Abstract
The dynamics of phase transition in a binary mixture occurring during a quench is studied taking into account composition fluctuations by solving Langer's equation in a domain composed of a certain number of micro-domains. The resulting Langer's equation governing the evolution of the distribution function becomes multidimensional. Circumventing the curse of dimensionality the proper generalized decomposition is applied. The influence of the interaction parameter in the vicinity of the critical point is analyzed. First we address the case of a system composed of a single micro-domain in which phase transition occurs by a simple symmetry change. Next, we consider a system composed of two micro-domains in which phase transition occurs by phase separation, with special emphasis on the effect of the Landau free energy non-local term. Finally, some systems consisting of many micro-domains are considered.
Highlights
In the last few decades considerable attention has been paid to second-order transition by spinodal decomposition or nucleation and growth occurring in a binary mixture quench [1]; and especially to the dynamics of order parameter fluctuations that increase when approaching the critical point
The order parameter is a conservative quantity when considering phase transitions and it measures the difference in volume fraction between the two components η = φA − φB, the limiting cases are η = −1 for space region containing only B molecules and η = +1 for space region containing only A molecules
We have studied phase separation by spinodal decomposition under a quench from one phase region, and we have focused especially on composition fluctuations dynamics increase when passing through the critical region
Summary
In the last few decades considerable attention has been paid to second-order transition by spinodal decomposition or nucleation and growth occurring in a binary mixture quench [1]; and especially to the dynamics of order parameter fluctuations that increase when approaching the critical point. The linear Cahn–Hilliard theory describe rigorously the initial stages of spinodal decomposition by giving an expression of the amplification factor and the effective diffusivity coefficient as functions of the wave number of the fluctuation which reproduces accurately experimental measurements It fails in reproducing the behavior at very early instants especially in the vicinity of the critical point where the deviation from experimental data becomes important. The weakness that exhibits this equation is that it does not take into account thermal fluctuations, the factor which initiates separation, and which increases when approaching the critical point even for later stages of separation This follows from the mean field approximation on which the Cahn–Hilliard model is based. Different scenarios are treated considering a one-dimensional physical space consisting of a different number of micro-domains
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