Phase-field modeling droplet dynamics with soluble surfactants

Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence

Metastable liquid lamellar structures in binary and ternary mixtures of Lennard-Jones fluids

We have carried out extensive equilibrium molecular dynamics (MD) simulations to investigate the Liquid-Vapor coexistence in partially miscible binary and ternary mixtures of Lennard-Jones (LJ) fluids. We have studied in detail the time evolution of the density profiles and the interfacial properties in a temperature region of the phase diagram where the condensed phase is demixed. The composition of the mixtures are fixed, 50% for the binary mixture and 33.33% for the ternary mixture. The results of the simulations clearly indicate that in the range of temperatures $78 < T < 102 ^{\rm o}$K, --in the scale of argon-- the system evolves towards a metastable alternated liquid-liquid lamellar state in coexistence with its vapor phase. These states can be achieved if the initial configuration is fully disordered, that is, when the particles of the fluids are randomly placed on the sites of an FCC crystal or the system is completely mixed. As temperature decreases these states become very well defined and more stables in time. We find that below $90 ^{\rm o}$K, the alternated liquid-liquid lamellar state remains alive for 80 ns, in the scale of argon, the longest simulation we have carried out. Nonetheless, we believe that in this temperature region these states will be alive for even much longer times.Comment: 18 Latex-RevTex pages including 12 encapsulated postscript figures. Figures with better resolution available upon request. Accepted for publication in Phys. Rev. E Dec. 1st issu

Structural transitions and arrest of domain growth in sheared binary immiscible fluids and microemulsions

We investigate spinodal decomposition and structuring effects in binary immiscible and ternary amphiphilic fluid mixtures under shear by means of three dimensional lattice Boltzmann simulations. We show that the growth of individual fluid domains can be arrested by adding surfactant to the system, thus forming a bicontinous microemulsion. We demonstrate that the maximum domain size and the time of arrest depend linearly on the concentration of amphiphile molecules. In addition, we find that for a well defined threshold value of amphiphile concentration, the maximum domain size and time of complete arrest do not change. For systems under constant and oscillatory shear we analyze domain growth rates in directions parallel and perpendicular to the applied shear. We find a structural transition from a sponge to a lamellar phase by applying a constant shear and the occurrence of tubular structures under oscillatory shear. The size of the resulting lamellae and tubes depends strongly on the amphiphile concentration, shear rate and shear frequency.Comment: 12 pages, 11 figure

Numerical approximation of a phase-field surfactant model with fluid flow

Modelling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of two Cahn-Hilliard-type equations and incompressible Navier-Stokes equation. With the introduction of two auxiliary variables, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. By certain subtle explicit-implicit treatments to stress and convective terms, we construct first and second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving only a sequence of linear elliptic equations, and computations of phase-field variables, velocity and pressure are fully decoupled. We further establish a rigorous proof of unconditional energy stability for the first-order scheme. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow, where the increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence

Effect of shear on droplets in a binary mixture

In this article we use a lattice-Boltzmann simulation to examine the effects of shear flow on a equilibrium droplet in a phase separated binary mixture. We find that large drops break up as the shear is increased but small drops dissolve. We also show how the tip-streaming, observed for deformed drops, leads to a state of dynamic equilibrium.Comment: 10 pages, LaTex, to appear in International Journal of Physics

Collective behavior of colloids due to critical Casimir interactions

If colloidal solute particles are suspended in a solvent close to its critical point, they act as cavities in a fluctuating medium and thereby restrict and modify the fluctuation spectrum in a way which depends on their relative configuration. As a result effective, so-called critical Casimir forces (CCFs) emerge between the colloids. The range and the amplitude of CCFs depend sensitively on the temperature and the composition of the solvent as well as on the boundary conditions of the order parameter of the solvent at the particle surfaces. These remarkable, moreover universal features of the CCFs provide the possibility for an active control over the assembly of colloids. This has triggered a recent surge of experimental and theoretical interest in these phenomena. We present an overview of current research activities in this area. Various experiments demonstrate the occurrence of thermally reversible self-assembly or aggregation or even equilibrium phase transitions of colloids in the mixed phase below the lower consolute points of binary solvents. We discuss the status of the theoretical description of these phenomena, in particular the validity of a description in terms of effective, one-component colloidal systems and the necessity of a full treatment of a ternary solvent-colloid mixture. We suggest perspectives on the directions towards which future research in this field might develop.Comment: review, 88 pages, 19 figure

Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: lattice-Boltzmann simulations

By means of a three-dimensional amphiphilic lattice-Boltzmann model with short-range interactions for the description of ternary amphiphilic fluids, we study how the phase separation kinetics of a symmetric binary immiscible fluid is altered by the presence of the amphiphilic species. We find that a gradual increase in amphiphile concentration slows down domain growth, initially from algebraic, to logarithmic temporal dependence, and, at higher concentrations, from logarithmic to stretched-exponential form. In growth-arrested stretched-exponential regimes, at late times we observe the self-assembly of sponge mesophases and gyroid liquid crystalline cubic mesophases, hence confirming that (a) amphiphile-amphiphile interactions need not be long-ranged in order for periodically modulated structures to arise in a dynamics of competing interactions, and (b) a chemically-specific model of the amphiphile is not required for the self-assembly of cubic mesophases, contradicting claims in the literature. We also observe a structural order-disorder transition between sponge and gyroid phases driven by amphiphile concentration alone or, independently, by the amphiphile-amphiphile and the amphiphile-binary fluid coupling parameters. For the growth-arrested mesophases, we also observe temporal oscillations in the structure function at all length scales; most of the wavenumbers show slow decay, and long-term stationarity or growth for the others. We ascribe this behaviour to a combination of complex amphiphile dynamics leading to Marangoni flows.Comment: 16 pages, 13 figures. Accepted for publication in Phys. Rev. E. (Replaced for the latest version, in press.) Higher-quality figures can be sent upon reques