Abstract

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

Highlights

  • Birkhoff [2] who noted that the classical Navier–Stokes equations give us uncomplete descriptions of water flows

  • In papers [4,5] the authors gave a general approach to dynamics of media having some inner structure and proposed some generalizations of the Euler and Navier–Stokes equations

  • We consider the dynamics of media formed by chiral, planar and rigid molecules molecules and propose some kind of Navier–Stokes equations for their description

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Summary

Introduction

In papers [4,5] the authors gave a general approach to dynamics of media having some inner structure and proposed some generalizations of the Euler and Navier–Stokes equations. We consider the dynamics of media formed by chiral, planar and rigid molecules (we call them CPR-molecules) molecules and propose some kind of Navier–. Recall that a molecule is called planar if it is formed by atoms lying in the same plane and it is chiral and rigid if its symmetry group belongs to SO(3).

The Configuration Space of a CPR-Molecule
Metric Associated with the Media
Levi–Civita Connection Associated with the Homogeneous Media
Thermodynamic State of Media
Divergence of Operator Fields
The Momentum Conservation Law
The Energy Conservation Law
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