  We study the interfacial phenomenology of a fluid in contact with a
microstructured substrate within the mean-field approximation. The sculpted
substrate is a one-dimensional array of infinitely long grooves of sinusoidal
section of periodicity length L and amplitude A. The system is modelled using
the Landau-Ginzburg functional, with fluid-substrate couplings which correspond
to either first-order or critical wetting for a flat substrate. We investigate
the effect of the roughness of the substrate in the interfacial phenomenology,
paying special attention to filling and wetting phenomena, and compare the
results with the predictions of the macroscopic and interfacial Hamiltonian
theories. At bulk coexistence, for values of L much larger than the bulk
correlation, we observe first-order filling transitions between dry and
partially filled interfacial states, which extend off-coexistence, ending at a
critical point; and wetting transitions between partially filled and completely
wet interfacial states with the same order as for the flat substrate (if
first-order, wetting extends off-coexistence in a prewetting line). On the
other hand, if the groove height is of order of the correlation length, only
wetting transitions between dry and complete wet states are observed. However,
their characteristics depend on the order of the wetting transition for the
flat substrate. So, if it is first-order, the wetting transition temperature
for the rough substrate is reduced with respect to the wetting transition
temperature for a flat substrate, and coincides with the Wenzel law prediction
for very shallow substrates. On the contrary, if the flat substrate wetting
transition is continuous, the roughness does not change the wetting
temperature.
