  Inspired by recent experiments on bilayer 3He, we consider a bilayer Hubbard
model on a triangular lattice. For appropriate model parameters, we observe a
band-selective Mott transition at a critical chemical potential, mu_c,
corresponding to the solidification of the fermions in the first layer. The
growth of the effective mass on the metallic side (mu < mu_c) is cut off by a
first order transition in which the first layer fermions drop out of the
Luttinger volume and their spin degrees of freedom become locked in a spin
singlet state. These results are obtained from a cluster dynamical mean-field
calculation on an eight-site cluster with a quantum Monte Carlo cluster solver.
