Fluid in a closed narrow slit

The behavior of a fluid inside a closed narrow slit between solid walls is examined on the basis of the density functional theory. It is shown that the constraint of constant number of molecules leads to interesting effects which are absent when the slit is open and in contact with a reservoir. If the slit walls are identical, the density profiles at low temperatures or at high average densities rhoav of the fluid molecules in the slit have a sharp maximum in the middle of the slit, the value of the density at maximum being comparable to that of a liquid. The density of fluid at the walls is in this case comparable to the density of a vapor phase. At high temperatures or at low rhoav the fluid density in the middle of the slit is of the same order of magnitude as at the walls. For nonidentical walls the density maximum is shifted towards the wall with a stronger wall-fluid interaction. The transition between the two types (with and without the sharp maximum) of density profiles with the change of temperature in the slit occurs in a narrow range of temperatures, this range being larger for narrower slits. The pressures which the fluid exerts on the walls as well as the forces per unit area arising due to stresses in the sidewalls of the system can decrease with increasing rhoav. Such a behavior is not possible for homogeneous systems and can be explained by analyzing the fluid density at the walls when rhoav increases. The normal and transversal components of the pressure tensor were calculated as functions of the distance from the wall using the equation of hydrostatic equilibrium and direct calculation of the forces between molecules, respectively. The normal component decreases with increasing distance near the wall in contrast to the normal component near the liquid-vapor interface reported previously in the literature. The behavior of the transverse component does not depend on the fluid-solid interaction and is comparable to that for a liquid-vapor interface.