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Evaporation of thin liquid droplets on heated surfaces

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Abstract

We carry out combined experimental and theoretical studies of liquid droplet evaporation on heated surfaces in a closed container filled with saturated vapor. The droplets are deposited on an electrically heated thin stainless steel foil. The evolution of droplet shapes is studied by optical methods simultaneously with high-resolution foil temperature measurements using thermochromic liquid crystals. A mathematical model is developed based on the assumptions that the droplet surface has uniform mean curvature and the contact line is pinned during evaporation. Both the dynamics of liquid–vapor interface and the temperature profiles at the foil are shown to be in good agreement with the experimental data.

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Abbreviations

c :

heat capacity, J/kg K

d :

thickness of the foil, μm

h :

nondimensional droplet height

h d :

droplet height, m

K :

kinetic parameter

k :

thermal conductivity, W/m K

Δh lv :

latent heat, J/kg

n :

nondimensional coordinate

q :

nondimensional heat source term

R :

gas constant per unit mass, J/kg K

R d :

droplet radius, m

r :

nondimensional radial coordinate

T :

nondimensional temperature

T s :

saturation temperature, °C

T*:

temperature, °C

ΔT*:

maximum temperature difference in the system, °C

t :

nondimensional time

t*:

time, s

V :

droplet volume, m³

z :

nondimensional coordinate

α :

nondimensional thermal diffusivity

ε :

ratio of foil thickness and initial droplet radius

ρ:

density, kg/m3

d:

droplet

f:

foil

s:

saturation

v:

vapor

References

  1. Ajaev VS (2005) Spreading of thin volatile liquid droplets on uniformly heated surfaces. J Fluid Mech 528:279–296

    Article  MATH  MathSciNet  Google Scholar 

  2. Anderson DM, Davis SH (1995) Spreading of volatile liquid droplets on heated surfaces. Phys Fluids 7:248–265

    Article  MATH  Google Scholar 

  3. Bai Q, Fujita Y (1999) Numerical simulation of the growth for a single bubble in nucleate boiling. Therm Sci Eng 7:45–53

    Google Scholar 

  4. Deegan RD, Dupont TF, Huber G, Nagel SR, Witten TA (2000) Contact line deposits in an evaporating drop. Phys Rev E 62:756–765

    Article  Google Scholar 

  5. Gokhale SJ, Plawsky JL, Wayner PC (2003) Experimental investigation of contact angle, curvature, and contact line motion in dropwise condensation and evaporation. J Colloid Interface Sci 259:354–366

    Article  Google Scholar 

  6. Höhmann C (2004) Temperaturmessverfahren zur räumlich hochauflösenden Untersuchung des Wärmetransports an einem verdampfenden Flüssigkeitsmeniskus. PhD Thesis, Darmstadt University of Technology, Darmstadt

  7. Hu H, Larson RG (2002) Evaporation of a sessile droplet on a substrate. J Phys Chem B 106:1334–1344

    Article  Google Scholar 

  8. Hu H, Larson RG (2005) Analysis of microfluid flow in an evaporating sessile droplet. Lagmuir 21:3963–3971

    Article  Google Scholar 

  9. Kern J, Stephan P (2003) Theoretical model for nucleate boiling heat and mass transfer of binary mixtures. Trans ASME, J Heat Transf 125:1106–1115

    Article  Google Scholar 

  10. Potash M, Wayner PC (1972) Evaporation from a two-dimensional extended menisci. Int J Heat Mass Transf 42:1851–1863

    Article  Google Scholar 

  11. Mollaret R, Sefiane K, Christy JRE, Veyret D (2004) Experimental and numerical investigation of the evaporation into air of a drop on a heated surface. Chem Eng Res Design 82(A4):471–480

    Article  Google Scholar 

  12. Moosman S, Homsy GM (1980) Evaporating menisci of wetting fluids. J Colloid Interface Sci 73:212–223

    Article  Google Scholar 

  13. Raad T, Myer JE (1971) Nucleation studies in pool boiling on thin plates using liquid crystals. AIChE 17:1260–1261

    Article  Google Scholar 

  14. Rose J (2000) Accurate approximate equations for intensive sub-sonic evaporation. Int J Heat Mass Transfer 43:3869–3875

    Article  MATH  Google Scholar 

  15. Schrage RW (1953) A theoretical study of interphase mass transfer. Columbia University Press, New York

    Google Scholar 

  16. Stasiek J, Collins M (1996) The use of liquid crystals and true color image processing in heat and fluid flow experiments. Atlas Visual 2:79–104

    Google Scholar 

  17. Stephan P, Brandt C (2004) Advanced capillary structures for high performance heat pipes. J Heat Transfer Eng 25:78–85

    Article  Google Scholar 

  18. Stephan P, Busse CA (1992) Analysis of the Heat Transfer Coefficient of Grooved Heat Pipe Evaporator Walls. Int J Heat Mass Transfer 35(2):383–391

    Article  Google Scholar 

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Authors and Affiliations

  1. Darmstadt University of Technology, Petersenstraße 30, 64287, Darmstadt, Germany

    C. Sodtke & P. Stephan

  2. Department of Mathematics, Southern Methodist University, Dallas, TX, 75275-0156, USA

    V. S. Ajaev

Authors
  1. C. Sodtke
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  2. V. S. Ajaev
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  3. P. Stephan
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Correspondence to P. Stephan.

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Sodtke, C., Ajaev, V.S. & Stephan, P. Evaporation of thin liquid droplets on heated surfaces. Heat Mass Transfer 43, 649–657 (2007). https://doi.org/10.1007/s00231-006-0126-6

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  • DOI: https://doi.org/10.1007/s00231-006-0126-6

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