Phase-field-theory-based lattice Boltzmann equation method for N immiscible incompressible fluids.

From the phase field theory, we develop a lattice Boltzmann equation (LBE) method for N (N≥2) immiscible incompressible fluids, and the Cahn-Hilliard equation, which could capture the interfaces between different phases, is also solved by LBE for an N-phase system. In this model, the interface force of N immiscible incompressible fluids is incorporated by chemical potential form, and the fluid-fluid surface tensions could be directly calculated and independently tuned. Numerical simulations including two stationary droplets, spreading of a liquid lens with and without gravity and two immiscible liquid lenses, and phase separation are conducted to validate the present LBE, and numerical results show that the predictions by LBE agree well with the analytical solutions and other numerical results.