Phase Transformations in Free Films

Abstract

The purpose of this dissertation is to present the derivation of the governing equations for a free-film undergoing phase separation using a long-wavelength approximation to the Navier-Stokes equations coupled with the Cahn-Hilliard equation for phase transformation in a binary liquid. The equations are derived for two cases, one where the diffuse interphase boundary is assumed to have a thickness larger than the film thickness and the other where it is assumed to be less than the film thickness. A linear stability analysis is performed for these two cases and the conditions for instability are examined. An equation describing the profile of the interphase boundary for the case where the interphase boundary thickness is less than the film thickness is also derived assuming a no-flow condition, using a matched asymptotic analysis. Typically one of the liquid phases will wet the gas-liquid interface. Therefore, another aim is to numerically simulate the phenomenon of the wetting in a free-film by one of the binary liquid phases. This is done in a one-dimensional case as well as for an axisymmetric cylindrical geometry. Finally, the effect of the free-film thickness on the wetting behavior of the phase boundary liquid phases along the film interface is investigated using numerical methods. It is shown that as the film thickness is gradually reduced, the wetting along the interface disappears.