  In this report, an analytic model to predict phase transitions of confined
fluids in nano systems is presented and it is used to predict the behavior of
the confined fluid in nanotubes and nanoslits. In our approach besides
including a third degree of freedom due to wall effect to define the state of
the system, the tensorial character for pressure is considered. Using the
perturbation theory of statistical mechanics it is shown that the van der Waals
equation of state is equally valid for small as well as large systems. The
model proposed is shown to predict the liquid-vapor phase transition as well as
the critical point in any size confined fluid systems. It is also shown that
the critical temperature increases with the size of the nano system and finally
it reaches the macroscopic critical temperature value as the diameter of the
nanotube (or width of the nanoslit) approaches infinity. The proposed model can
also demonstrate the existence of the local density and phase fragmentations
during phase transitions in a confined nano system.
