Wetting transition of a nematic liquid crystal on a periodic wedge-structured substrate

It is known that the wetting behaviour of a fluid is deeply altered by the presence of rough or structured substrates. We first review some simple considerations about isotropic fluids and rough substrates, and then we generalize Wenzel's law, which assigns an effective contact angle to a droplet on a rough substrate, when the wetting layer has an ordered phase, like a nematic. We estimate the conditions for which the wetting behavior of an ordered fluid can be qualitatively different from that usually found in a simple fluid. To support our general considerations, we use the Landau-de Gennes mean field approach to investigate theoretically and numerically the wetting transition of a nematic phase on a periodic triangular structured substrate.