We propose a fully quantitative theory for the finite-size scaling of the filling transition in a three- dimensional double wedge geometry, based on the exact transfer-matrix solution of a phenomenological interfacial model. Antisymmetric fields act at the top and bottom wedges; so each one favours a different bulk phase under coexistence conditions, i.e. gas and liquid phases in fluid models such as the lattice gas, or equivalently ferromagnetic domains of opposed magnetization in the Ising model. From this formalism we obtain an analytical form for the magnetization probability distribution function at critical filling which is valid for any aspect ratio. To test our predictions we revisit and perform new simulation studies of filling in the Ising model double-wedge geometry and use our finite-size scaling theory to locate accurately the critical filling transition

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The structural properties of the Jagla fluid are studied by Monte Carlo (MC) simulations, numerical solutions of integral equation theories, and the (semi-analytical) rational-function approximation (RFA) method. In the latter case, the results are obtained from the assumption (supported by our MC simulations) that the Jagla potential and a potential with a hard core plus an appropriate piecewise constant function lead to practically the same cavity function. The predictions obtained for the radial distribution function, g(r), from this approach are compared against MC simulations and integral equations for the Jagla model, and also for the limiting cases of the triangle-well potential and the ramp potential, with a general good agreement. The analytical form of the RFA in Laplace space allows us to describe the asymptotic behavior of g(r) in a clean way and compare it with MC simulations for representative states with oscillatory or monotonic decay. The RFA predictions for the Fisher-Widom and Widom lines of the Jagla fluid are obtained.

We study the interfacial phenomenology of a fluid in contact with a one-dimensional array of infinitely long grooves of sinusoidal section, characterized by the periodicity length L and amplitude A. The system is modelled by the Landau-Ginzburg-Wilson functional, with fluid-substrate couplings which control the wettability of the substrate. We investigate the filling and wetting phenomena within the mean-field approximation, and compare with the predictions of the macroscopic and interfacial Hamiltonian theories. For large values of L and under bulk coexistence conditions, we observe first-order filling transitions between dry (D) and partially filled (F) interfacial states, and wetting transitions between partially filled F and completely wet (W) interfacial states of the same order as for the flat substrate. Depending on the order of the wetting transition, the transition temperature is either shifted towards lower temperatures for first-order wetting or it coincides with the wetting temperature on the flat substrate for continuous wetting. On the other hand, if the groove height is of order of the correlation length, only wetting transitions between D and W states are observed under bulk coexistence conditions. For this case, the transition temperature shift obeys approximately Wenzel's phenomenological law if the substrate favors first-order wetting, but it remains unshifted for continuous wetting. The borderline between the small and large L regimes correspond to a D - F - W triple point if wetting is first-order, and a D - F critical point for continuous wetting. Beyond bulk coexistence conditions, filling and first-order wetting transitions continue into off-coexistence filling and prewetting lines, which end up at critical points. Our findings show that the macroscopic theory only describes accurately the filling transition close to bulk coexistence and large L, while microscopic structure of the fluid is essential to understand wetting and filling away from bulk coexistence.