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, Ne 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 2 pi/k(parallel to,m) and the inverse growth rate omega(parallel to,m)(-1) of the most unstable modes diverge when L approaches L-c.