  We consider a model describing the behavior of a mixture of two
incompressible fluids with the same density in isothermal conditions. The model
consists of three balance equations: continuity equation, Navier-Stokes
equation for the mean velocity of the mixture, and diffusion equation
(Cahn-Hilliard equation). We assume that the chemical potential depends upon
the velocity of the mixture in such a way that an increase of the velocity
improves the miscibility of the mixture. We examine the thermodynamic
consistence of the model which leads to the introduction of an additional
constitutive force in the motion equation. Then, we prove existence and
uniqueness of the solution of the resulting differential problem.
