  Diffuse-interface theory provides a foundation for the modeling and
simulation of microstructure evolution in a very wide range of materials, and
for the tracking/capturing of dynamic interfaces between different materials on
larger scales. Smoothed particle hydrodynamics (SPH) is also widely used to
simulate fluids and solids that are subjected to large deformations and have
complex dynamic boundaries and/or interfaces, but no explicit interface
tracking/capturing is required, even when topological changes such as
fragmentation and coalescence occur, because of its Lagrangian particle nature.
Here we developed an SPH model for single-component two-phase fluids that is
based on diffuse-interface theory. In the model, the interface has a finite
thickness and a surface tension that depend on the coefficient, k, of the
gradient contribution to the Helmholtz free energy functional and the density
dependent homogeneous free energy. In this model, there is no need to locate
the surface (or interface) or to compute the curvature at and near the
interface. One- and two-dimensional SPH simulations were used to validate the
model.
