The order of filling transitions in acute wedges

Using a square-gradient density functional model we test the prediction that the filling transition for a fluid in a wedge geometry changes from continuous to first-order as the wedge becomes more acute. Our numerical findings confirm such a change of order, but the value of the tilt angle at which it occurs, α* ≈ 45°, is considerably smaller than the original theoretical prediction. We critically reassess this work, which was based on allowing for the self-interaction of the fluid interface, and argue that the interfacial curvature and effective wavevector dependent surface tension can further lower the predicted value of α*, in keeping with our numerical findings. Interfacial fluctuation effects, occurring beyond mean-field level, are also discussed using effective Hamiltonian theory and are shown to substantially increase the value of α*.