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


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.


Dropwise condensation Droplet morphology Heat transfer Wenzel state Cassie state 

List of symbols


Contact angle (°)


Contact angle hysteresis (°)


Pillar diameter (m)


Pillars center-to-center distance (m)


Acceleration of gravity (m s−2)


Pillars height (m)


Latent heat of condensation (J kg−1)


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


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


Pillars conductivity (W m−1 K−1)


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


Population density of large droplets (m−3)


Population density of small droplets (m−3)


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


Heat transfer rate through a droplet (W)

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

Total heat flux (W m−2)


Droplet radius (m)


Minimum droplet radius (m)


Maximum droplet radius (m)


Effective radius (m)


Droplet curvature thermal resistance (k W−1)


Droplet conduction thermal resistance (K W−1)


Trapped gas thermal resistance (K W−1)


Hydrophobic coating thermal resistance (K W−1)


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


Pillars thermal resistance (K W−1)


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


Condensate thermal resistance (K W−1)


Temperature (K)


Droplet base Temperature (K)


Liquid–vapor interface temperature (K)


Surface temperature (K)


Saturation temperature (K)


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)


Specific volume of gas (kg m−3)

Greek symbols


Condensation coefficient


Density (kg m−3)


Contact angle (°)


Sweeping period (s)


Surface tension (N m−1)


Thickness (m)


Inclination angle (°)


Solid fraction















Hydrophobic coating


Vapor–liquid interface

















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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

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