  The Cassie-Wenzel transition of a symmetric binary liquid mixture in contact
with a nano-corrugated wall is studied. The corrugation consists of a periodic
array of nano-pits with square cross sections. The substrate potential is the
sum over Lennard-Jones interactions, describing the pairwise interaction
between the wall particles $C$ and the fluid particles. The liquid is composed
of two species of particles, $A$ and $B$, which have the same size and equal $A
- A$ and $B - B$ interactions. The liquid particles interact between each other
also via $A - B$ Lennard-Jones potentials. We have employed classical density
functional theory to determine the equilibrium structure of binary liquid
mixtures in contact with the nano-corrugated surface. Liquid intrusion into the
pits is studied as a function of various system parameters such as the
composition of the liquid, the strengths of various inter-particle
interactions, as well as the geometric parameters of the pits. The binary
liquid mixture is taken to be at its mixed-liquid-vapor coexistence. For
various sets of parameters the results obtained for the Cassie - Wenzel
transition, as well as for the metastability of the two corresponding
thermodynamic states, are compared with macroscopic predictions in order to
check the range of validity of the macroscopic theories for systems exposed to
nanoscopic confinements. Distinct from the macroscopic theory, it is found that
the Cassie - Wenzel transition cannot be predicted based on the knowledge of a
single parameter, such as the contact angle within the macroscopic theory.
