Local Pressure of Confined Fluids inside Nanoslit Pores (a Density Functional Theory Prediction)

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.