Towards a consistent lattice Boltzmann model for two-phase fluid

TL;DR

This paper introduces a kinetic lattice Boltzmann model for two-phase fluids that ensures thermodynamic and hydrodynamic consistency, validated through benchmarks and complex 3D simulations with large density ratios.

Contribution

It develops a lattice Boltzmann framework based on a non-ideal fluid kinetic model that recovers Navier-Stokes and Korteweg equations, ensuring thermodynamic and hydrodynamic consistency.

Findings

Thermodynamic properties like surface tension and co-existence densities are accurately captured.

The model demonstrates Galilean invariance and convergence in various benchmarks.

Validated on complex 3D cases with large density ratios, such as drop impact and coalescence.

Abstract

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