The Effect of Crystal-Melt Surface Energyon the Stability of Ultra-Thin Melt Films

Abstract

The stability and evolution of very thin, single component, metallic-melt films isstudied 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 thefilm. Linear analysis reveals that there is a maximum applied far-field temperature in thegas, beyond which there is no film instability. Instabilities observed in the absence of CMsurface energy are oscillatory for all marginally stable states. The effect of the CM surfaceenergy is to expand the parameter range over which a film is unstable. The new range ofinstabilities are of longer wavelength and are stationary, compared to the range found inthe absence of CM surface energy. Numerical analysis illustrates how perturbations grow torupture 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 ofmuch faster growing shorter wavelength (oscillatory) instabilities, leading to an acceleratedfilm rupture process.