Mixtures with continuous diversity: general theory and application to polymer solutions

This work concerns a generalization of the classical theory of mixtures appropriate for multicomponent media made up of an infinite number of constituents with continuously varying properties. Such a concept affords a valuable starting point for the description of many thermodynamic systems found in physical, geological, chemical and biological sciences. The main matter of this study lies in an extension of the entropy principle of continuum thermodynamics to the higher-dimensional spaces which characterize such kind of multicomponent media. To illustrate the potential of the theory, it is applied to the analysis of induced anisotropy in rigid rodlike polymer solutions, in different concentration regimes. Among other interesting inferences of the constitutive theory, it is shown that the microstructure evolution is governed by a hyperbolic equation, which after suppression of inertial effects reduces to a non-linear evolution equation of the Fokker-Planck type. Finally, an analogy between the results derived by this continuum approach and those usually obtained from molecular theories is established, by particularizing the predictions for ideal solutions.