Advertisement

Journal of Thermal Analysis and Calorimetry

, Volume 138, Issue 5, pp 2979–2988 | Cite as

The effect of droplet morphology on the heat transfer performance of micro-/nanostructured surfaces in dropwise condensation

A numerical study
  • Hamid Reza Talesh BahramiEmail author
  • Saeed Zarei
  • Hamid Saffari
Article

Abstract

It has been proved that dropwise condensation (DWC) has better heat transfer than filmwise condensation. DWC occurs on hydrophobic or superhydrophobic surfaces (SHS). Low surface energy and surface roughness are two key specifications of SHS. Roughness leads to appearing of Cassie and Wenzel morphologies on SHS. In the Cassie state, droplet suspends over roughness while in the Wenzel state droplets penetrates through roughness. Single Cassie droplets have higher mobility (an advantage) than Wenzel droplets while having a lower heat transfer rate (a disadvantage). The advantage of Cassie droplets leads to that droplets depart the surface at lower radius, sweep other droplets and prepare fresh surface for nucleating of new droplets. Some researchers have shown that surfaces with Wenzel droplets have better heat transfer and some have indicated that surfaces with Cassie droplets have better performance. Hence, a numerical investigation has been done in this study to explore which of these two morphologies have better performance in DWC. Results show that advantage and disadvantage of the morphologies can prevail on the other according to surface conditions. For example, a surface with Cassie state droplets may have higher or lower total heat transfer than a surface with Wenzel droplets depending on roughness height.

Keywords

Dropwise condensation Droplet morphology Heat transfer Wenzel state Cassie state 

List of symbols

CA

Contact angle (°)

CAH

Contact angle hysteresis (°)

d

Pillar diameter (m)

l

Pillars center-to-center distance (m)

g

Acceleration of gravity (m s−2)

h

Pillars height (m)

\(h_{\text{fg}}\)

Latent heat of condensation (J kg−1)

\(h_{\text{i}}\)

Liquid–vapor interface heat transfer coefficient (W m−1 K−1)

khc

Promoter layer thermal conductivity (W m−1 K−1)

kp

Pillars conductivity (W m−1 K−1)

\(k_{\text{w}}\)

Water thermal conductivity (W m−1 K−1)

N

Population density of large droplets (m−3)

n

Population density of small droplets (m−3)

Ns

Number of nucleation sites per unit area (m−2)

qd

Heat transfer rate through a droplet (W)

\(q^{\prime \prime }\)

Total heat flux (W m−2)

r

Droplet radius (m)

rmin

Minimum droplet radius (m)

rmax

Maximum droplet radius (m)

re

Effective radius (m)

Rc

Droplet curvature thermal resistance (k W−1)

Rd

Droplet conduction thermal resistance (K W−1)

Rg

Trapped gas thermal resistance (K W−1)

Rhc

Hydrophobic coating thermal resistance (K W−1)

Ri

Liquid–vapor interfacial thermal resistance (K W−1)

Rp

Pillars thermal resistance (K W−1)

Rv

Specific gas constant of vapor (J kg−1 K−1)

Rw

Condensate thermal resistance (K W−1)

T

Temperature (K)

Tb

Droplet base Temperature (K)

Ti

Liquid–vapor interface temperature (K)

Ts

Surface temperature (K)

Tsat

Saturation temperature (K)

ΔT

Surface subcooling temperature (K)

\(\Delta T_{\text{C}}\)

Temperature drop of droplet curvature (K)

\(\Delta T_{\text{d}}\)

Temperature drop of conduction through droplet (K)

\(\Delta T_{\text{i}}\)

Interface Temperature drop resistance (K)

\(\Delta T_{\text{int,Wenzel}}\)

Temperature drop of liquid–solid interface of Wenzel state (K)

vg

Specific volume of gas (kg m−3)

Greek symbols

\(\alpha\)

Condensation coefficient

\(\rho\)

Density (kg m−3)

\(\theta\)

Contact angle (°)

\(\tau\)

Sweeping period (s)

\(\sigma\)

Surface tension (N m−1)

\(\delta\)

Thickness (m)

Θ

Inclination angle (°)

\(\varphi\)

Solid fraction

Subscripts

a

Advancing

b

Base

c

Curvature

d

Drop

e

Effective

g

Gas

hc

Hydrophobic coating

i

Vapor–liquid interface

max

Maximum

min

Minimum

p

Pillar

r

Receding

sat

Saturated

s

Surface

w

Water

Notes

References

  1. 1.
    Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems. J Therm Anal Calorim. 2018;131:2027–39.CrossRefGoogle Scholar
  2. 2.
    Somesaraee MT, Rad EA, Mahpeykar MR. Analytical investigation of simultaneous effects of convergent section heating of Laval nozzle, steam inlet condition, and nozzle geometry on condensation shock. J Therm Anal Calorim. 2018;133:1023–39.CrossRefGoogle Scholar
  3. 3.
    Tahri T, Abdul-Wahab SA, Bettahar A, Douani M, Al-Hinai H, Al-Mulla Y. Simulation of the condenser of the seawater greenhouse. J Therm Anal Calorim. 2009;96:35–42.CrossRefGoogle Scholar
  4. 4.
    Dikici B, Eno E, Compere M. Pool boiling enhancement with environmentally friendly surfactant additives. J Therm Anal Calorim. 2014;116:1387–94.CrossRefGoogle Scholar
  5. 5.
    Vemuri S, Kim KJ. An experimental and theoretical study on the concept of dropwise condensation. Int J Heat Mass Transf. 2006;49:649–57.CrossRefGoogle Scholar
  6. 6.
    Talesh Bahrami HR, Saffari H. Theoretical study of stable dropwise condensation on an inclined micro/nano-structured tube. Int J Refrig. 2017;75:141–54.CrossRefGoogle Scholar
  7. 7.
    Zarei S, Talesh Bahrami HR, Saffari H. Effects of geometry and dimension of micro/nano-structures on the heat transfer in dropwise condensation: a theoretical study. Appl Therm Eng. 2018;137:440–50.CrossRefGoogle Scholar
  8. 8.
    Schmidt E, Schurig W, Sellschopp W. Condensation of water vapour in film-and drop form. Tech Mech Thermodyn. 1930;1:53–63.Google Scholar
  9. 9.
    Quan X, Yang L, Cheng P. Effects of electric fields on onset of dropwise condensation based on Gibbs free energy and availability analyses. Int Commun Heat Mass Transf. 2014;58:105–10.CrossRefGoogle Scholar
  10. 10.
    Bum-Jin C, Sin K, Min Chan K, Ahmadinejad M. Experimental comparison of film-wise and drop-wise condensations of steam on vertical flat plates with the presence of air. Int Commun Heat Mass Transf. 2004;31:1067–74.CrossRefGoogle Scholar
  11. 11.
    Talesh Bahrami HR, Saffari H. Mathematical modeling and numerical simulation of dropwise condensation on an inclined circular tube. J Aerosp Technol Manag. 2017;9:476–88.CrossRefGoogle Scholar
  12. 12.
    LeFevre EJ, Rose JW. A theory of heat transfer by dropwise condensation. Chemical Engineering Progress. AMER INST CHEMICAL ENGINEERS 345 E 47TH ST, NEW YORK, NY 10017; 1966. p. 86.Google Scholar
  13. 13.
    Abu-Orabi M. Modeling of heat transfer in dropwise condensation. Int J Heat Mass Transf. 1998;41:81–7.CrossRefGoogle Scholar
  14. 14.
    Rose JW, Glicksman LR. Dropwise condensation—the distribution of drop sizes. Int J Heat Mass Transf. 1973;16:411–25.CrossRefGoogle Scholar
  15. 15.
    Kim S, Kim KJ. Dropwise condensation modeling suitable for superhydrophobic surfaces. J Heat Transf. 2011;133:081502.CrossRefGoogle Scholar
  16. 16.
    Cassie ABD, Baxter S. Wettability of porous surfaces. Trans Faraday Soc. 1944;40:546–51.CrossRefGoogle Scholar
  17. 17.
    Wenzel RN. Resistance of solid surfaces to wetting by water. Ind Eng Chem. 1936;28:988–94.CrossRefGoogle Scholar
  18. 18.
    Miljkovic N, Enright R, Wang EN. Effect of droplet morphology on growth dynamics and heat transfer during condensation on superhydrophobic nanostructured surfaces. ACS Nano. 2012;6:1776–85.CrossRefGoogle Scholar
  19. 19.
    Lee S, Yoon HK, Kim KJ, Kim S, Kennedy M, Zhang BJ. A dropwise condensation model using a nano-scale, pin structured surface. Int J Heat Mass Transf. 2013;60:664–71.CrossRefGoogle Scholar
  20. 20.
    Chen C-H, Cai Q, Tsai C, Chen C-L, Xiong G, Yu Y, et al. Dropwise condensation on superhydrophobic surfaces with two-tier roughness. Appl Phys Lett. 2007;90:173108.CrossRefGoogle Scholar
  21. 21.
    Chen X, Wu J, Ma R, Hua M, Koratkar N, Yao S, et al. Nanograssed micropyramidal architectures for continuous dropwise condensation. Adv Funct Mater. 2011;21:4617–23.CrossRefGoogle Scholar
  22. 22.
    Hou Y, Yu M, Chen X, Wang Z, Yao S. Recurrent filmwise and dropwise condensation on a beetle mimetic surface. ACS Nano. 2014;9:71–81.CrossRefGoogle Scholar
  23. 23.
    Umur A, Griffith P. Mechanism of dropwise condensation. ASME J Heat Transf. 1965;87:275–82.CrossRefGoogle Scholar
  24. 24.
    Schrage RW. A theoretical study of interphase mass transfer. New York City: Columbia University Press; 1953.CrossRefGoogle Scholar
  25. 25.
    Enright R, Miljkovic N, Dou N, Nam Y, Wang EN. Condensation on superhydrophobic copper oxide nanostructures. J Heat Transfer. 2013;135:091304.CrossRefGoogle Scholar
  26. 26.
    Glicksman LR, Hunt AW. Numerical simulation of dropwise condensation. Int J Heat Mass Transf. 1972;15:2251–69.CrossRefGoogle Scholar
  27. 27.
    Khandekar S, Muralidhar K. Dropwise condensation on inclined textured surfaces. Berlin: Springer; 2013.Google Scholar
  28. 28.
    Miljkovic N, Enright R, Wang EN. Modeling and optimization of superhydrophobic condensation. J Heat Transf. 2013;135:111004.CrossRefGoogle Scholar
  29. 29.
    Kim H-Y, Lee HJ, Kang BH. Sliding of liquid drops down an inclined solid surface. J Colloid Interface Sci. 2002;247:372–80.CrossRefGoogle Scholar
  30. 30.
    Talesh Bahrami HR, Ahmadi B, Saffari H. Optimal condition for fabricating superhydrophobic copper surfaces with controlled oxidation and modification processes. Mater Lett. 2017;189:62–5.CrossRefGoogle Scholar
  31. 31.
    Talesh Bahrami HR, Ahmadi B, Saffari H. Preparing superhydrophobic copper surfaces with rose petal or lotus leaf property using a simple etching approach. Mater Res Express. 2017;4:055014.CrossRefGoogle Scholar
  32. 32.
    Lee CY, Zhang BJ, Park J, Kim KJ. Water droplet evaporation on Cu-based hydrophobic surfaces with nano- and micro-structures. Int J Heat Mass Transf. 2012;55:2151–9.CrossRefGoogle Scholar
  33. 33.
    Aksan SN, Rose JW. Dropwise condensation—the effect of thermal properties of the condenser material. Int J Heat Mass Transf. 1973;16:461–7.CrossRefGoogle Scholar
  34. 34.
    Le Fevre EJ, Rose JW. An experimental study of heat transfer by dropwise condensation. Int J Heat Mass Transf. 1965;8:1117–33.CrossRefGoogle Scholar
  35. 35.
    He B, Patankar NA, Lee J. Multiple equilibrium droplet shapes and design criterion for rough hydrophobic surfaces. Langmuir. 2003;19:4999–5003.CrossRefGoogle Scholar
  36. 36.
    Lee SM, Jung ID, Ko JS. The effect of the surface wettability of nanoprotrusions formed on network-type microstructures. J Micromech Microeng. 2008;18:125007.CrossRefGoogle Scholar
  37. 37.
    Miljkovic N, Enright R, Wang EN. Growth dynamics during dropwise condensation on nanostructured superhydrophobic surfaces. In: ASME 2012 third international conference on micro/nanoscale heat and mass transfer. American Society of Mechanical Engineers; 2012. p. 427–36.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  • Hamid Reza Talesh Bahrami
    • 1
    Email author
  • Saeed Zarei
    • 1
  • Hamid Saffari
    • 1
  1. 1.School of Mechanical EngineeringIran University of Science and TechnologyNarmak, TehranIran

Personalised recommendations