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Capillary Contact Angle in a Completely Wet Groove

We consider the phase equilibria of a fluid confined in a deep capillary groove of width $L$ with identical side walls and a bottom made of a different material. All walls are completely wet by the liquid. Using density functional theory and interfacial models, we show that the meniscus separating liquid and gas phases at two phase capillary-coexistence meets the bottom capped end of the groove at a capillary contact angle $θ^{\rm cap}(L)$ which depends on the difference between the Hamaker constants. If the bottom wall has a weaker wall-fluid attraction than the side walls, then $θ^{\rm cap}>0$ even though all the isolated walls are themselves completely wet. This alters the capillary condensation transition which is now first-order; this would be continuous in a capped capillary made wholly of either type of material. We show that the capillary contact angle $θ^{\rm cap}(L)$ vanishes in two limits, corresponding to different capillary wetting transitions. These occur as the width i) becomes macroscopically large, and ii) is reduced to a microscopic value determined by the difference in Hamaker constants. This second wetting transition is characterised by large scale fluctuations and essential critical singularities arising from marginal interfacial interactions.