Using the unified approach within the classical density functional theory, we have calculated the equilibrium local density profiles, the components of the pressure tensor, and the thicknesses of thin flat and spherical interlayers between a lyophilic or lyophobic solid surface and a gas or liquid phase, respectively.

These interlayers are not isotropic, and there is a disjoining pressure in them. Dependences of this pressure on the interlayer thickness have been found. In the presence of a capillary pressure inside the interlayers, the disjoining pressure counteracts it and leads to the appearance of stable long-living droplets around lyophilic solid particles and stable long-living bubbles around lyophobic particles. It has been shown that the mechanical and thermodynamic definitions of the disjoining pressure in a spherical interlayer agree with each other. In contrast to case of liquid films on lyophilic particles, the disjoining pressure in stable spherical vapor layers around a nanosized lyophobic solid particle is found to be greater than in flat vapor layers near a planar lyophobic substrate. Increasing lyophobicity provides that the disjoining pressure isotherms change from non-monotonic to monotonic functions of the vapor layer thickness.