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The strong influence of substrate conductivity on droplet evaporation

Published online by Cambridge University Press:  06 March 2009

G. J. DUNN ,
S. K. WILSON ,
B. R. DUFFY ,
S. DAVID  and
K. SEFIANE
G. J. DUNN
Affiliation:
Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK
S. K. WILSON*
Affiliation:
Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK
B. R. DUFFY
Affiliation:
Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK
S. DAVID
Affiliation:
School of Engineering and Electronics, The University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh, EH9 3JLUK
K. SEFIANE
Affiliation:
School of Engineering and Electronics, The University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh, EH9 3JLUK
*
†Email address for correspondence: [email protected]
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Abstract

We report the results of physical experiments that demonstrate the strong influence of the thermal conductivity of the substrate on the evaporation of a pinned droplet. We show that this behaviour can be captured by a mathematical model including the variation of the saturation concentration with temperature, and hence coupling the problems for the vapour concentration in the atmosphere and the temperature in the liquid and the substrate. Furthermore, we show that including two ad hoc improvements to the model, namely a Newton's law of cooling on the unwetted surface of the substrate and the buoyancy of water vapour in the atmosphere, give excellent quantitative agreement for all of the combinations of liquid and substrate considered.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 329 - 351
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Ajaev, V. S. 2005 Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech. 528, 279–296.CrossRefGoogle Scholar
Anderson, D. M. & Davis, S. H. 1995 The spreading of volatile liquid droplets on heated surfaces. Phys. Fluids 7, 248–265.CrossRefGoogle Scholar
Bernardin, J. D., Mudawar, I., Walsh, C. B. & Franses, E. I. 1997 Contact angle temperature dependence for water droplets on practical aluminium surfaces. Intl J. Heat Mass Transfer 40, 1017–1033.CrossRefGoogle Scholar
Birdi, K. S., Vu, D. T. & Winter, A. 1989 A study of the evaporation rates of small water drops placed on a solid surface. J. Phys. Chem. 93, 3702–3703.CrossRefGoogle Scholar
Bourgès-Monnier, C. & Shanahan, M. E. R. 1995 Influence of evaporation on contact angle. Langmuir 11, 2820–2829.CrossRefGoogle Scholar
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463–494.CrossRefGoogle Scholar
Cachile, M., Bénichou, O. & Cazabat, A. M. 2002 a Evaporating droplets of completely wetting liquids. Langmuir 18, 7985–7990.CrossRefGoogle Scholar
Cachile, M., Bénichou, O., Poulard, C. & Cazabat, A. M. 2002 b Evaporating droplets. Langmuir 18, 8070–8078.CrossRefGoogle Scholar
Chandra, S., di Marzo, M., Qiao, Y. M. & Tartarini P. 1996 Effect of liquid–solid contact angle on droplet evaporation. Fire Safety J. 27, 141–158.CrossRefGoogle Scholar
Crafton, E. F. & Black, W. Z. 2004 Heat transfer and evaporation rates of small liquid droplets on heated horizontal surfaces. Intl J. Heat Mass Transfer 47, 1187–1200.CrossRefGoogle Scholar
David, S. 2007 An investigation of the wetting behaviour of evaporative drops. PhD thesis, University of Edinburgh.Google Scholar
David, S., Sefiane, K. & Tadrist, L. 2007 Experimental investigation of the effect of thermal properties of the substrate in the wetting and evaporation of sessile drops. Colloids Surf. A 298, 108–114.CrossRefGoogle Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 1997 Capillary flow as the cause of ring stains from dried liquid drops. Nature 389, 827–829.CrossRefGoogle Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 2000 Contact line deposits in an evaporating drop. Phys. Rev. E 62, 756–765.Google Scholar
Dunn, G. J., Wilson, S. K., Duffy, B. R., David, S. & Sefiane, K. 2008 A mathematical model for the evaporation of a thin sessile liquid droplet: comparison between experiment and theory. Colloids Surf. A 323, 50–55.CrossRefGoogle Scholar
Erbil, H. Y., McHale, G. & Newton, M. I. 2002 a Analysis of evaporating thick liquid films on solids. J. Adhesion Sci. Technol. 16, 1869–1881.CrossRefGoogle Scholar
Erbil, H. Y., McHale, G. & Newton, M. I. 2002 b Drop evaporation on solid surfaces: constant contact angle mode. Langmuir 18, 2636–2641.CrossRefGoogle Scholar
Fang, G. & Ward, C. A. 1999 Temperature measured close to the interface of an evaporating liquid. Phys. Rev. E 59, 417–428.Google Scholar
Grandas, L., Reynard, C., Santini, R. & Tadrist, L. 2005 Experimental study of the evaporation of a sessile drop on a heated wall. Wetting influence. Intl J. Therm. Sci. 44, 137–146.CrossRefGoogle Scholar
Guéna, G., Allançon, P. & Cazabat, A. M. 2007 a Receding contact angle in the situation of complete wetting: experimental check of a model used for evaporating droplets. Colloids Surf. A 300, 307–314.CrossRefGoogle Scholar
Guéna, G., Poulard, C. & Cazabat, A. M. 2007 b Evaporating drops of alkane mixtures. Colloids Surf. A 298, 2–11.CrossRefGoogle Scholar
Guéna, G., Poulard, C. & Cazabat, A. M. 2007 c The leading edge of evaporating droplets. J. Coll. Interface Sci. 312, 164–171.CrossRefGoogle Scholar
Guéna, G., Poulard, C., Voué, M., De Coninck, J. & Cazabat, A. M. 2006 Evaporation of sessile liquid droplets. Colloids Surf. A 291, 191–196.CrossRefGoogle Scholar
Howison, S. D., Moriarty, J. A., Ockendon, J. R., Terrill, E. L. & Wilson, S. K. 1997 A mathematical model for drying paint layers. J. Engng Math. 32, 377–394.CrossRefGoogle Scholar
Hu, H. & Larson, R. G. 2002 Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B 106, 1334–1344.CrossRefGoogle Scholar
Hu, H. & Larson, R. G. 2005 a Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 21, 3972–3980.CrossRefGoogle Scholar
Hu, H. & Larson, R. G. 2005 b Analysis of the microfluid flow in an evaporating sessile droplet. Langmuir 21, 3963–3971.CrossRefGoogle Scholar
Hu, H. & Larson, R. G. 2006 Marangoni effect reverses coffee-ring depositions. J. Phys. Chem. B 110, 7090–7094.CrossRefGoogle ScholarPubMed
Lebedev, N. N. 1965 Special Functions and Their Applications. Prentice Hall.CrossRefGoogle Scholar
Lide, D. R. & Kehiaian, H. V. 1994 CRC Handbook of Thermophysical and Thermochemical Data. CRC Press.Google Scholar
Lugg, A. G. 1968 Diffusion coefficients of some organic and other vapors in air. Analyt. Chem. 40, 1072–1077.CrossRefGoogle Scholar
Mollaret, R., Sefiane, K., Christy, J. R. E. & Veyret, D. 2004 Experimental and numerical investigation of the evaporation into air of a drop on a heated surface. Chemical Engineering Research and Design 82, 471–480.CrossRefGoogle Scholar
Monteith, J. L. 1973 Principles of Environmental Physics. Edward Arnold.Google Scholar
Panwar, A. K., Barthwal, S. K. & Ray, S. 2003 Effect of evaporation on the contact angle of a sessile drop on solid substrates. J. Adhesion Sci. Technol. 17, 1321–1329.CrossRefGoogle Scholar
Perry, R. H. & Green, D. W. 1997 Perry's Chemical Engineers' Handbook, 7th ed. McGraw-Hill.Google Scholar
Picknett, R. G. & Bexon, R. 1977 The evaporation of sessile or pendant drops in still air. J. Coll. Interface Sci. 61, 336–350.CrossRefGoogle Scholar
Popov, Y. O. 2005 Evaporative deposition patterns: spatial dimensions of the deposit. Phys. Rev. E 71, 036313-1–036313-17.Google ScholarPubMed
Poulard, C., Bénichou, O. & Cazabat, A. M. 2003 Freely receding evaporating droplets. Langmuir 19, 8828–8834.CrossRefGoogle Scholar
Poulard, C., Guéna, G. & Cazabat, A. M. 2005 a Diffusion-driven evaporation of sessile drops. J. Phys.: Condens. Matter 17, S4213–S4227.Google Scholar
Poulard, C., Guéna, G., Cazabat, A. M., Boudaoud, A. & Ben Amar, M. 2005 b Rescaling the dynamics of evaporating drops. Langmuir 21, 8226–8233.CrossRefGoogle ScholarPubMed
Raznjevic, K. 1995 Handbook of Thermodynamic Tables. Begell House.CrossRefGoogle Scholar
Reid, R. C., Prausnitz, J. M. & Poling, B. E. 1987 The Properties of Gases & Liquids, 4th ed. McGraw-Hill.Google Scholar
Ristenpart, W. D., Kim, P. G., Domingues, C., Wan, J. & Stone, H. A. 2007 Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett. 99, 234502-1–234502-4. Supplementary material EPAPS document number E-PRLTAO-99-072744 available at http://www.aip.org/pubservs/epaps.html.CrossRefGoogle ScholarPubMed
Rowan, S. M., Newton, M. I. & McHale, G. 1995 Evaporation of microdroplets and the wetting of solid surfaces. J. Phys. Chem. 99, 13268–13271.CrossRefGoogle Scholar
Savino, R., Paterna, D. & Favaloro, N. 2002 Buoyancy and Marangoni effects in an evaporating drop. J. Thermophys. Heat Transfer 16, 562–574.CrossRefGoogle Scholar
Sefiane, K. & Tadrist, L. 2006 Experimental investigation of the de-pinning phenomenon on rough surfaces of volatile drops. Intl Comm. Heat Mass Transfer 33, 482–490.CrossRefGoogle Scholar
Shahidzadeh-Bonn, N., Rafaï, S., Azouni, A. & Bonn, D. 2006 Evaporating droplets. J. Fluid Mech. 549, 307–313.CrossRefGoogle Scholar
Shanahan, M. E. R. 2001 a Condensation transport in dynamic wetting. Langmuir 17, 3997–4002.CrossRefGoogle Scholar
Shanahan, M. E. R. 2001 b Spreading of water: condensation effects. Langmuir 17, 8229–8235.CrossRefGoogle Scholar
Sodtke, C., Ajaev, V. S. & Stephan, P. 2007 Evaporation of thin liquid droplets on heated surfaces. Heat Mass Transfer 43, 649–657.CrossRefGoogle Scholar
Sultan, E., Boudaoud, A. & Ben Amar, M. 2005 Evaporation of a thin film: diffusion of the vapour and Marangoni instabilities. J. Fluid Mech. 543, 183–202.CrossRefGoogle Scholar
Tanaka, K., Fujita, I. & Uematsu, M. 2007 Isobaric specific heat capacity of {xCH3OH + (1 − x)H 2O} with x = (1.0000, 0.7943, 0.4949, 0.2606, 0.1936, 0.1010, and 0.0496) at T = (280, 320, and 360) K in the pressure range from (0.1 to 15) MPa. J. Chem. Thermodyn. 39, 961–966.CrossRefGoogle Scholar
Tennent, R. M. 1971 Science Data Book. Oliver and Boyd.Google Scholar
Xu, X. & Luo, J. 2007 Marangoni flow in an evaporating water droplet. Appl. Phys. Lett. 91, 124102-1–124102-3.CrossRefGoogle Scholar