  A new diffuse interface model for a two-phase flow of two incompressible
fluids with different densities is introduced using methods from rational
continuum mechanics. The model fulfills local and global dissipation
inequalities and is also generalized to situations with a soluble species.
Using the method of matched asymptotic expansions we derive various sharp
interface models in the limit when the interfacial thickness tends to zero.
Depending on the scaling of the mobility in the diffusion equation we either
derive classical sharp interface models or models where bulk or surface
diffusion is possible in the limit. In the two latter cases the classical
Gibbs-Thomson equation has to be modified to include kinetic terms. Finally, we
show that all sharp interface models fulfill natural energy inequalities.
