Dynamics of multiphase systems with complex microstructure. I. Development of the governing equations through nonequilibrium thermodynamics

Abstract

In this paper we present a general model for the dynamic behavior of multiphase systems in which the bulk phases and interfaces have a complex microstructure (for example, immiscible polymer blends with added compatibilizers, or polymer stabilized emulsions with thickening agents dispersed in the continuous phase). The model is developed in the context of the GENERIC framework (general equation for the nonequilibrium reversible irreversible coupling). We incorporate scalar and tensorial structural variables in the set of independent bulk and surface excess variables, and these structural variables allow us to link the highly nonlinear rheological response typically observed in complex multiphase systems, directly to the time evolution of the microstructure of the bulk phases and phase interfaces. We present a general form of the Poisson and dissipative brackets for the chosen set of bulk and surface excess variables, and show that to satisfy the entropy degeneracy property, we need to add several contributions to the moving interface normal transfer term, involving the tensorial bulk and interfacial structural variables. We present the full set of balance equations, constitutive equations, and boundary conditions for the calculation of the time evolution of the bulk and interfacial variables, and this general set of equations can be used to develop specific models for a wide range of complex multiphase systems.