Surface-directed spinodal decomposition in binary fluid mixtures on an amorphous wall: A molecular dynamics study

We present molecular dynamics (MD) results to discuss wetting kinetics in binary fluid mixtures ($A:B=50:50$) undergoing surface-directed spinodal decomposition (SDSD) on an amorphous wall. Our simulations show the formation of a wetting layer rich in the preferred $A$-type particles and bicontinuous domain morphology in the bulk. In addition, the mixture maintains connectivity between the bulk and the wetting layer through $A$-rich tubes throughout the depletion region. The wetting layer thickness coarsens as a power law, $R_1(t)\sim t^{\alpha}$, with two distinct growth regimes of $\alpha=1/3$ and $\alpha=1$ active for at least a decade. The computed crossover time for $\alpha=1/3 \to 1$ equaled the reported bulk crossover time, and the corresponding crossover length scale $R_c$ agrees well with the expression $\Lambda = \sqrt{2k/\gamma_0}$ given by Scholten et al.~[\emph{Macromolecules}2005, 38, 3515] for bicontinuous domains in aqueous polymer mixtures in the presence of only one dominant length scale. This agreement supports a hydrodynamic picture of diffusive growth for the interconnected wetting layer and bulk domains, where the bending contribution ($k$) of curvature-dependent $AB$ interfacial tension ($\gamma$) governs small-scale coarsening, producing $t^{1/3}$ growth. For length scales beyond $\Lambda$, capillary flows yield the viscous hydrodynamic regime ($\sim t$). Our results show no orientational effects on the domain coarsening parallel and perpendicular to the wall, contrasting many continuum models, including combinations with Flory-Huggins theory.