Towards a consistent lattice Boltzmann model for two-phase fluid

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.

References in corpus (11)

• Pancake bouncing on superhydrophobic surfaces
• Lattice Boltzmann methods for multiphase flow and phase-change heat transfer
• Coalescence of Liquid Drops
• Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model
• Generalized Lattice Boltzmann Method with multi-range pseudo-potential
• Mesoscopic modeling of a two-phase flow in the presence of boundaries: the Contact Angle
• Contact angles in the pseudopotential lattice Boltzmann modeling of wetting
• Drops bouncing off macro-textured superhydrophobic surfaces
• Continuum Free-Energy formulation for a class of Lattice Boltzmann multiphase models
• Extended Lattice Boltzmann Model for Gas Dynamics
• A Mesoscale Perspective on the Tolman Length