Evaporation of Sessile Water Droplets in Presence of Contact Angle Hysteresis

S. Semenov; V.M. Starov; R.G. Rubio; H. Agogo; M.G. Velarde

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 4, page 82-98
  • ISSN: 0973-5348

Abstract

top
In this paper we present a theory describing the diffusion limited evaporation of sessile water droplets in presence of contact angle hysteresis. Theory describes two stages of evaporation 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 from static advancing contact angle to static receding contact angle, during stage (II) the contact angle remains equal to the static receding contact angle. Universal dependences are deduced for both evaporation stages. Obtained universal curves are validated against available in the literature experimental data.

How to cite

top

Semenov, S., et al. "Evaporation of Sessile Water Droplets in Presence of Contact Angle Hysteresis." Mathematical Modelling of Natural Phenomena 7.4 (2012): 82-98. <http://eudml.org/doc/222269>.

@article{Semenov2012,
abstract = {In this paper we present a theory describing the diffusion limited evaporation of sessile water droplets in presence of contact angle hysteresis. Theory describes two stages of evaporation 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 from static advancing contact angle to static receding contact angle, during stage (II) the contact angle remains equal to the static receding contact angle. Universal dependences are deduced for both evaporation stages. Obtained universal curves are validated against available in the literature experimental data.},
author = {Semenov, S., Starov, V.M., Rubio, R.G., Agogo, H., Velarde, M.G.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {evaporation; sessile droplets; contact angle hysteresis},
language = {eng},
month = {7},
number = {4},
pages = {82-98},
publisher = {EDP Sciences},
title = {Evaporation of Sessile Water Droplets in Presence of Contact Angle Hysteresis},
url = {http://eudml.org/doc/222269},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Semenov, S.
AU - Starov, V.M.
AU - Rubio, R.G.
AU - Agogo, H.
AU - Velarde, M.G.
TI - Evaporation of Sessile Water Droplets in Presence of Contact Angle Hysteresis
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/7//
PB - EDP Sciences
VL - 7
IS - 4
SP - 82
EP - 98
AB - In this paper we present a theory describing the diffusion limited evaporation of sessile water droplets in presence of contact angle hysteresis. Theory describes two stages of evaporation 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 from static advancing contact angle to static receding contact angle, during stage (II) the contact angle remains equal to the static receding contact angle. Universal dependences are deduced for both evaporation stages. Obtained universal curves are validated against available in the literature experimental data.
LA - eng
KW - evaporation; sessile droplets; contact angle hysteresis
UR - http://eudml.org/doc/222269
ER -

References

top
  1. D.C. Agrawal, V.J. Menon. Surface tension and evaporation : an empirical relation for water. Physical Review A, 46 (1992), 2166-2169.  
  2. V.S. Ajaev. Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech.528 (2005), 279-296.  Zbl1165.76313
  3. D. Bensimon, A. Bensimon, F. Heslot. Process for aligning macromolecules by passage of a meniscus and applications. Patent No. : US 7754425 B2, (2010).  
  4. R. Bhardwaj, X. Fang, D. Attinger. Pattern formation during the evaporation of a colloidal nanoliter drop : a numerical and experimental study. New J. Phys.11 (2009), 075020.  
  5. C. Bourges-Monnier, M.E.R. Shanahan. Influence of evaporation on contact angle. Langmuir11 (1995), 2820-2829.  
  6. P.G. Campbell, L.E. Weiss. Tissue engineering with the aid of inkjet printers. Expert Opin. Biol. Ther.7 (2007), 1123-1127.  
  7. C.-T. Chen, F.-G. Tseng, C.-C. Chieng. Evaporation evolution of volatile liquid droplets in nanoliter wells. Sens. and Actuators A130-131 (2006), 12-19.  
  8. 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 :.  URI10.1016/j.energy.2010.10.044
  9. R.V. Craster, O.K. Matar, K. Sefiane. Pinning, retraction, and terracing of evaporating droplets containing nanoparticles. Langmuir25 (2009), 3601-3609.  
  10. S. David, K. Sefiane, L. Tadrist. Experimental investigation of the effect of thermal properties of the substrate in the wetting and evaporation of sessile drops. Colloids Surf. A : Physicochem. Eng. Aspects298 (2007), 108-114.  
  11. R.D. Deegan. Pattern formation in drying drops. Phys. Rev. E61 (2000), 475-485.  
  12. R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten. Contact line deposits in an evaporating drop. Phys. Rev. E62 (2000), 756-765.  
  13. V. Dugas, J. Broutin, E. Souteyrand. Droplet evaporation study applied to DNA chip manufacturing. Langmuir21 (2005), 9130-9136.  
  14. G.J. Dunn, S.K. Wilson, B.R. Duffy, S. David, K. Sefiane. A mathematical model for the evaporation of a thin sessile liquid droplet : comparison between experiment and theory. Colloids Surf. A : Physicochem. Eng. Aspects323 (2008), 50-55.  
  15. G.J. Dunn, S.K. Wilson, B.R. Duffy, S. David, K. Sefiane. The strong influence of substrate conductivity on droplet evaporation. J. Fluid Mech.623 (2009), 329-351.  Zbl1157.76303
  16. S.B. Fuller, E.J. Wilhelm, J.M. Jacobson. Ink-jet printed nanoparticle microelectromechanical systems. J. MEMS11 (2002), 54-60.  
  17. K.P. Galvin. A conceptually simple derivation of the Kelvin equation. Chem. Eng. Sci.60 (2005), 4659-4660.  
  18. B.-J. de Gans, P.C. Duineveld, U.S. Schubert. Inkjet printing of polymers : state of the art and future developments. Adv. Mater.16 (2004), 203-213.  
  19. F. Girard, M. Antoni, K. Sefiane. On the effect of Marangoni flow on evaporation rates of heated water drops. Langmuir24 (2008), 9207-9210.  
  20. F. Girard, M. Antoni, S. Faure, A. Steinchen. Evaporation and Marangoni driven convection in small heated water droplets. Langmuir22 (2006), 11085-11091.  
  21. F. Girard, M. Antoni, S. Faure, A. Steinchen. Numerical study of the evaporating dynamics of a sessile water droplet. Microgr. Sci. Technol. XVIII-3/4 (2006), 42-46.  
  22. F. Girard, M. Antoni, S. Faure, A. Steinchen. Influence of heating temperature and relative humidity in the evaporation of pinned droplets. Colloids Surf. A323 (2008), 36-49.  
  23. F. Girard, M. Antoni. Influence of substrate heating on the evaporation dynamics of pinned water droplets. Langmuir24 (2008), 11342-11345.  
  24. G. Guena, C. Poulard, M. Voue, J.D. Coninck, A.M. Cazabat. Evaporation of sessile liquid droplets. Colloids Surf. A291 (2006), 191-196.  
  25. H. Hu, R.G. Larson. Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B106 (2002), 1334-1344.  
  26. H. Hu, R.G. Larson. Analysis of the microfluid flow in an evaporating sessile droplet. Langmuir, 21 (2005), 3963-3971.  
  27. H. Hu, R.G. Larson. Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir, 21 (2005), 3972-3980.  
  28. 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 :.  Zbl1209.80010URI10.1016/j.ijheatmasstransfer.2010.09.070
  29. C. Ingrosso, J.Y. Kim, E. Binetti, V. Fakhfouri, M. Striccoli, A. Agostiano, M.L. Curri, J. Brugger. Drop-on-demand inkjet printing of highly luminescent CdS and CdSe@ZnS nanocrystal based nanocomposites. Microelectr. Eng.86 (2009), 1124-1126.  
  30. S. Karlsson, A. Rasmuson, I.N. Björn, S. Schantz. Characterization and mathematical modelling of single fluidised particle coating. Powder Technol.207 (2011), 245-256.  
  31. H. Kim, J. Kim. 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 
  32. J.H. Kim, Wei-Xian Shi, R.G. Larson. Methods of stretching DNA molecules using flow fields. Langmuir23 (2007), 755-764.  
  33. S.H. Ko, J. Chung, N. Hotz, K.H. Nam, C.P. Grigoropoulos. Metal nanoparticle direct inkjet printing for low-temperature 3D micro metal structure fabrication. J. Micromech. Microeng. 20 (2010), 125010.  
  34. Du Peng, Li Luhai, Zhao Wen, Leng Xian, Hu Xuwei. Study on the printing performance of coated paper inkjet ink. Adv. Mater. Res.174 (2011), 358-361.  
  35. R.G. Picknett, R. Bexon. The evaporation of sessile or pendant drops in still air. J. Colloid Interface Sci.61 (1977), 336-350.  
  36. A.Ye. Rednikov, P. Colinet. Truncated versus extended microfilms at a vapor-liquid contact line on a heated substrate. Langmuir27(5) (2011), 1758-1769.  
  37. W.D. Ristenpart, P.G. Kim, C. Domingues, J. Wan, H.A. Stone. Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett.99 (2007), 234502.  
  38. N. Savva, S. Kalliadasis. Dynamics of moving contact lines : a comparison between slip and precursor film models. Europhys. Lett.94 (2011), 64004.  
  39. N.C. Schirmer, S. Ströhle, M.K. Tiwari, D. Poulikakos. On the principles of printing sub-micrometer 3D structures from dielectric-liquid-based colloids. Adv. Funct. Mater.XX (2010), 1-8, DOI :.  URI10.1002/adfm.201001426
  40. F. Schonfeld, K.H. Graf, S. Hardt, H.J. Butt. Evaporation dynamics of sessile liquid drops in still air with constant contact radius. Int. J. Heat Mass Transfer51 (2008), 3696-3699.  Zbl1148.80367
  41. K. Sefiane, L. Tadrist. Experimental investigation of the de-pinning phenomenon on rough surfaces of volatile drops. Int. Commun. Heat Mass Transfer33 (2006), 482-490.  
  42. S. Semenov, V.M. Starov, R.G. Rubio, M.G. Velarde. Instantaneous distribution of fluxes in the course of evaporation of sessile liquid droplets : computer simulations. Colloids Surf. A : Physicochem. Eng. Aspects372 (2010), 127-134.  
  43. Wetting and spreading dynamics /Victor M. Starov, Manuel G. Velarde, Clayton J. Radke; Boca Raton, Fla., CRC/Taylor & Francis, London, 2007.  
  44. E. Sultan, A. Boudaoud, M.B. Amar. Evaporation of a thin film : diffusion of the vapour and Marangoni instabilities. J. Fluid Mech.543 (2005), 183-202.  Zbl1088.76013
  45. H. Yildirim Erbil, G. McHale, S.M. Rowan, M.I. Newton. Determination of the receding contact angle of sessile drops on polymer surfaces by evaporation. Langmuir15 (1999), 7378-7385.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.