With
being the velocity vector,
being the surface tension
coefficient and the
being the two-fluid interface unit normal vector.
Note that the divergence term is the curvature, as is well known from vector
calculus. This term is the most complex to acquire using SPH. According to the Adami
model
1, the SPH formulation for this term
becomes:
(2)
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 (v
2020.1) 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. 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.
Important: Enabling of surface
tension models in the simulation and requirement to resolve small droplets (for
example, ref_curv set to 1000) can be very computationally
expensive. Unless it is of utter importance to accurately resolve small droplets
(for example, Rdroplet < 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.