Evaporation-driven Contact Angles in a Pure-vapor Atmosphere : the Effect of Vapor Pressure Non-uniformity

A.Y. Rednikov; P. Colinet

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 4, page 53-63
  • ISSN: 0973-5348

Abstract

top
A small vicinity of a contact line, with well-defined (micro)scales (henceforth the “microstructure”), is studied theoretically for a system of a perfectly wetting liquid, its pure vapor and a superheated flat substrate. At one end, the microstructure terminates in a non-evaporating microfilm owing to the disjoining-pressure-induced Kelvin effect. At the other end, for motionless contact lines, it terminates in a constant film slope (apparent contact angle as seen on a larger scale), the angle being non-vanishing despite the perfect wetting due to an overall dynamic situation engendered by evaporation. Here we go one step beyond the standard one-sided model by incorporating the effect of vapor pressure non-uniformity as caused by a locally intense evaporation flow, treated in the Stokes approximation. Thereby, the film dynamics is primarily affected through thermodynamics (shift of the local saturation temperature and evaporation rate), the direct mechanical impact being rather negligible. The resulting integro-differential lubrication film equation is solved by handling the newly introduced effect (giving rise to the “integro” part) as a perturbation. In the ammonia (at 300   K) example dealt with here, it proves to be rather weak indeed: the contact angle decreases while the integral evaporation flux increases just by a few percent for a superheat of  ~1   K. However, the numbers grow (roughly linearly) with the superheat.

How to cite

top

Rednikov, A.Y., and Colinet, P.. "Evaporation-driven Contact Angles in a Pure-vapor Atmosphere : the Effect of Vapor Pressure Non-uniformity ." Mathematical Modelling of Natural Phenomena 7.4 (2012): 53-63. <http://eudml.org/doc/222309>.

@article{Rednikov2012,
abstract = {A small vicinity of a contact line, with well-defined (micro)scales (henceforth the “microstructure”), is studied theoretically for a system of a perfectly wetting liquid, its pure vapor and a superheated flat substrate. At one end, the microstructure terminates in a non-evaporating microfilm owing to the disjoining-pressure-induced Kelvin effect. At the other end, for motionless contact lines, it terminates in a constant film slope (apparent contact angle as seen on a larger scale), the angle being non-vanishing despite the perfect wetting due to an overall dynamic situation engendered by evaporation. Here we go one step beyond the standard one-sided model by incorporating the effect of vapor pressure non-uniformity as caused by a locally intense evaporation flow, treated in the Stokes approximation. Thereby, the film dynamics is primarily affected through thermodynamics (shift of the local saturation temperature and evaporation rate), the direct mechanical impact being rather negligible. The resulting integro-differential lubrication film equation is solved by handling the newly introduced effect (giving rise to the “integro” part) as a perturbation. In the ammonia (at 300   K) example dealt with here, it proves to be rather weak indeed: the contact angle decreases while the integral evaporation flux increases just by a few percent for a superheat of  ~1   K. However, the numbers grow (roughly linearly) with the superheat.},
author = {Rednikov, A.Y., Colinet, P.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {contact angle; evaporation; superheat; pure vapor; thin films; nonlocal effect},
language = {eng},
month = {7},
number = {4},
pages = {53-63},
publisher = {EDP Sciences},
title = {Evaporation-driven Contact Angles in a Pure-vapor Atmosphere : the Effect of Vapor Pressure Non-uniformity },
url = {http://eudml.org/doc/222309},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Rednikov, A.Y.
AU - Colinet, P.
TI - Evaporation-driven Contact Angles in a Pure-vapor Atmosphere : the Effect of Vapor Pressure Non-uniformity
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/7//
PB - EDP Sciences
VL - 7
IS - 4
SP - 53
EP - 63
AB - A small vicinity of a contact line, with well-defined (micro)scales (henceforth the “microstructure”), is studied theoretically for a system of a perfectly wetting liquid, its pure vapor and a superheated flat substrate. At one end, the microstructure terminates in a non-evaporating microfilm owing to the disjoining-pressure-induced Kelvin effect. At the other end, for motionless contact lines, it terminates in a constant film slope (apparent contact angle as seen on a larger scale), the angle being non-vanishing despite the perfect wetting due to an overall dynamic situation engendered by evaporation. Here we go one step beyond the standard one-sided model by incorporating the effect of vapor pressure non-uniformity as caused by a locally intense evaporation flow, treated in the Stokes approximation. Thereby, the film dynamics is primarily affected through thermodynamics (shift of the local saturation temperature and evaporation rate), the direct mechanical impact being rather negligible. The resulting integro-differential lubrication film equation is solved by handling the newly introduced effect (giving rise to the “integro” part) as a perturbation. In the ammonia (at 300   K) example dealt with here, it proves to be rather weak indeed: the contact angle decreases while the integral evaporation flux increases just by a few percent for a superheat of  ~1   K. However, the numbers grow (roughly linearly) with the superheat.
LA - eng
KW - contact angle; evaporation; superheat; pure vapor; thin films; nonlocal effect
UR - http://eudml.org/doc/222309
ER -

References

top
  1. V.S. Ajaev. Spreading of thin volatile liquid droplets on uniformly heated surfaces.J. Fluid Mech., 528 (2005), 279–296.  Zbl1165.76313
  2. D. Bonn, J. Eggers, J. Indekeu, J. Meunier, E. Rolley. Wetting and spreading.Rev. Mod. Phys., 81 (2009), 739–805.  
  3. J.P. Burelbach, S.G. Bankoff, S.H. Davis. Nonlinear stability of evaporating/condensing liquid films.J. Fluid Mech., 195 (1988), 463–494.  Zbl0653.76035
  4. P.G. de Gennes. Wetting : statics and dynamics.Rev. Mod. Phys., 57 (1985), 827–863.  
  5. P.G. de Gennes, F. Brochard-Wyart, D. Quéré. Capillarity and wetting phenomena. Springer, 2004.  Zbl1139.76004
  6. S. Moosman, G.M. Homsy. Evaporating menisci of wetting fluids.J. Colloid Interface Sci., 73 (1980), 212–223.  
  7. S.J.S. Morris. Contact angles for evaporating liquids predicted and compared with existing experiments.J. Fluid Mech., 432 (2001), 1–30.  Zbl1030.76058
  8. A. Oron, S.H. Davis, S.G. Bankoff. Long-scale evolution of thin liquid films.Rev. Mod. Phys., 69 (1997), 931–980.  
  9. M. Potash, P.C. Wayner. Evaporation from a two dimensional extended meniscus.Int. J. Heat Mass Transfer, 15 (1972), 1851–1863.  
  10. A.Ye. Rednikov, P. Colinet. Vapor-liquid steady meniscus at a superheated wall : asymptotics in an intermediate zone near the contact line. Microgravity Sci. Tech., 22 (2010), 249–255.  
  11. A.Ye. Rednikov, S. Rossomme, P. Colinet. Steady microstructure of a contact line for a liquid on a heated surface overlaid with its pure vapor : parametric study for a classical model.Multiphase Sci. Tech., 21 (2009), 213–248.  
  12. R.W. Schrage. A Theoretical Study of Interface Mass Transfer. Columbia University Press, New York, 1953.  
  13. P.C. Stephan, C.A. Busse. Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls.Int. J. Heat Mass Transfer, 35 (1992), 383–391.  

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.