Lattice-gas simulations of minority-phase domain growth in binary immiscible and ternary amphiphilic fluids

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 simulations. 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.

Numerical simulations of phase separation dynamics in a water–oil–surfactant system

“…We observe a slight decrease in the exponent, R(t) ∼ t 1/3.5 . This finding is consistent with previous results [10,11]. For example, previous results using a lattice gas model have shown that the surfactant slows down the growth [11].…”

Lattice-Gas Simulations of Ternary Amphiphilic Fluid Flow in Porous Media

“…In this report, as in previous studies [1][2][3][4] β = 1.0 and the coupling constants are given the values α = 1.0 µ = 0.001 ǫ = 8.0 ζ = 0.005, strongly encouraging surfactant molecules to accumulate at oil-water interfaces while maintaining the normal oil-water immiscible behavior. Different porous media have been constructed.…”

“…The lattice gas automaton (LGA) model introduced by Boghosian, Coveney and Emerton [1] has been used to investigate a variety of amphiphilic phenomena including the growth kinetics of binary immiscible fluid and ternary microemulsion systems [2,3], the effect of shear on ternary systems [4] and self-reproducing micelles [5]. In this article we describe the developments that have been made to allow invasive flow within a porous medium to be studied using this model.…”

A lattice Boltzmann model of ternary fluid mixtures

“…This is a difficult problem because of the interplay between several relevant transport mechanisms, the diffusion of the constituent components and their hydrodynamic flow. To date models of amphiphilic rheology which treat hydrodynamic effects include time-dependent Ginzburg-Landau approaches [3,4], molecular dynamics[5] and a lattice gas cellular automaton scheme based on microscopic interactions [6,7].The aim of this Letter is to introduce an alternative numerical scheme that can model the dynamics of amphiphilic systems in such a way that diffusive and hydrodynamic mechanisms are included. The numerical approach that we use is lattice Boltzmann simulations which have emerged as a useful tool to study the dynamics of complex fluids [8].…”

“…This is a difficult problem because of the interplay between several relevant transport mechanisms, the diffusion of the constituent components and their hydrodynamic flow. To date models of amphiphilic rheology which treat hydrodynamic effects include time-dependent Ginzburg-Landau approaches [3,4], molecular dynamics[5] and a lattice gas cellular automaton scheme based on microscopic interactions [6,7].…”