Analysis of Ginzburg-Landau-type models of surfactant-assisted liquid phase separation

Two-component lattice Boltzmann model for solute transport in bubbly flows

A free energy lattice Boltzmann model has been developed to describe a binary system consisting of a nonideal solvent and a gaseous ideal solute. A free energy functional to describe this mixture has been derived, and it is used to determine the driving forces for two lattice Boltzmann equations, one for each component. The well-balanced lattice Boltzmann method is used to avoid discretization errors, which allows correct thermodynamic equilibrium to be achieved for both components as well as high density ratios. In this model, the distribution of the solute between the liquid and vapor phases of the solvent follows Henry's law due to the contributions of the two components to the free energy density. The momenta of the two components are coupled through the use of a mixture velocity in the equilibrium distributions of both components. The model also includes surface tension due to gradients of the solvent density and diffusion due to an added mobility term. The effects of model parameters on phase composition, surface tension, and the rate of solute transport are characterized, with examples of static gas bubbles and flat interfaces demonstrated. Mass transfer of the soluble component in the liquid phase of the nonideal component is characterized, and an equation for the solute diffusion coefficient is provided.

Phase-field theory of multicomponent incompressible Cahn-Hilliard liquids

In this paper, a generalization of the Cahn-Hilliard theory of binary liquids is presented for multicomponent incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion-type dynamics is derived on the basis of the Lagrange multiplier formalism. Next, a generalization of the binary Cahn-Hilliard free-energy functional is presented for an arbitrary number of components, offering the utilization of independent pairwise equilibrium interfacial properties. We show that the equilibrium two-component interfaces minimize the functional, and we demonstrate that the energy penalization for multicomponent states increases strictly monotonously as a function of the number of components being present. We validate the model via equilibrium contact angle calculations in ternary and quaternary (four-component) systems. Simulations addressing liquid-flow-assisted spinodal decomposition in these systems are also presented.

A phase-field approach to nonequilibrium phase transformations in elastic solids via an intermediate phase (melt) allowing for interface stresses

A phase-field approach for phase transformations between three different phases at nonequilibrium temperatures with mechanics and interfacial stresses is developed.

Phase field modelling of spinodal decomposition in the oil/water/asphaltene system

In this paper the quantitative applicability of van der Sman/van der Graaf type Ginzburg–Landau theories of surfactant assisted phase separation [van der Smanet al.,Rheol. Acta, 2006,46, 3] is studied for real systems displaying high surfactant concentrations at the liquid–liquid interface.