# Nonlocal models for multiphase flow

We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like functionadded to the Navier-Stokes momentum conservation equation. The non-local surface tension model has an inherent length scale that can be tuned to model both macro-scale and nano-scale fluids.

The non-local surface tension offers computational advantages over local surface tension models, because it relies on computing integrals instead of approximating a smoothed Dirac delta function, which can be present difficulties when the interface width is changing.

## Relevant publications

Howard, Amanda A., & Tartakovsky, Alexandre M. (2021). A conservative level set method for N-phase flows with a free-energy-based surface tension model. Journal of Computational Physics, 426, 109955.

Howard, Amanda A., & Tartakovsky, Alexandre M. (2020). Non-local model for surface tension in fluid-fluid simulations. Journal of Computational Physics, 109732.

Howard, Amanda A., Zhou, Yongcheng, & Tartakovsky, Alexandre M. (2019). Analytical steady-state solutions for pressure with a multiscale non-local model for two-fluid systems. arXiv:1905.08052.