SPINODAL DECOMPOSITION IN BINARY-MIXTURES

We study the early stage of the phase separation of a binary mixture f ar from its critical point of demixing. Whenever the mixture of two mu tually repulsive species is quenched to a temperature below its critic al point of miscibility, the effect of the enthalpic repulsive force p revails upon the entropic tendency to mix, so that the system eventual ly separates into two coexisting phases. We have developed a highly no nlinear model, in close analogy with the linear theory of Cahn and Hil liard, where a generalized free energy is defined in terms of two para meters psi and a, the first describing the equilibrium composition of the two phases, and the second denoting a characteristic length scale that is inversely proportional to the equilibrium surface tension. The linear stability analysis predicts that any perturbation of the initi al mixture composition with wave number k smaller than root 2 psi/a wi ll grow exponentially in time, with a maximum growth corresponding to K-max = root psi/a. A numerical solution of the equation shows that no nlinear effects saturate the exponential growth, and that the concentr ation distribution tends to a steady state, periodic profile with wave length lambda = 2 pi a/root psi corresponding to the fastest growing m ode of the linear regime. The main result of our theoretical model is that this steady state does not depend on the form of the initial pert urbation to the homogeneous composition profile.