On the importance of zero-resultant correction of surface tension in flows with numerous small interfacial structures

In this study, we propose a strategy to ensure the conservative properties of surface tension within the continuum surface force framework. The liquid--gas interface is first identified using a connected component labeling algorithm, and surface tension is computed on computational cells with assigned labels. To enforce a zero-resultant surface tension over a closed interface, an algebraic curvature-weighted correction is applied. The proposed strategy is verified using a static bubble case, a translating bubble case, and an oscillating elliptical bubble case. The static bubble case demonstrates that the correction does not violate the well-balanced property, while the translating and oscillating bubble cases show improved accuracy in spurious velocity and bubble position after correction. Further validation is conducted in turbulent flows with numerous small bubbles. The results confirm momentum conservation after correction, whereas the conventional continuum surface force method leads to a physically inaccurate momentum balance.