Mathematics – Analysis of PDEs
Scientific paper
2008-05-07
Mathematics
Analysis of PDEs
37 pages, 6 figures. PDFLaTeX with RevTeX4 macros
Scientific paper
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. Since we are interested in the long-time behaviour of the phase-separating fluid, we restrict our attention to films that do not rupture. To do this, we introduce a regularising Van der Waals potential. We analyse the resulting fourth-order equations by constructing a solution as the limit of a Galerkin approximation, and obtain existence and regularity results. In our analysis, we find a nonzero lower bound for the height of the film, which precludes the possibility of rupture. The lower bound depends on the parameters of the problem, and we compare this dependence with numerical simulations. We find that while the theoretical lower bound is crucial to the construction of a smooth, unique solution to the PDEs, it is not sufficiently sharp to represent accurately the parametric dependence of the observed dips in free-surface height.
Naraigh Lennon O.
Thiffeault Jean-Luc
No associations
LandOfFree
Nonlinear dynamics of phase separation in ultra-thin films does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonlinear dynamics of phase separation in ultra-thin films, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear dynamics of phase separation in ultra-thin films will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-491888