Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First-order Approximation to the Boltzmann-Curtiss Equations for Flows
  with Local Spin   The first-order approximation to the solution of the Boltzmann--Curtiss
transport equation is derived. The resulting distribution function treats the
rotation or gyration of spherical particles as an independent classical
variable, deviating from the quantum mechanical treatment of molecular rotation
found in the Wang Chang-Uhlenbeck equation. The Boltzmann-Curtiss equation,
therefore, does not treat different rotational motions as separate molecular
species. The first-order distribution function yields momentum equations for
the translational velocity and gyration that match the form of the governing
equations of morphing continuum theory (MCT), a theory derived from the
approach of rational continuum thermomechanics. The contribution of the local
rotation to the Cauchy stress and the viscous diffusion are found to be
proportional to an identical expression based off the relaxation time, number
density, and equilibrium temperature of the fluid. When gyration is equated to
the macroscopic angular velocity, the kinetic description reduces to the
first-order approximation for a classical monatomic gas, and the governing
equations match the form of the Navier--Stokes equations. The relaxation time
used for this approximation is shown to be more complex due to the additional
variable of local rotation. The approach of De Groot and Mazur is invoked to
give an initial approximation for the relaxation of the gyration. The
incorporation of this relaxation time, and other physical parameters, into the
coefficients of the governing equations provides a more in-depth physical
treatment of the new terms in the MCT equations, allowing experimenters to test
these expressions and get a better understanding of new coefficients in MCT.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin