Continuum mechanics of liquid mixtures on mesoscopic scales

In this talk, I present the derivation of a generic continuum model describing the time evolution of quasi-incompressible liquid mixtures on mesoscopic scales. In the first part of the talk, I employ conventional continuum mechanics and non-equilibrium thermodynamics to derive phenomenological dynamic equations allowing spatiotemporal density variations in the absence of sound waves. The numerical implementation of the model is based on the generalisation of Chorin's projection method, which is tested for multicomponent Cahn-Hilliard liquids. In the second part of the talk, I will present a more rigorous derivation of the general dynamic equations in the framework of statistical physics. I will show that the derivation naturally provides the principles of phenomenological thermodynamics, but also raises issues concerning the consistent incorporation of dissipative phenomena.