A generalized approach to heterogeneous media

This paper is devoted to the description of a generalized approach developed for over-coming the fundamental difficulties that occur when the phenomenological field theory is extended from homogeneous to heterogeneous media. The origin of these difficulties lies in the kinematics of heterogeneous media where different constituents have in general different velocities at the same macroscopic point. The key idea of the generalized approach consists in choosing a reference velocity field v* independent of the movement of the matter. The consequences are examined at different levels. First of all, generalized balance relations lead to a consistent expression of the fundamental law of mechanics and of the first and second principles of thermodynamics in heterogeneous media. Unexpected consequences are linked to the objective nature of the entropy source. Moreover, this generalized approach exhibits a new set of relations between phenomenological and physical variables. Finally, it provides a common, consistent background for different existing theories derived for heterogeneous media.