A systematic approach to the thermodynamics of single and mixed flowing media with microstructure. Part I: balance equations and jump conditions

In this first part of the work on the thermodynamics of microstructured flowing media, a complete set of balance equations and jump conditions for single and mixed continua is presented. These equations are appropriate for a wide range of applications, from the creep of polycrystals to the flow of granular media and chemically reacting mixtures of liquid crystals. Thanks to the use of the framework of mixtures with continuous diversity, both isotropic and anisotropic media can be considered at the same footing, and a straightforward comparison of the present results with those found in kinetic, statistical and continuum theories is allowed. Among other conclusions, it is shown that most of the previous theories are either oversimplified or conceptually deficient, due to different reasons. Four different levels of description of the balance equations and jump conditions are addressed, from orientation-dependent relations for the constituents to mixture relations. In particular, the adoption of an orientation-dependent description of microstructured mixtures reveals the occurrence of net orientational diffusive fluxes of mass, which arise in such mixtures from a combination of inertial effects with rotatory diffusion. According to the definitions employed here, these orientational mass fluxes are neither conductive nor convective and their effects disappear after consideration of all microstructural orientations.