  Realistic fluid-solid interaction potentials are essential in description of
confined fluids especially in the case of geometric heterogeneous surfaces.
Correlated random field is considered as a model of random surface with high
geometric roughness. We provide the general theory of effective coarse-grained
fluid-solid potential by proper averaging of the free energy of fluid molecules
which interact with the solid media. This procedure is largely based on the
theory of random processes. We apply first passage time probability problem and
assume the local Markov properties of random surfaces. General expression of
effective fluid-solid potential is obtained. In the case of small surface
irregularities analytical approximation for effective potential is proposed.
Both amorphous materials with large surface roughness and crystalline solids
with several types of fcc lattices are considered. It is shown that the wider
the lattice spacing in terms of molecular diameter of the fluid, the more
obtained potentials differ from classical ones. A comparison with published
Monte-Carlo simulations shows good qualitative agreement with the theory
predictions. The work provides a promising approach to explore how the random
geometric heterogeneity affects on thermodynamic properties of the fluids.
