A Kinetic Theory Approach to Ordered Fluids

TL;DR

This paper introduces a comprehensive kinetic theory for ordered fluids, extending phase space with generalized angular momenta to model microstructured continuum fluids.

Contribution

It develops a unified mesoscopic model for ordered fluids with microstructure, based on kinetic theory and symmetry considerations, applicable to various complex liquids.

Findings

Derived a mesoscopic model for ordered fluids from kinetic principles.

Identified conserved quantities via Noether's theorem for different microstructures.

Discussed conditions for an H-theorem and collective behavior emergence.

Abstract

We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely determined mesoscopic model for any continuum with microstructure that is characterized by Capriz's order parameter manifold. We illustrate our theory with three running examples: liquids saturated with non-diffusive gas bubbles, liquids composed of calamitic (rodlike) molecules, and liquids composed of calamitic molecules with additional head-to-tail symmetry. We discuss the symmetries of the microscopic interactions via Noether's theorem, and use them to characterize the conserved quantities mesoscopic dynamics. We derive the mesoscopic model for ordered fluids from a kinetic point of view assuming that the microscopic interactions are of weak nature when it comes to the ordering of the fluid. Lastly, we discuss under which conditions an H-theorem result holds at the mesoscopic scale and for which Vlasov potential we can expect the emergence of collective behavior.