  We consider a kinetic model of two species of particles interacting with a
reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank
equations. We prove that in the diffusive limit the evolution is described by a
macroscopic equation in the form of the gradient flux of the macroscopic free
energy functional. Moreover, we study the sharp interface limit and find by
formal Hilbert expansions that the interface motion is given in terms of a
quasi stationary problem for the chemical potentials. The velocity of the
interface is the sum of two contributions: the velocity of the Mullins-Sekerka
motion for the difference of the chemical potentials and the velocity of a
Hele-Shaw motion for a linear combination of the two potentials. These
equations are identical to the ones in Otto-E modelling the motion of a sharp
interface for a polymer blend.
