Nonlinear dynamics of phase separation in thin films

Abstract

We present a long-wavelength approximation to the Navier-Stokes Cahn-Hilliard equations to describe phase separation in thin films. The equations we derive underscore the coupled behaviour of free-surface variations and phase separation. We introduce a repulsive substrate-film interaction potential and analyse the resulting fourth-order equations by constructing a Lyapunov functional, which, combined with the regularizing repulsive potential, gives rise to a positive lower bound for the free-surface height. The value of this lower bound depends on the parameters of the problem, a result which we compare with numerical simulations. While the theoretical lower bound is an obstacle to the rupture of a film that initially is everywhere of finite height, it is not sufficiently sharp to represent accurately the parametric dependence of the observed dips or `valleys' in free-surface height. We observe these valleys across zones where the concentration of the binary mixture changes sharply, indicating the formation of bubbles. Finally, we carry out numerical simulations without the repulsive interaction, and find that the film ruptures in finite time, while the gradient of the Cahn--Hilliard concentration develops a singularity.

26 pages, 20 figures, PDFLaTeX with RevTeX4 macros. A thorough analysis of the equations is presented in arXiv:0805.1038

References in corpus (7)

• Aggregation of finite size particles with variable mobility
• Turbulence and coarsening in active and passive binary mixtures
• Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states
• Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems
• Bubbles and Filaments: Stirring a Cahn-Hilliard Fluid
• Decomposition driven interface evolution for layers of binary mixtures: {II}. Influence of convective transport on linear stability
• Dynamical Effects and Phase Separation in Thin Films

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