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

Abstract

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 Lc 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 Lc.