Domain Growth and Aging in a Phase Separating Binary Fluid Confined Inside a Nanopore

TL;DR

This work investigates how hydrodynamics and confinement modify phase separation kinetics in a binary fluid inside cylindrical nanopores. Using molecular dynamics simulations with a hydrodynamics-preserving thermostat of a symmetric Lennard-Jones A+B mixture quenched below $T_c$, the study analyzes domain growth via $\ell(t)$ and aging via the two-time autocorrelation $C_{\rm ag}(t,t_w)$. It finds stripe morphologies with a growth crossover from diffusive $\ell(t)\sim t^{1/3}$ to inertial hydrodynamic $\ell(t)\sim t^{2/3}$, saturating at $\ell\approx D$, and aging characterized by a temperature-independent power law $C_{\rm ag}\sim x^{-\lambda}$ with $\lambda\simeq 2.55$, validated by finite-size scaling. These results show robust power-law aging and altered growth dynamics in quasi-one-dimensional confinement, differing from bulk behavior and offering insights for nanofluidic applications and theories of confined phase separation.

Abstract

Hydrodynamics is known to have strong effects on the kinetics of phase separation. There exist open questions on how such effects manifest in systems under confinement. Here, we have undertaken extensive studies of the kinetics of phase separation in a two-component fluid that is confined inside pores of cylindrical shape. Using a hydrodynamics-preserving thermostat, we carry out molecular dynamics simulations to obtain results for domain growth and aging for varying temperature and pore-width. We find that all systems freeze into a morphology where stripes of regions rich in one or the other component of the mixture coexist in a locked situation. Our analysis suggests that, irrespective of the temperature the growth of the average domain size, $\ell(t)$, prior to the freezing into stripped patterns, follows the power law $\ell(t)\sim t^{2/3}$, suggesting an inertial hydrodynamic growth, which typically is applicable for bulk fluids only in the asymptotic limit. Similarly, the aging dynamics, probed by the two-time order-parameter autocorrelation function, also exhibits a temperature-independent power-law scaling with an exponent $λ\simeq 2.55$, much smaller than what is observed for a bulk fluid.

Figures (11)

• Figure 1: Sketch of a model cylinder of length $L$ and diameter $D$. The wall consists of Lennard-Jones particles, while the interior contains A and B particles shown in different colors. The schematic plot below shows the interaction function between the cylindrical surface and a fluid particle separated by a distance $d_r$.
• Figure 2: Evolution snapshots obtained after quenching a system, with $D=20$ and $L=200$, from high temperature disordered phase to $T = 0.8$. Different species are marked in different colors. We have kept the cylinder length fixed throughout this study.
• Figure 3: Plots of $\ell(t)$ (at $T=0.8$), as a function of time, on a log-log scale, where different colors and symbols are used to represent results for different diameter sizes, with $L$ fixed at $200$. The dotted line corresponds to diffusive ($\alpha=1/3$) and the solid line corresponds to inertial hydrodynamic ($\alpha=2/3$) growth laws. Inset: instantaneous exponent $\alpha_{i}$, corresponding to the data in the main frame, are plotted versus $1/t$.
• Figure 4: Snapshots of the configurations obtained at $t=6000$ after quenching binary mixtures, with $D=20$ and $L=200$, from high temperature phase to different final temperatures $T$, as indicated in the figure. Color coding is same as in Fig. \ref{['fig2']}.
• Figure 5: Plots of the characteristic length scale $\ell(t)$ ($D=20, L=200$), versus time, on a log-log scale, for different $T$. The dotted line corresponds to diffusive ($\alpha=1/3$) and solid line represents inertial hydrodynamic ($\alpha=2/3$) growth laws. Inset: $\alpha_{i}$, obtained from the data in the main frame for three different temperatures, is plotted against $1/t$.