ABSTRACT
Some experimental results in the study of disordered systems, polymeric fluids, solutions of micelles and surfactants, ionic-glass conductors, and others show a hydrodynamic behavior labeled "anomalous" with properties described by some kind of fractional power laws in place of the standard ones. This is a consequence of the fractal-like structure that is present in these systems of which we do not have a detailed description, thus impairing the application of the conventional ensemble formalism of statistical mechanics. In order to obtain a physical picture of the phenomenon for making predictions which may help with technological and industrial decisions, one may resort to different styles (so-called nonconventional) in statistical mechanics. In that way can be introduced a theory for handling such impaired situations, a nonconventional mesoscopic hydrothermodynamics (MHT). We illustrate the question presenting an application in a contracted description of such nonconventional MHT, consisting in the use of the Renyi approach to derive a set of coupled nonstandard evolution equations, one for the density, a nonconventional Maxwell-Cattaneo equation, which in a limiting case goes over a non-Fickian diffusion equation, and other for the velocity in fluids under forced flow. For illustration the theory is applied to the study of the hydrodynamic motion in several soft-matter systems under several conditions such as streaming flow appearing in electrophoretic techniques and flow generated by harmonic forces arising in optical traps. The equivalence with Lévy processes is discussed and comparison with experiment is done.
ABSTRACT
The connection between the Maxwell-Cattaneo heat transport equation and a nonequilibrium entropy is examined through four different thermodynamic approaches, and it is shown that all of them lead to the same form of the nonequilibrium entropy. Furthermore, it is seen that this form is also consistent with three microscopic formalisms. This robustness underlines the consistency and relevance of the entropy.
ABSTRACT
We study the shear-flow effects on phase separation of entangled polymer blends by incorporating into the chemical potential a nonequilibrium contribution due to the flow. The results are compared with those of a previous analysis by other authors which did not modify the chemical potential but used a different assumption for the stress tensor of the blend.
ABSTRACT
We propose a Legendre transform linking two different choices of nonequilibrium variables (viscous pressure tensor and configuration tensor) in the thermodynamics of flowing polymer solutions. This may avoid some current confusions in the analysis of thermodynamic effects in polymer solutions under flow.
