  Various thermodynamical phenomena have occurred with change of pressure and
temperature, volume. We can choose these parameters but not these constraints,
in order to need the thermodynamics with physical properties in the fields of
various situations. The Hele-Shaw flow is one of the classical fluid dynamics
problems in chemical engineering. Indeed, the Stokes flow is represented as the
Stokes equations which is simplified from the famous Navier-Stokes equations.
However we have often to deal with the Hele-Shaw flow with the Darcy's law.
This law is derived by the Stokes equations. The basic ideas are the executive
concepts. Our original work would like to solve the unknown relationship
between the phase field method and the vortex sheet approach to the Hele-Shaw
model.
