Dynamics of complex interfaces. I. Rheology, morphology, and diffusion

摘要

In this paper, we investigate, on two levels of description, the isothermal coupling: (i) between rheology and morphology in immiscible blends (A/B) and (ii) among rheology, morphology, and diffusion in mixtures consisting of an immiscible blend (A/B) and one simple fluid, s. The interface separating the phases A and B is described, on the kinetic level by an area density distribution function and on the mesoscopic level by a scalar and a traceless symmetric second order tensor. The nonlinear formulations are derived using the general equation for nonequilibrium reversible and irreversible coupling formalism which ensures the consistency of dynamics with thermodynamics. In addition to the non-Fickian character of mass transport, the coupled three-dimensional governing equations explicitly show the effects of the external flow and diffusion on the size and shape of the interface. New expressions for the stress tensor emerge naturally in the models including the contributions of the diffusion fluxes and the isotropic (Laplace) and anisotropic deformations of the interface. Asymptotic solutions of the governig equations also show that the transport coefficients (diffusivity, etc.) are explicitly dependent on the interfacial tension and on the velocity gradient of the applied flow. The latter dependence renders the process of mass transfer highly anisotropic even in the absence of internal stresses created by the deformation of the interface. The diffusion-free models of Doi-Ohta and Lee-Park are recovered as particular cases.