The order of condensation in capillary grooves

We consider capillary condensation in a deep groove of width L. The transition occurs at a pressure p_co(L) described, for large widths, by the Kelvin equation p_sat - p_co(L) = 2σcosθ/L, where θ is the contact angle at the side walls and σ is the surface tension. The order of the transition is determined by the contact angle of the capped end θ_cap it is continuous if the liquid completely wets the cap, and first-order otherwise. When the transition is first-order, corner menisci at the bottom of the capillary lead to a pronounced metastability, determined by a complementary Kelvin equation Δp(L) = 2σsinθ_cap/L. On approaching the wetting temperature of the capillary cap, the corner menisci merge and a single meniscus unbinds from the bottom of the groove. Finite-size scaling shifts, crossover behaviour and critical singularities are determined at mean-field level and beyond. Numerical and experimental results showing the continuous nature of condensation for θ_cap = 0 and the influence of corner menisci on adsorption isotherms are presented.