Diverging time and length scales of spinodal decomposition modes in thin films

We study the early-time spinodal decomposition of binary mixtures in thin slabs of thickness L on the basis of a Ginzburg-Landau–type treatment. After deriving a general classification of the linear demixing modes, we calculate explicitly the L -dependent mode spectrum for a symmetric slab with wall-induced interactions that tend to stabilize the mixture. We show that there exists a critical thickness L c below which no spontaneous demixing takes place. Both the wavelength 2π/ k ∥,m and the inverse growth rate ω ∥,m −1 of the most unstable modes diverge when L approaches L c .