Drumhead model of

Recent work has demonstrated novel fluid interfacial behaviour occurring at filling or wedge-wetting transitions in two- and three-dimensional systems. In particular, in two dimensions (2D) studies of filling in shallow wedges, for both pure and impure systems, reveal simple covariance relations which relate criticality at filling to strong-fluctuation regime wetting and restrict the allowed critical singularities. Here we introduce a drumhead interfacial model of filling in acute wedges which can be adapted to include an orientation-dependent surface tension. We calculate the excess wedge free energy and scaling form of the mid-point height probability distribution function (PDF) and demonstrate that the covariance relations are the same as found in the shallow wedge approximation. Connections with exact Ising model results and a bubble model interpretation of the interfacial height PDF at wetting are made