Hard disks in confinement: the thermodynamic effects of container shape

Surface thermodynamics has a long rich history with subtleties that still drive research over a century after the foundational work of Gibbs. In recent work, we have examined, using molecular simulation, the role of surface curvature on the surface free energy, $\gamma$, of fluids at convex bounding walls. Here, we extend this work to examine the surface thermodynamics of fluids under confinement by closed curved walls. We present simulation results that demonstrate the dependence of $\gamma$ on the bounding curvature in 2-dimensions, using a model hard-disk fluid contained within circular hard walls of varying size (and curvature). These results are compared to our recent work for the hard-disk fluid at convex circular walls. We also compare to the theoretical predictions of Morphometric Thermodynamics (MT), which gives an expression for the surface free energy that is a linear function of the mean curvature of the surface. While MT is formulated as a theory restricted to convex wall geometries, its applicability to convex surfaces, such as those considered here has never been tested.