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RESEARCH PAPERS: Micro-Scale Heat Transfer

Instability of Ultra-Thin Water Films and the Mechanism of Droplet Formation on Hydrophilic Surfaces

[+] Author and Article Information
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 121(4), 964-971 (Nov 01, 1999) (8 pages) doi:10.1115/1.2826087 History: Received December 01, 1998; Revised May 06, 1999; Online December 05, 2007

Abstract

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.

Copyright © 1999 by The American Society of Mechanical Engineers
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