Towards a consistent lattice Boltzmann model for two-phase fluids

We revisit the construction of discrete kinetic models for single-component isothermal two-phase flows. Starting from a model non-ideal fluid, we show that, under conventional scaling, Navier–Stokes equations with equation state are recovered in hydrodynamic limit. A scaling based on smallness velocity increments is then introduced, which recovers full Navier–Stokes–Korteweg equations. The proposed realized standard lattice and validated variety benchmarks. Through detailed study thermodynamic properties including co-existence densities, surface tension, Tolman length sound speed, consistency, well-posedness convergence model. Furthermore, consistency demonstrated by verification Galilean invariance dissipation rate shear normal modes visco-capillary coupling effects. Finally, dynamic test cases three dimensions complex geometries large density ratios such as drop impact textured surfaces mercury drops coalescence.