GENERIC model for multiphase systems

GENERIC is a nonequilibrium thermodynamic formalism in which the dynamic behavior of a system is described by a single compact equation involving two types of brackets: a Poisson bracket and a dissipative bracket. This formalism has proved to be a very powerful instrument to model the dynamic behavior of complex bulk phases. In this paper we review the basic principles of the GENERIC formalism, and show how it can be applied to multicomponent multiphase systems with interfaces displaying viscous stress deformation behavior. The generalization of the GENERIC formalism to multiphase systems provides a powerful tool to model nonlinear dynamic behavior of complex interfaces in for example emulsions or foam. Adding several interfacial contributions to the standard two-bracket formulation we derive the conservation laws for mass, momentum, and energy for the bulk phases of the system. We also derive the jump balance equations for the surface mass density, surface momentum, and surface energy. In addition to these balance equations we obtain constitutive equations for the extra stress tensor, energy flux vector, and mass flux vectors in the bulk phase, and the surface extra stress tensor, the surface energy flux vector, and surface mass flux vectors of the interface. The GENERIC formalism also allows us to derive constitutive equations for the transport of mass, momentum, and energy from the bulk phase to the interface. The resulting set of equations is compared to those derived using the rational thermodynamic and classical irreversible thermodynamic formalisms, and is in good agreement with the balance equations derived using these formalisms.