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We propose a kinetic framework for single-component non-ideal isothermalflows. Starting from a kinetic model for a non-ideal fluid, we show that underconventional scaling the Navier-Stokes equations with a non-ideal equation ofstate are recovered in the hydrodynamic limit. A scaling based on the smallnessof velocity increments is then introduced, which recovers the fullNavier-Stokes-Korteweg equations. The proposed model is realized on a standardlattice and validated on a variety of benchmarks. Through a detailed study ofthermodynamic properties including co-existence densities, surface tension,Tolman length and sound speed, we show thermodynamic consistency,well-posedness and convergence of the proposed model. Furthermore, hydrodynamicconsistency is demonstrated by verification of Galilean invariance of thedissipation rate of shear and normal modes and the study of visco-capillarycoupling effects. Finally, the model is validated on dynamic test cases inthree dimensions with complex geometries and large density ratios such as dropimpact on textured surfaces and mercury drops coalescence.

Towards a consistent lattice Boltzmann model for two-phase fluid