This paper presents a new theory of droplet formation during condensation of water on a hydrophilic surface. The theory uses hydration, electrostatic, van der Waals, and elastic strain interactions between a hydrophilic solid surface and a water film, and shows that contributions to the disjoining pressure are dominated by hydration forces for films thinner than 3 nm. The equilibrium film thickness is found to remain almost constant at about 0.5 nm for a wide range of relative humidity, although it increases sharply as the relative humidity approaches unity. The competition between strain energy on one hand, and hydration, van der Waals, and liquid-vapor surface tension on the other, induces instability for films thicker than a critical value. The critical wavelength of instability, Lcr is also predicted as a function of film thickness. The theory proposes that as the relative humidity increases, nucleation initially occurs in monolayer fashion due to strong hydration forces. Using nucleation thermodynamics it predicts a critical nucleus size, d*, and internuclei spacing, I, as a function of subcooling, ΔT, of the solid surface and shows that both length scales decrease with increasing subcooling. Since these monolayer nuclei are formed on the adsorbed water film, it is shown that when the internuclei spacing is larger than the critical wavelength, l > Lcr instability occurs in the film resulting in droplet formation. The theory predicts that beyond a certain value of subcooling, the interdroplet spacing is “choked” and cannot decrease further.
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Instability of Ultra-Thin Water Films and the Mechanism of Droplet Formation on Hydrophilic Surfaces
A. Majumdar,
A. Majumdar
Department of Mechanical Engineering, University of California, Berkeley, CA 94720
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I. Mezic
I. Mezic
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106
Search for other works by this author on:
A. Majumdar
Department of Mechanical Engineering, University of California, Berkeley, CA 94720
I. Mezic
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106
J. Heat Transfer. Nov 1999, 121(4): 964-971 (8 pages)
Published Online: November 1, 1999
Article history
Received:
December 1, 1998
Revised:
May 6, 1999
Online:
December 5, 2007
Citation
Majumdar, A., and Mezic, I. (November 1, 1999). "Instability of Ultra-Thin Water Films and the Mechanism of Droplet Formation on Hydrophilic Surfaces." ASME. J. Heat Transfer. November 1999; 121(4): 964–971. https://doi.org/10.1115/1.2826087
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