# Dropwise condensation

## Dropwise Condensation Formation Theories

Several theories have been proposed to explain the mechanism of dropwise condensation. The first model has been supported by many experimental studies. 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. 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.

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## Critical Droplet Radius for Dropwise Condensation

As mentioned before, upon formation in their nucleation sites, droplets grow only if they form with a radius that exceeds the equilibrium radius. The analysis that leads to the definition of the critical equilibrium radius is presented below. A good place to start this derivation lies in the Gibbs free energy minimum principle.

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## Thermal Resistances in the Dropwise Condensation Processes

The condensation process must overcome a series of thermal resistances for the heat and mass transfer to occur. These resistances include the thermal resistance found in the vapor, thermal resistance encountered during the phase change from vapor to liquid, resistance caused by capillary depression of the equilibrium saturation temperature at the interface, thermal resistance found in the liquid phase, and thermal resistance found at the wall where heat is conducted from the surface into the wall.

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## Heat Transfer Coefficient for Dropwise Condensation

By substituting the expressions for temperature drops through the interface, capillary depression, and liquid droplets into the following equation

ΔTtotal = TvaporTw = ΔTvapor + ΔTδ + ΔTcap + ΔTdroplet

and neglecting the temperature drop in the vapor phase, the temperature drop is obtained:

$\Delta T_{total}=T_{sat}-T_{w}=\frac{2q_{d}}{h_{\delta }\pi D^{2}}+\left ( T_{v}-T_{w} \right )\frac{D_{min}}{D}+\frac{q_{d}}{2k_{l}\pi D}$

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## References

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.