# The Order of Condensation in Capillary Grooves

C. Rascón, A.O. Parry, R. Nurnberg, A. Pozzato, M. Tormen, L. Bruschi, G. Mistura, J. Phys.: Condens. Matter 25.192101 (2013)

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 $p_{sat}-p_{co}(L)=2\sigma\cos\theta/L$, where $\theta$ is the contact angle at the side walls and $\sigma$ is the surface tension. The order of the transition is determined by the contact angle of the capped end $\theta_ {cap}$; 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 $\Delta p(L)=2\sigma\sin\theta_{cap}/L$. 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, cross-over behaviour and critical singularities are determined at mean-field level and beyond. Numerical and experimental results showing the continuous nature of
condensation for $\theta_{cap}=0$ and the influence of corner menisci on adsorption isotherms are presented.