  We study the order of capillary condensation and evaporation transitions of a
simple fluid adsorbed in a deep capillary groove using a fundamental measure
density functional theory (DFT). The walls of the capillary interact with the
fluid particles via long-ranged, dispersion, forces while the fluid-fluid
interaction is modelled as a truncated Lennard-Jones-like potential. We find
that below the wetting temperature $T_w$ condensation is first-order and
evaporation is continuous with the metastability of the condensation being well
described by the complementary Kelvin equation. In contrast above $T_w$ both
phase transitions are continuous and their critical singularities are
determined. In addition we show that for the evaporation transition above $T_w$
there is an elegant mapping, or covariance, with the complete wetting
transition occurring at a planar wall. Our numerical DFT studies are
complemented by analytical slab model calculations which explain how the
asymmetry between condensation and evaporation arises out of the combination of
long-ranged forces and substrate geometry.
