A lattice Boltzmann model of ternary fluid mixtures

Abstract

Abstract. -A lattice Boltzmann model is introduced which simulates oil-water-surfactant mixtures. The model is based on a Ginzburg-Landau free energy with two scalar order parameters. Diffusive and hydrodynamic transport is included. Results are presented showing how the surfactant diffuses to the oil-water interfaces thus lowering the surface tension and leading to spontaneous emulsification. The rate of emulsification depends on the viscosity of the ternary fluid.Introduction. -The addition of surfactant to a binary mixture of oil and water can produce many different complex structures on a mesoscopic length scale. The surfactant molecules move to the interface and lower the oil-water interfacial tension. This can result in, for example, lamellar, micellar, microemulsion or hexagonal arrangements of the oil and water domains [1,2].The equilibrium behaviour of such amphiphilic systems is well understood. However the dynamics of the self-assembly of the mesoscale phases and their rheology are less well investigated. 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]. We base our approach on that described by Orlandini et. al. [9,10] where the correct equilibrium of the fluid is imposed by choosing an appropriate free energy and including it in such a way that the fluid spontaneously reaches the equilibrium described by its minimum.Previous lattice Boltzmann models of amphiphilic systems have been based on a single order

Lattice-Boltzmann model for interacting amphiphilic fluids

“…We found that these instabilities occur when the forcing terms cause the right-hand side of Eqs. (14) and (17) to become negative and are caused by a combination of the mean-field treatment of interparticle interactions and the restriction of the lattice-Boltzmann scheme to low Mach numbers. With these considerations in mind, and after a restricted search in the parameter space of the model we arrived at the following set of canonical parameters which, unless stated otherwise, are used throughout our simulations (the timestep ∆t is set to 1 throughout) g σσ = 0, g σσ = 0.03, g σs = −0.01, g ss = 0.01, τ σ = τ s = 1, τ d = 2, m σ = 1, m s = 2, d 0 = 1 and β = 10.…”

Simulation of multiphase flows with variable surface tension using the Lattice Boltzmann method

“…At t = 2000 (not pictured) the pressure difference has dropped to 0.0107 (we recall that ∆p = 0.0122 at t = 0). A major difference between the chromodynamic method and the Shan-Chen method is that the former scheme enforces surface tension and phase separation in separate operations, (7) and (8), while these effects are intimately coupled together in the Shan-Chen method through the forcing terms in (9). Therefore, in figure 2 we see diffusion occurring between the red and blue phases once the surfactant is applied.…”

“…In order to simulate the effects of microemulsions, lattice Boltzmann models with amphiphile surfactants are largely based on the free energy model of Orlandini et al [7], see for example references [8][9][10][11]. The model used here is simpler, since the purpose is primarily to investigate the deformative effects of surface tension rather than the effects on the interface structure.…”

Large-scale lattice Boltzmann simulations of complex fluids: advances through the advent of computational Grids

“…Some of these phases have long-range order, yet remain able to flow, and are called liquid crystal mesophases. Of particular interest to us are those with cubic symmetry, whose properties have been studied experimentally (Seddon & Templer 1993;Seddon & Templer 1995;Czeslik & Winter 2002) in lipid-water mixtures (Seddon & Templer 1995), diblock copolymers (Shefelbine et al 1999), and in many biological systems (Landh 1995).…”