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