# Multiphase Surface Tension

nanoFluidX implementation of the multiphase surface tension model
heavily relies on the work of Adami et al. ^{1}

^{1}, the SPH formulation for this term becomes:

Where the indices $i$ and $j$ stand for so called ‘owner’ and ‘neighboring’ particles respectively, and the $ij$ index is a difference between the respective variables of particle $i$ and particle $j$ . The $d$ stands for the number of dimensions of the problem, the $\nabla W$ is the gradient of the kernel, r is the position vector and $V$ is the particle volume.

`surften_model`specifies the selected surface tension model. The current version (v2021) has three options and those are: NONE, SINGLE_PHASE or ADAMI. For the SINGLE_PHASE surface tension model, refer to the section on Adhesion Model and Single Phase Surface Tension Models. The second important parameter is the reference curvature

`ref_curv`[1/m] in the Domain parameters, which is the largest expected surface curvature. Third, in the Phase parameters,we specify the surface tension coefficient

`surf_ten`[N/m] for the two-phase interaction, e.g. if we have an oil phase and an air phase, we specify the same surface tension coefficient for both phases. If surface tension model is set to ADAMI or SINGLE_PHASE, the reference curvature, and surface tension coefficient definitions are mandatory.

`ref_curv`set to 1000) can be very computationally expensive. Unless it is of utter importance to accurately resolve small droplets (for example, R

_{droplet}< 1 cm), we recommend using relatively high

`ref_curv`value of ≈ 20. This will make runs much faster, while still including surface tension effects for surface fluid structures which are of the approximate size of 5 cm.

^{1}S. Adami, X. Hu und N. Adams, „A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation,“

*Journal of Computational Physics,*Nr. 229, pp. 5011-5021, 2010.

^{2}M. P. Allen und D. J. Tildesley, Computer simulation of liquids, New York: Oxford University Press, 1989.