Critical Effects at 3D Wedge-Wetting

We show that continuous filling or wedge-wetting transitions are possible in 3D wedge-geometries made from (angled) substrates exhibiting first-order wetting transitions and develop a comprehensive fluctuation theory yielding a complete classification of the critical behaviour. Our fluctuation theory is based on the derivation of a Ginzburg criterion for filling and also an exact transfer-matrix analysis of a novel effective Hamiltonian which we propose as a model for wedge fluctuation effects. The influence of interfacial fluctuations is shown to be very strong and, in particular, leads to a remarkable universal divergence of the interfacial roughness ${\xi }_{\perp }\sim (T_F-T{)}^{-1\mathrm{/}4}$ on approaching the filling temperature $T_F$, valid for all possible types of intermolecular forces.