Comparison of Surface Tension Models in the Navier–Stokes Equation Coupled With a Conservative Phase Field Model

ABSTRACT Surface tension matters in the simulation of two‐phase flow. It is formulated mostly via the continuum surface force model or the surface‐energy‐based model. This paper compares the performance of three surface tension models, two based on the continuum surface force model and one on the other, in the Navier–Stokes equation coupled with the conservative Allen‐Cahn/phase field model. The numerical model was solved using an explicit finite difference method on a half‐staggered grid. A mesh independence study was conducted to select the appropriate mesh size. The surface tension models were compared in a couple of drop impacts, including a vigorous rebound and a weak rebound. It was found that the surface‐energy‐based model conserves mass the best. One of the continuum surface force models can capture fine structures like capillary waves on a drop impacting a solid surface. However, the continuum surface force models suffer from much more severe mass loss. Moreover, a theoretical analysis on mass conservation was conducted, and guidance for conserving mass was proposed.