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

Abstract

Different formulations of interfacial force have been adopted in the existing 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 at discrete level. In this article, four-type formulations of interfacial force available in the literature, namely, stress tensor form (STF), chemical potential form (CPF), pressure form, and continuum surface force (CSF) form, are summarized and theoretical analyzed. A systematic study of the performances of all formulations is made by a series of benchmark problems, including stationary droplet, two merging droplets, Capillary wave, rising bubble and drop deformation in shear flow. 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 presents better numerical stability in terms of Peclet number.