  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.
