  We formulate a straightforward scheme of statistical mechanics for
inhomogeneous systems that includes the virial series in powers of the activity
for the grand free energy and density distributions. There, cluster integrals
formulated for inhomogeneous systems play a main role. We center on second
order terms that were analyzed in the case of hard-wall confinement, focusing
in planar, spherical and cylindrical walls. Further analysis was devoted to the
Lennard-Jones system and its generalization the 2k-k potential. For this
interaction potentials the second cluster integral was evaluated analytically.
We obtained the fluid-substrate surface tension at second order for the planar,
spherical and cylindrical confinement. Spherical and cylindrical cases were
analyzed using a series expansion in the radius including higher order terms.
We detected a $\ln R^{-1}/R^{2}$ dependence of the surface tension for the
standard Lennard-Jones system confined by spherical and cylindrical walls, no
matter if particles are inside or outside of the hard-walls. The analysis was
extended to bending and Gaussian curvatures, where exact expressions were also
obtained.
