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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.00145 |
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| _version_ | 1866909053670653952 |
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| author | Tsuzuki, Satori |
| author_facet | Tsuzuki, Satori |
| contents | We derive a retained-spin micropolar hydrodynamic closure from the Boltzmann--Curtiss equation using a generalized Chapman--Enskog construction in which the local mean spin is retained as a quasi-slow variable. Starting from the one-particle kinetic balance identities and the corresponding exact coarse-grained finite-size balances for mass, linear momentum, and intrinsic angular momentum, we keep the collisional-transfer contribution to the antisymmetric stress explicit in the spin balance, decompose the first-order source into irreducible scalar, axial, and symmetric-traceless sectors, and show explicitly how the standard micropolar constitutive structure with coefficients $(η,ξ,η_r,α,β,γ)$ emerges. This decomposition makes clear that the one-particle kinetic stress contributes only to the symmetric stress, whereas the rotational viscosity belongs to a collisional-transfer channel. For perfectly rough elastic hard spheres, we further obtain explicit dilute-gas estimates for the rotational viscosity $η_r$ from homogeneous spin relaxation and for the transverse spin-diffusion combination $β+γ$ from a transport-relaxation calculation. Targeted event-driven molecular-dynamics simulations are used as a posteriori checks: expanded homogeneous-spin density and roughness sweeps support the predicted $n^2$ and $K/(K+1)$ trends for $η_r$, while finite-$k$ transverse runs provide a qualitative diagnostic of the retained-spin response. The result is a self-contained derivation and coefficient-level estimate of retained-spin micropolar hydrodynamics that clarifies which parts of the closure are exact balance-law statements, which are first-order generalized Chapman--Enskog results, and which remain controlled rough-sphere estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00145 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Retained-spin micropolar hydrodynamics from the Boltzmann--Curtiss equation Tsuzuki, Satori Soft Condensed Matter Mathematical Physics We derive a retained-spin micropolar hydrodynamic closure from the Boltzmann--Curtiss equation using a generalized Chapman--Enskog construction in which the local mean spin is retained as a quasi-slow variable. Starting from the one-particle kinetic balance identities and the corresponding exact coarse-grained finite-size balances for mass, linear momentum, and intrinsic angular momentum, we keep the collisional-transfer contribution to the antisymmetric stress explicit in the spin balance, decompose the first-order source into irreducible scalar, axial, and symmetric-traceless sectors, and show explicitly how the standard micropolar constitutive structure with coefficients $(η,ξ,η_r,α,β,γ)$ emerges. This decomposition makes clear that the one-particle kinetic stress contributes only to the symmetric stress, whereas the rotational viscosity belongs to a collisional-transfer channel. For perfectly rough elastic hard spheres, we further obtain explicit dilute-gas estimates for the rotational viscosity $η_r$ from homogeneous spin relaxation and for the transverse spin-diffusion combination $β+γ$ from a transport-relaxation calculation. Targeted event-driven molecular-dynamics simulations are used as a posteriori checks: expanded homogeneous-spin density and roughness sweeps support the predicted $n^2$ and $K/(K+1)$ trends for $η_r$, while finite-$k$ transverse runs provide a qualitative diagnostic of the retained-spin response. The result is a self-contained derivation and coefficient-level estimate of retained-spin micropolar hydrodynamics that clarifies which parts of the closure are exact balance-law statements, which are first-order generalized Chapman--Enskog results, and which remain controlled rough-sphere estimates. |
| title | Retained-spin micropolar hydrodynamics from the Boltzmann--Curtiss equation |
| topic | Soft Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2604.00145 |