liquid contact line on a heated substrate. Langmuir 27(5) (2011), 1758-1769. Google Scholar
W.D., Ristenpart, P.G., Kim, C., Domingues, J., Wan, Stone, H.A.. Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett. 99 (2007), 234502. Google Scholar
N., Savva, Kalliadasis, S.. Dynamics of moving contact lines : a comparison between slip and precursor film models. Europhys. Lett. 94 (2011), 64004. Google Scholar
Schirmer, N.C., Ströhle, S., Tiwari, M.K., Poulikakos, D.. On the principles of printing sub-micrometer 3D structures from dielectric-liquid-based colloids. Adv. Funct. Mater. XX (2010), 1-8, DOI :10.1002/adfm.201001426. Google Scholar
Schonfeld, F., Graf, K.H., Hardt, S., Butt, H.J.. Evaporation dynamics of sessile liquid drops in still air with constant contact radius. Int. J. Heat Mass Transfer 51 (2008), 3696-3699. CrossRefGoogle Scholar
Sefiane, K., Tadrist, L.. Experimental investigation of the de-pinning phenomenon on rough surfaces of volatile drops. Int. Commun. Heat Mass Transfer 33 (2006), 482-490. CrossRefGoogle Scholar
Semenov, S., Starov, V.M., Rubio, R.G., Velarde, M.G.. Instantaneous distribution of fluxes in the course of evaporation of sessile liquid droplets : computer simulations. Colloids Surf. A : Physicochem. Eng. Aspects 372 (2010), 127-134. CrossRefGoogle Scholar
Wetting and spreading dynamics /Victor M. Starov, Manuel G. Velarde, Clayton J. Radke; Boca Raton, Fla., CRC/Taylor & Francis, London, 2007.
Sultan, E., Boudaoud, A., Amar, M.B.. Evaporation of a thin film : diffusion of the vapour and Marangoni instabilities. J. Fluid Mech. 543 (2005), 183-202. CrossRefGoogle Scholar
Yildirim Erbil, H., McHale, G., Rowan, S.M., Newton, M.I.. Determination of the receding contact angle of sessile drops on polymer surfaces by evaporation. Langmuir 15 (1999), 7378-7385. CrossRefGoogle Scholar