Three-body corrections to Brownian hard-sphere viscosity
Abstract
For Brownian hard spheres without hydrodynamic interactions, we obtain a conditional enclosure between 1.8266948 and 1.8267157 for the third-order zero-shear Brownian viscosity coefficient. It applies when the physical three-body correction coincides with the finite-energy weak solution and the remote remainder in the pair adjoint identity vanishes. Kirkwood superposition gives zero because three nonzero pair contributions cancel exactly. An elementary radial identity exposes this cancellation, and a common contact-stress convention allows direct comparison of closure predictions. Although superposition solves the bulk equation, it leaves a shared-contact flux error. Correcting this error defines a unique weak response with positive Dirichlet energy. Explicit symmetric trials yield a variational lower bound and a residual upper bound using the rotational structure of shear and three-sphere geometry. Exact integration and outward interval evaluation enclose the fixed-trial functionals. Under the stated physical conditions, the resulting interval excludes all closure coefficients compared here and supplies a quantitative benchmark for dilute three-body Brownian stress.
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BibTeX
@misc{olszewski2026threebody,
title = {{Three-body corrections to Brownian hard-sphere viscosity}},
author = {Julian Olszewski and Zijian Liu and Jie Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24948},
eprint = {2610.24948},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24948},
}
RIS
TY - UNPB
TI - Three-body corrections to Brownian hard-sphere viscosity
AU - Julian Olszewski
AU - Zijian Liu
AU - Jie Xu
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.24948
UR - https://arxiv.org/abs/2610.24948
AB - For Brownian hard spheres without hydrodynamic interactions, we obtain a conditional enclosure between 1.8266948 and 1.8267157 for the third-order zero-shear Brownian viscosity coefficient. It applies when the physical three-body correction coincides with the finite-energy weak solution and the remote remainder in the pair adjoint identity vanishes. Kirkwood superposition gives zero because three nonzero pair contributions cancel exactly. An elementary radial identity exposes this cancellation, and a common contact-stress convention allows direct comparison of closure predictions. Although superposition solves the bulk equation, it leaves a shared-contact flux error. Correcting this error defines a unique weak response with positive Dirichlet energy. Explicit symmetric trials yield a variational lower bound and a residual upper bound using the rotational structure of shear and three-sphere geometry. Exact integration and outward interval evaluation enclose the fixed-trial functionals. Under the stated physical conditions, the resulting interval excludes all closure coefficients compared here and supplies a quantitative benchmark for dilute three-body Brownian stress.
ER -