Lattice-Gas Simulations of Minority-Phase Domain Growth in Binary Immiscible and Ternary Amphiphilic Fluid

TL;DR

This study uses lattice-gas simulations to analyze the growth dynamics of minority-phase domains in binary and ternary amphiphilic fluids, revealing algebraic, nucleation, and slow growth regimes with concentration-dependent behaviors.

Contribution

First simulation of self-assembly kinetics in ternary amphiphilic fluids, demonstrating various growth regimes and phase transitions with concentration effects.

Findings

Binary fluid domain growth follows algebraic scaling with an exponent ~0.45.

Ternary fluid shows a transition from algebraic to logarithmic growth with increasing surfactant.

Phase transition from droplet to sponge phase observed with varying surfactant concentration.

Abstract

We investigate the growth kinetics of binary immiscible fluids and emulsions in two dimensions using a hydrodynamic lattice-gas model. We perform off-critical quenches in the binary fluid case and find that the domain size within the minority phase grows algebraically with time in accordance with theoretical predictions. In the late time regime we find a growth exponent n = 0.45 over a wide range of concentrations, in good agreement with other simluations. In the early time regime we find no universal growth exponent but a strong dependence on the concentration of the minority phase. In the ternary amphiphilic fluid case the kinetics of self assembly of the droplet phase are studied for the first time. At low surfactant concentrations, we find that, after an early algebraic growth, a nucleation regime dominates the late-time kinetics, which is enhanced by an increasing concentration of surfactant. With a further increase in the concentration of surfactant, we see a crossover to logarithmically slow growth, and finally saturation of the oil droplets, which we fit phenomenologically to a stretched exponential function. Finally, the transition between the droplet and the sponge phase is studied.