# Surface Tension - Multiphase

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

Analytically, the surface tension term in the momentum equation can be expressed as:

- $i$ and $j$ indices
- Stand for owner and neighboring particles respectively
- $ij$ index
- Difference between the respective variables of particle $i$ and particle $j$
- $d$
- Stands for the number of dimensions of the problem
- $\nabla W$
- Gradient of the kernel
- r
- Position of the vector
- $V$
- Particle volume

The surface tension model has only four options required for the setup. First, and
most important, is to turn the surface tension model on. In the Simulation
parameters, the option `surften_model` specifies the selected
surface tension model. The current version (v2024) has three
options: NONE, SINGLE_PHASE or
ADAMI. For the SINGLE_PHASE surface tension
model, refer to Surface Tension - Single Phase and Adhesion.

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

`surf_ten`[N/m] for the two-phase interaction, for example if you have an oil phase and an air phase, you would 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, it is recommended to use a 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.

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.

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