On the formulations of interfacial force in the phase-field-based lattice Boltzmann method

TL;DR

This paper compares four formulations of interfacial force in phase-field-based lattice Boltzmann methods, analyzing their numerical performance across various two-phase flow benchmarks to guide formulation choice.

Contribution

It systematically evaluates and compares four interfacial force formulations, providing insights into their numerical stability and suitability for different flow problems.

Findings

CPF is suitable for small surface deformations

STF is preferred for dynamic problems

Both STF and CSF show good numerical stability

Abstract

Different formulations of interfacial force have been adopted in phase-field-based lattice Boltzmann method for two-phase flows. Although they are identical mathematically, their numerical performances may be different due to truncation errors in the discretization. In this paper, four-type formulations of interfacial force available in the literature, namely stress tensor form (STF), chemical potential form (CPF), pressure form (PF) and continuum surface force (CSF) form, are compared and discussed. A series of benchmark problems, including stationary droplet, two merging droplets, Capillary wave, rising bubble and drop deformation in shear flow, are simulated. Numerical results show that CPF is a good choice for small surface deformation problems while STF is preferred for dynamical problems, both STF and CSF demonstrate good numerical stability.