Study of phase-field lattice Boltzmann models based on the conservative Allen-Cahn equation.

Conservative phase-field (CPF) equations based on the Allen-Cahn model for interface tracking in multiphase flows have become more popular in recent years, especially in the lattice-Boltzmann (LB) community. This is largely due to their simplicity and improved efficiency and accuracy over their Cahn-Hilliard-based counterparts. Additionally, the improved locality of the resulting LB equation (LBE) for the CPF models makes them more ideal candidates for LB simulation of multiphase flows on nonuniform grids, particularly within an adaptive-mesh refinement framework and massively parallel implementation.

Numerical simulation of dissolved air flotation using a lattice Boltzmann method.

In this paper, the behavior of a bubble and droplet rising in a system, namely, a dissolved air flotation system, is investigated under different conditions. A lattice Boltzmann model which is based on the Cahn-Hilliard equations for ternary flows is implemented. This model can handle high density and viscosity ratios, remove parasitic currents, and capture partial and total spreading conditions.

Numerical simulation of three-component multiphase flows at high density and viscosity ratios using lattice Boltzmann methods.

In this paper, we propose a multiphase lattice Boltzmann model for numerical simulation of ternary flows at high density and viscosity ratios free from spurious velocities. The proposed scheme, which is based on the phase-field modeling, employs the Cahn-Hilliard theory to track the interfaces among three different fluid components. Several benchmarks, such as the spreading of a liquid lens, binary droplets, and head-on collision of two droplets in binary- and ternary-fluid systems, are conducted to assess the reliability and accuracy of the model.