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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...
We study pressure-driven, two-layer flow in inclined channels with high density and
viscosity contrasts. We use a combination of asymptotic reduction, boundary-layer theory and the
Karman-Polhausen approximation to derive evolution equations that describe the interfacial dynamics.
Two distinguished limits are considered: where the viscosity ratio is small with density
ratios of order unity, and where both density and viscosity ratios are small. The evolution equations
account for the presence of...
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