  In this work, the Minkowski functionals are used as a framework to study how
morphology (i.e. the shape of a structure) and topology (i.e. how different
structures are connected) influence wall adsorption and capillary condensation
under tight confinement. Numerical simulations based on classical density
functional theory (DFT) are run for a wide variety of geometries using both
hard-sphere and Lennard-Jones fluids. These DFT computations are compared to
results obtained using the Minkowski functionals. It is found that the
Minkowski functionals can provide a good description of the behavior of
Lennard-Jones fluids down to small system sizes. In addition, through
decomposition of the free energy, the Minkowski functionals provide a good
framework to better understand what are the dominant contributions to the
physics of a system. Lastly, while studying the phase envelope shift as a
function of the Minkowski functionals it is found that topology has a different
effect depending on whether the phase transition under consideration is a
first- or a second-order transition.
