# Dropwise condensation formation theories

Several theories have been proposed to explain the mechanism of dropwise condensation. The first model, proposed by Eucken (1937), has been supported by many experimental studies, such as that by McCormick and Baer (1963). It states that liquid droplets form only heterogeneously at nucleate sites; if they are formed with a radius exceeding that of equilibrium, they will continue to grow and then join with surrounding droplets. Once the mass of the condensate reaches a critical point, it will be removed from the surface by gravitational forces or by drag forces produced by the surrounding gas. As droplets are removed, the surface is wiped clean of condensate and the process restarts at the nucleate sites. This periodic cleaning constitutes the advantage of dropwise condensation over filmwise condensation, as there is no resistance to heat transfer through the condensate when the condensate layer is removed; and thus the heat transfer rate increases greatly.

The second approach postulates that between drops there exists a thin and unstable liquid film on a solid surface. As the condensation process continues and the thin film grows thicker, the film reaches a critical thickness – estimated to be in the order of 1μm – at which point it breaks up into droplets. Condensation then continues in the dry areas between the recently-ruptured droplets, and on top of the already-formed droplets. The majority of new condensate does occur on the wall surface because there is less resistance to heat conduction than if the new condensate formed on the already-existing droplets. These new condensate droplets are then drawn to the neighboring droplets by surface tension effects, producing a new thin film. This film will then grow and rupture at the critical thickness, and the process will repeat continuously.

Dropwise condensation takes place if the condensate cannot wet the surface. The wettability can be measured by a contact angle defined as

 $\cos \theta = \frac{\sigma_{sv}-\sigma_{sl}}{\sigma_{lv}}$ (1)

where σsvsllv are surface tensions between solid-vapor, solid-liquid, and liquid-vapor interfaces. When the contact angle, θ, is greater than 90°, the condensate cannot wet the surface and dropwise condensation occurs. The criterion for dropwise condensation is the critical surface tension σcr which is characteristics of the surface alone. If the surface tension between liquid-vapor interface σlv is greater than σcr, dropwise condensation occurs (Shafrin and Zisman, 1960). Critical surface tensions for selected solid surfaces are given in the following table. It can be seen that the critical surface tensions for all solids listed in the following table are below the surface tension of water at 1 atm (σlv = 58.91x10 − 3N / m ). Therefore, a metal surface, on which film condensation usually occurs, can be coated with another substance with lower critical surface tension to promote dropwise condensation.

Critical surface tension for selected solid surfaces

Solid Surface σlv(10 − 3N / m)
Kel-F ® 31
Nylon 46
Platinum with perfluorobutyric acid monolayer 10
Platinum with perfluorolauric acid monolayer 6
Polyethylene 31
Polystyrene 33
Polyvinyl Chloride 39
Teflon ® 18

## References

Eucken, A., 1937, Naturwissenschaften, Vol. 25, pp. 209.

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

McCormick, J.L., and Baer, E., 1963, “On the Mechanism of Heat Transfer in Dropwise Condensation,” Journal of Colloid Science, Vol. 18, pp. 208-216.

Shafrin, E.G., and Zisman, W. A., 1960, “Constitutive relations in the wetting of low energy surfaces and the theory of the retraction method of preparing monolayers,” Journal of Physical Chemistry, Vol. 64, pp. 519-524.