  In this two-part study we investigate the phase behaviour of a fluid
spatially confined in a semi-infinite rectangular pore formed by three
orthogonal walls and connected to a reservoir maintaining constant values of
pressure and temperature in the fluid. Far from the capping wall this
prototypical two-dimensional system reduces to a one-dimensional slit pore.
However, the broken translational symmetry leads to a wetting behavior
strikingly different from that of a slit pore. Using a realistic model of an
atomic fluid with long-ranged Lennard-Jones fluid-fluid and fluid-substrate
interactions, we present for the first time detailed computations of full phase
diagrams of two-dimensional capped capillaries. Our analysis is based on the
statistical mechanics of fluids, in particular density functional theory. We
show the existence of capillary wetting temperature, which is a property of the
pore, and relatively to the fluid temperature determines whether capillary
condensation is a first-order or a continuous phase transition. We also report
for the first time a first-order capillary wetting transition, which can be
preceded by a first-order capillary prewetting. A full parametric study is
undertaken and we support our findings with exhaustive examples of density
profiles, adsorption and free energy isotherms, as well as full phase diagrams.
