Wedge filling, cone filling and the strong fluctuation regime

Interfacial fluctuation effects occuring at wedge and cone filling transitions are investigated and shown to exhibit very different characteristics. For both geometries we show how the conditions for observing critical (continuous) filling are much less restrictive than for critical wetting, which is known to require fine tuning of the Hamaker constants. Wedge filling is critical if the wetting binding potential does not exhibit a local maximum, whilst conic filling is critical if the integrated strength of the potential is attractive. This latter scenario is particularly encouraging for future experimental studies. Using mean-field and effective Hamiltonian approaches, which allow for breather-mode fluctuations which translate the interface up and down the sides of the confining geometry, we are able to completely classify the possible critical behaviour (for purely thermal disorder). For the three dimensional wedge, the interfacial fluctuations are very strong and characterised by a universal roughness critical exponent $\nu_{\perp} =1/4$ independent of the range of the forces. For the physical dimensions d=2 and d=3, we show that the influence of the cone geometry on the fluctuations at critical filling is to mimic the analogous interfacial behaviour occuring at critical wetting in the strong-fluctuation regime. In particular, for d=3 and for quite arbitary choices of intermolecular potential, the filling height and roughness show the same critical properties as those predicted for three dimensional critical wetting with short-ranged forces in the large wetting parameter ($\omega>2$) regime.