CAHN-HILLIARD THEORY AND IRREVERSIBLE THERMODYNAMICS

The Cahn-Hilliard theory of fluid mixtures is imbedded into irreversible thermodynamics. The balances of momentum, energy, and entropy differ from the classical ones due to the density gradient contribution to the energy. From the entropy principle restrictions on the constitutive equations for the irreversible fluxes are derived. As a consequence the classical constitutive equation for the diffusional mass flow has to be modified. In the case of uniform temperature and vanishing total mass flow the Cahn-Hilliard equation follows as a diffusion equation from the entropy principle. As an example, the time evolution of a phase boundary in a two-component fluid mixture to which a temperature jump is applied is investigated.