According to Eqn (10), the state of a multiple-phase fluid will evolve
in the direction of decreasing total chemical potential, which
in turn relies on the Helmholtz free energy. The Helmholtz free energy
is an internal energy of the material that determines the final
stable state. By properly setting different forms of Helmholtz free
energy equations, the NSCH model can produce various energydriven
visual effects. For cases containing less than 3 phases, proper
energy functions can be designed with the help of energy plots or
the so-called Gibbs triangle. We will demonstrate such designation
method in this section.
We first begin with two-phase fluids. In this case the energy plot can
be represented by an energy-curve plot relying on the mass fraction
of one of the two phases, which is between 0 and 1. To capture
rich visual results in a two-phase system, we use the following free
energy equation unless explicitly mentioned: