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Condensation and evaporation transitions in deep capillary grooves

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.