(300g) Diffuse-Interface Modeling of Phase Segregation in Amphiphilic Liquid Mixtures

Adding a surfactant to a binary mixture of oil and water can produce many different complex structures on the mesoscale. Depending on the temperature and concentration of each component, the amphiphile can self-assemble and force the oil/water mixture into a number of different equilibrium structures. This process is controlled by the competing attractive/repulsive interaction among the species and can result in, for example, lamellar, gyroid or hexagonal arrangements of the oil and water domains. Although the equilibrium behavior of such amphiphilic systems is well understood, their rheology and the dynamics of self-assembly have been investigated to a lesser extent. These properties are important not only from a fundamental standpoint, but also because of their widespread applications. In this study we are motivated by an optimization of surfactant/de-emulsifier manipulation for improving the separation behavior during extraction and refining of heavy oil mixtures. To date, several models have been proposed for amphiphilic systems, classified in terms of type of approach: molecular dynamics, time-dependent Ginzburg-Landau (diffuse-interface) approaches, and membrane approaches. While molecular dynamics simulations can be useful for investigating structural properties of adsorbed amphiphiles, these simulations are unable to access the meso- and micro-scales of the self-assembly process. We also focus on diffuse-interface models since most theories on phase-separation dynamics are constructed using a mesoscale continuum theory which relates short-scale modification of hydrodynamics to molecular interactions. Although most mesoscale simulations of amphiphilic fluids have been perfomed using lattice-gas or lattice-Boltzmann schemes, these numerical models are limited to low accuracy and, in some cases, modeling uncertainties are introduced as a result of bottom-up approaches. Such simplifications make the resulting predictions, at best, qualitative and the models unpredictive. In this study, we extend our previous work on mixing and phase separation of binary mixtures to the modeling of ternary (or quaternary) liquid mixtures as regular solutions with a Flory-Huggins and Cahn-Hilliard representation of the excess and non-local components of the free energy of mixing. In this diffuse-interface model convection and diffusion are coupled via a non-equilibrium Korteweg force expressing the tendency of the ternary (or quaternary) system to minimize its free energy. Using a hybrid compact/pseudo-spectral discretization, the governing equations are integrated in a two- or three-dimensional periodic box and in a channel for simulating gravity-driven segregation of an initially phase-separated mixture at equilibrium. Subsequently we will present a comprehensive assessment of the model by comparing the numerical predictions with experimental results.

4.192.17 on 5-11-2009-->