DIVERGING TIME AND LENGTH SCALES OF SPINODAL DECOMPOSITION MODES IN THIN-FILMS

We study the early-time spinodal decomposition of binary mixtures in t hin slabs of thickness L on the basis of a Ginzburg-Landau-type treatm ent. After deriving a general classification of the linear demixing mo des, Ne calculate explicitly the L-dependent mode spectrum for a symme tric slab with wall-induced interactions that tend to stabilize the mi xture. We show that there exists a critical thickness L-c below which no spontaneous demixing takes place. Both the wavelength 2 pi/k(parall el to,m) and the inverse growth rate omega(parallel to,m)(-1) of the m ost unstable modes diverge when L approaches L-c.