  In this paper we derive a class of thermodynamically consistent
diffuse-interface mixture models of incompressible multicomponent fluids. The
class of mixture models is fully compatible with the continuum theory of
mixtures. The resulting mixture models may be formulated either in constituent
or in mixture quantities. This permits a direct comparison with the
Navier-Stokes Cahn-Hilliard model with non-matching densities, which reveals
the key modeling simplifications of the latter.
