Phase separation of fluids in porous media: A molecular dynamics study

We present comprehensive molecular dynamics results for phase-separation kinetics of fluids in a porous medium. This system is modeled by a symmetric Lennard-Jones fluid mixture with a quenched random field. The presence of disorder slows down domain growth from power-law to a logarithmic form. It also modifies the correlation functions and structure factors which characterize the morphology. In particular, the structure-factor tail shows a non-Porod behavior, which is the consequence of scattering from rough interfaces.

Figure 1

Schematic picture of the interactions in our system. The black circles indicate the disorder sites placed on a cubic lattice. The red (gray) circles indicate the fluid particles. A particle $i$ interacts with the other fluid particles via the truncated LJ potential, and with the nearest disorder site ($K$, in this case) via a random field.

Figure 2

(a) Three-dimensional (size ${32}^3$) snapshots of the fluid mixture at $t=2000$ (LJ units), with different disorder amplitudes. The $A$ and $B$ particles are marked green (gray) and blue (black), respectively. (b) Two-dimensional (size ${32}^2$) cross sections of the snapshots in (a). Here, only $B$ particles are shown, for clarity.

Figure 3

Scaling plots of the correlation function, $C(r,t)$ vs $r/\ell$, for the fluid mixture. (a) Data sets for $f=2$, at different times. (b) Data sets for $t=2000$, at different disorder amplitudes. All times are measured in LJ units.

Figure 4

Scaling plots of the structure factor, $S(k,t){\ell }^{-3}$ vs $k\ell$. The data sets correspond to three different values of $f$, as indicated, at $t=2000$. The dashed line denotes the Porod law [$S(k,t)\sim k^{-(d+1)}$] for scattering from sharp interfaces. The solid line corresponds to a non-Porod behavior [$S(k,t)\sim k^{-(d+\theta )}$ with $\theta =0.2$], which is characteristic of scattering from rough interfaces.

Figure 5

(a) Time dependence of domain size for different disorder amplitudes, plotted on a log-log scale. (b) Instantaneous dynamical exponent ($z_{\mathrm{eff}}$) vs $\ell$ for data sets in (a). The horizontal dashed lines mark the disorder-dependent intermediate-time exponent $\overline{z}$. (c) Plot of $\overline{z}$ vs $f$. The solid line denotes the best linear fit. (d) Plot of $z_{\mathrm{eff}}-\overline{z}$ vs $\ell /\lambda$ at late times ($z_{\mathrm{eff}}>\overline{z}$) for $f=1,2,5$. The choice of $\lambda$ is explained in the text. The dashed line denotes the best fit to Eq. (5).