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

TL;DR

This study uses molecular dynamics to investigate surface-directed spinodal decomposition of a symmetric binary fluid near an amorphous wall, revealing a wetting-layer growth that transitions from diffusion-like to viscous hydrodynamic kinetics. The wetting-layer thickness scales as $R_1(t) \propto t^{\alpha}$ with $\alpha \approx 1/3$ initially and $\alpha \approx 1$ at late times, with a crossover around $t_c \approx 3\times 10^3$ and $R_1(t_c) \approx 5.3$, consistent with a crossover length $\Lambda \approx 5.7$ given by $\Lambda = \sqrt{2k/\\gamma_0}$. The amorphous wall eliminates layering effects, allows observation of a bicontinuous domain structure, and shows isotropic coarsening in directions parallel and perpendicular to the wall, supporting a bending-energy–driven diffusion picture up to $\Lambda$ and capillary-driven flow beyond. These results bridge microscopic interfacial mechanics with macroscopic SDSD kinetics and align with theoretical and experimental crossovers in confined fluid mixtures.

Abstract

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, $R_1(t)\sim t^α$, with two distinct growth regimes of $α=1/3$ and $α=1$ active for at least a decade. The computed crossover time for $α=1/3 \to 1$ equaled the reported bulk crossover time, and the corresponding crossover length scale $R_c$ agrees well with the expression $Λ= \sqrt{2k/γ_0}$ 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 ($γ$) governs small-scale coarsening, producing $t^{1/3}$ growth. For length scales beyond $Λ$, 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.

Figures (9)

• Figure 1: The time evolutionary snapshots of surface-directed spinodal decomposition in a simulation box of volume $L_x\times L_y \times L_D = 128\sigma\times 128\sigma\times 128\sigma$. Wetting occurs on the top wall located at $z=0$. The two particle types in the binary mixture ($A+B$) are shown in blue ($A$-type) and pink ($B$-type) colors. The snapshots shown here are for the time $t>0$ for a single quench to $T=0.7T_c$ at $t=0$, where $T_c(\simeq 1.423)$ is the bulk critical temperature. The snapshots belong to times $(a)\;\; t=200$, $(b)\;\; t=500$, and $(c)\;\; t=3000$.
• Figure 2: Laterally averaged order-parameter profiles, $\psi_{\text{av}} (z,t)$, with time specified. The profiles are constructed using a slab width of $\Delta z=0.5$.
• Figure 3: Time evolution of the domain interfaces resulting from the interplay of wetting and phase separation kinetics in a binary mixture. The two phases in the binary mixture ($A+B$) undergoing SDSD are shown in blue and red transparent voxels without edges. The inner sides of $A$-rich and $B$-rich phase domains are constructed as red ($\psi\to +1$) and blue ($\psi\to -1$) isosurfaces, respectively. The isosurfaces are constructed on the noise-eliminated coarse-grained simulation box composed of the lattice structure (as discussed in the text). We only show the part of the lattice lying above the wetting layer ($z>R_1(t)$) at three different timestamps: $(a)\; 400$, $(b)\; 2000$, and $(c)\;5000$, which range from diffusive growth regime to viscous hydrodynamics regime. The tubular structures are visible across the depletion region with openings toward the wetting layer; with no dominant droplet morphology present above the wetting layer, and the mixture remains purely bicontinuous (interconnected) near the surface and in bulk.
• Figure 4: ($a$) Scaled version of the laterally-averaged order parameter $\psi_{\text{av}(z,t)}$ profiles shown in Fig. \ref{['fig:figure2']}. The scaling factor is $R_1(t)$, which is calculated as the first-zero crossing of $\psi_{\text{av}(z,t)}$ along $z$. $(b)$ The wetting layer thickness, $R_1 (t)$, vs. time plotted on a log-log scale. The solid lines have slopes of $1/5$, $1/3$, and $1$, depicting potential-dependent, diffusive, and viscous-hydrodynamics growth. Light colored (cyan) solid lines represent $R_1(t)$ growth computed from different simulation trajectories with an independent initial starting configuration. Inset:$R_1(t)$ growth for different slab widths denoting the different levels of precision.
• Figure 5: Left Panel: Computation of the length offset $R'_1$ from the fitting of the instantaneous exponent $\alpha_i$ as a function of increasing wetting layer thickness $R_1(t)$. Right Panel: Fitting of $R_1(t) - R'_1$ vs. simulation time $t$, which exhibits a linear growth. From fitting of the diffusive coarsening of the wetting layer in Fig. \ref{['fig:figure2-1b']}: $y=0.3t^{0.33}$ and the linear growth $y=0.0014x^{0.98}$, and equating $At^{1/3}=Bt$, we get the crossover time of $\approx 3000$. The crossover time is in the range of crossover seen for the bulk domain coarsening (Fig. \ref{['fig:figure1']}).SSS10SSS12