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

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 available literature, namely, stress tensor form (STF), chemical potential (CPF), pressure form, and continuum surface (CSF) summarized theoretical analyzed. A systematic study all is made by a series benchmark problems, including stationary droplet, two merging droplets, Capillary wave, rising bubble drop deformation shear flow. Numerical results show that CPF good choice small problems while STF preferred dynamical both CSF presents better stability terms Peclet number.