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.