  We discuss the sharp interface limit of a diffuse interface model for a
two-phase flow of two partly miscible viscous Newtonian fluids of different
densities, when a certain parameter \epsilon>0 related to the interface
thickness tends to zero. In the case that the mobility stays positive or tends
to zero slower than linearly in \epsilon we will prove that weak solutions tend
to varifold solutions of a corresponding sharp interface model. But, if the
mobility tends to zero faster than \epsilon^3 we will show that certain
radially symmetric solutions tend to functions, which will not satisfy the
Young-Laplace law at the interface in the limit.
