Crossover, locking-in, and intermittency of droplet growth rates in phase separation

Abstract

Nonuniversal behavior in the dynamics of phase separation is discussed. An equation which exhibits a nonuniversal growth rate in a long-time limit is derived relying on the dynamic-scaling assumption. Two contradictory behaviors, a crossover to larger growth rate and a formation of a locked-in structure, are shown to be described by this equation in two limiting cases. The intermittent region lies between regions with these two contradictory behaviors. Two types of intermittent-growth-rate exponents are obtained. One, $a_{I1\mathrm{}}$, is valid at high temperatures, while the other, $a_{I2\mathrm{}}$, is valid at low temperatures. These two exponents are, respectively, $a_{I1\mathrm{}}=w_1{a}_1+w_2{a}_2$, and $a_{I2\mathrm{}}={(\frac{w_1}{a_1}+\frac{w_2}{a_2})}^{-1\mathrm{}}$. Here $w_i \mathrm{}(i=1,2\mathrm{})\mathrm{}$ are the probabilities of finding configuration associated, respectively, with the growth rates $R\propto t^{a_1}$ and $R\propto t^{a_2}$. $a_1$ is the largest exponent due to the curvature-driven force and $a_2$ is the next largest exponent; $a_2=0\mathrm{}$ at zero temperature. Thus, for certain values of system parameters, the intermittent exponent $a_I$ varies from $0 \mathrm{to} a_{I1\mathrm{}}$ as the temperature is increased. Several aspects of the growth rates in parameter space are predicted. They are consistent with numerical simulations and fluid mixtures.