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Math. Model. Nat. Phenom. Vol. 3, No. 1, 2008, pp. 75-97
DOI: 10.1051/mmnp:2008034
The Effect of Crystal-Melt Surface Energy on the Stability of Ultra-Thin Melt Films
M. Beerman1 and L. N. Brush21 Andrews Space Inc., Seattle, WA, 98104, USA
2 Department of Materials Science and Engineering, University of Washington, Seattle, WA, 98195, USA
brush@u.washington.edu
Published online: 17 July 2008
Abstract
The stability and evolution of very thin, single component, metallic-melt films is
studied by analysis of coupled strongly nonlinear equations for gas-melt (GM) and crystal-melt (CM) interfaces, derived using the lubrication approximation. The crystal-melt interface is deformable by freezing and melting, and there is a thermal gradient applied across the
film. Linear analysis reveals that there is a maximum applied far-field temperature in the
gas, beyond which there is no film instability. Instabilities observed in the absence of CM
surface energy are oscillatory for all marginally stable states. The effect of the CM surface
energy is to expand the parameter range over which a film is unstable. The new range of
instabilities are of longer wavelength and are stationary, compared to the range found in
the absence of CM surface energy. Numerical analysis illustrates how perturbations grow to
rupture by standing waves. With CM surface energy, an initially longer (stationary) wavelength perturbation has a relatively slow growth rate, but it can trigger the appearance of
much faster growing shorter wavelength (oscillatory) instabilities, leading to an accelerated
film rupture process.
Mathematics Subject Classification. 76D08, 76E17, 76E30, 80A22
Key words: phase change -- lubrication theory -- interface instability -- nonlinear -- latent heat -- crystal -- van der Waals -- long wavelength