An Advanced Kinetic Theory For Morphing Continuum With Inner Structures

TL;DR

This paper develops a generalized kinetic theory for polyatomic gas flows with inner structures, introducing a new distribution function and deriving governing equations that connect with morphing continuum theories.

Contribution

It proposes a new Boltzmann-Curtiss distribution for polyatomic gases and links kinetic theory with morphing continuum models, enhancing understanding of complex fluid flows.

Findings

Derived generalized Boltzmann-Curtiss distribution for polyatomic gases

Established governing equations at equilibrium state

Connected kinetic theory with morphing continuum framework

Abstract

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.