Scaling behavior of phase-separating binary liquids in porous media

A computer simulation is performed to study the phase-separation dynamics of binary liquids in a porous glass. The pores are modeled with two-dimensional interconnected tunnels, the liquid molecules with Ising spins, the wetting effect of the pore walls with an external field that the wall atoms provide to their neighboring spins, and the time evolution with the Kawasaki spin-exchange dynamics. Because of the highly correlated nature of the tunnel walls, the Pythagorean distance is irrelevant for the spin correlation. Thus we use the minimum distance in measuring the correlation function. The resultant correlation function shows scaling behavior at late times when the wetting effect is weak, and at early times when the wetting effect is adequately strong. In the scaling regimes, the domain growth shows the ${\mathit{t}}^{1/3}$ behavior. The growth pattern also displays a finite-size effect of the average tunnel width, which can be scaled using a Family-Vicsek type of scaling law. The relaxation of the short-range correlation function displays the usual exponential diffusive dynamics at early times and the nonexponential activated dynamics at late times.