Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-25T11:05:02.972Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of volatile liquid droplets on heated surfaces: theory versus experiment

Published online by Cambridge University Press:  08 August 2008

CHRISTOF SODTKE ,
VLADIMIR S. AJAEV  and
PETER STEPHAN
CHRISTOF SODTKE
Affiliation:
Darmstadt University of Technology, Petersenstrasse 30, 64287 Darmstadt, Germany
VLADIMIR S. AJAEV
Affiliation:
Southern Methodist University, Dallas, TX 75275, USA
PETER STEPHAN
Affiliation:
Darmstadt University of Technology, Petersenstrasse 30, 64287 Darmstadt, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the evaporation of volatile liquid droplets deposited on a heated substrate in a pure saturated vapour environment. A mathematical model is developed that incorporates the effects of surface tension, evaporation, thermocapillarity, gravity, disjoining pressure, as well as unsteady heat conduction in the solid substrate. The apparent contact line is treated mathematically as a transition region between the macroscopic droplet shape and the adsorbed film of liquid on the heated substrate. Theoretical parametric studies are conducted to clarify the effects of thermocapillarity and wetting properties on the droplet dynamics. An experimental study is conducted in a closed container with de-ionized water droplets on a stainless steel foil heated by an electric current. The interface shapes are recorded together with the temperature profiles under the droplets, measured using thermochromic liquid crystals. Experiment and theory are in very good agreement as long as the conditions of applicability of our lubrication-type mathematical model are satisfied.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 610 , 10 September 2008 , pp. 343 - 362
Copyright
Copyright © Cambridge University Press 2008

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

REFERENCES

Ajaev, V. S. 2005 Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech. 528, 279–296.CrossRefGoogle Scholar
Ajaev, V. S. & Homsy, G. M. 2001 Steady vapor bubbles in rectangular microchannels. J. Colloid Interface Sci. 240, 259–271.CrossRefGoogle ScholarPubMed
Anderson, D. M. & Davis, S. H. 1995 The spreading of volatile liquid droplets on heated surfaces. Phys. Fluids 7, 248–265.Google Scholar
Bourgés-Monnier, C. & Shanahan, M. E. R. 1995 Influence of evaporation on contact angle. Langmuir 11, 2820–2829.CrossRefGoogle Scholar
Braun, R. J., Murray, B. T., Boettinger, W. J. & McFadden, G. B. 1995 Lubrication theory for reactive spreading of a thin drop. Phys. Fluids 7, 1797–1810.CrossRefGoogle Scholar
Brown, P. N., Byrne, G. D. & Hindmarsh, A. C. 1989 Vode: A variable coefficient ode solver. SIAM J. Sci. Statist. Comput. 10, 1038–1051.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
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
Derjaguin, B. V., Churaev, N. V. & Muller, V. M. 1987 Surface Forces. Plenum.CrossRefGoogle Scholar
Freund, J. B. 2005 The atomistic detail of an evaporating meniscus. Phys. Fluids 17, 022104.CrossRefGoogle Scholar
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.CrossRefGoogle Scholar
Gokhale, S. J., Plawsky, J. L. & Wayner, P. C. 2003 Experimental investigation of contact angle, curvature, and contact line motion in dropwise condensation and evaporation. J. Colloid Interface Sci. 259, 354–366.Google Scholar
Gotkis, Y., Ivanov, I., Murisic, N. & Kondic, L. 2006 Dynamic structure formation at the fronts of volatile liquid drops. Phys. Rev. Lett. 93, 186101.CrossRefGoogle Scholar
Hocking, L. M. 1995 On contact angles in evaporating liquids. Phys. Fluids 7, 2950–2955.CrossRefGoogle Scholar
Höhmann, C. 2004 Temperaturmessverfahren zur räumlich hochauflösenden Untersuchung des Wärmetransports an einem verdampfenden Flüssigkeitsmeniskus. PhD thesis, Darmstadt University of Technology, Darmstadt.Google Scholar
Honig, C. D. F. & Ducker, W. A. 2007 No-slip hydrodynamic boundary condition for hydrophilic particles. Phys. Rev. Lett. 98, 028305.CrossRefGoogle ScholarPubMed
Hu, H. & Larson, R. G. 2005 Analysis of the microfluid flow in an evaporating sessile droplet. Langmuir 21, 3963–3971.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. Trans. IChemE A 82, 471–480.Google Scholar
Moosman, S. & Homsy, G. M. 1980 Evaporating menisci of wetting fluids. J. Colloid Interface Sci. 73, 212–223.CrossRefGoogle Scholar
Potash, M. & Wayner, P. C. 1972 Evaporation from a two-dimensional extended meniscus. Intl J. Heat Mass Transfer 15, 1851–1863.Google Scholar
Poulard, C., Bénichou, O. & Casabat, A. M. 2003 Freely receding evaporating droplets. Langmuir 19, 8828–8834.CrossRefGoogle Scholar
Rose, J. W. 2000 Accurate approximate equations for intensive sub-sonic evaporation. Intl J. Heat Mass Transfer 43, 3869–3875.CrossRefGoogle Scholar
Schrage, R. W. 1953 A Theoretical Study of Interface Mass Transfer. Columbia University Press.CrossRefGoogle Scholar
Vinogradova, O. I. & Yakubov, G. E. 2003 Dynamic effects on force measurements. Part 2. Lubrication and the atomic force microscope. Langmuir 19, 1227–1234.CrossRefGoogle Scholar
Wong, H., Morris, S. & Radke, C. J. 1992 Three-dimensional menisci in polygonal capillaries. J. Colloid Interface Sci. 148, 317–336.Google Scholar