  In this work, the local pressure of fluids confined inside nanoslit pores is
predicted within the framework of the density functional theory. The
Euler-Lagrange equation in the density functional theory of statistical
mechanics is used to obtain the force balance equation which leads to a general
equation to predict the local normal component of the pressure tensor. Our
approach yields a general equation for predicting the normal pressure of
confined fluids and it satisfies the exact bulk thermodynamics equation when
the pore width approaches infinity. As two basic examples, we report the
solution of the general equation for hard-sphere (HS) and Lennard-Jones (LJ)
fluids confined between two parallel-structureless hard walls. To do so, we use
the modified fundamental measure theory (mFMT) to obtain the normal pressure
for hard-sphere confined fluid and mFMT incorporated with the Rosenfeld
perturbative DFT for the LJ fluid. Effects of different variables including
pore width, bulk density and temperature on the behavior of normal pressure are
studied and reported. Our predicted results show that in both HS and LJ cases
the confined fluids normal pressure has an oscillatory behavior and the number
of oscillations increases with bulk density and temperature. The oscillations
also become broad and smooth with pore width at a constant temperature and bulk
density. In comparison with the HS confined fluid, the values of normal
pressure for the LJ confined fluid as well as its oscillations at all distances
from the walls are less profound.
