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Updated: Jun 4, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Rigorous hydrodynamics from linear Boltzmann equations and viscosity-capillarity balance
Florian Kogelbauer1, Ilya Karlin1
1Department of Mechanical and Process Engineering, <a href="https://ror.org/05a28rw58">ETH Zurich</a>, CH-8092 Zurich, Switzerland.
Abstract:
Exact closure for hydrodynamic variables is rigorously derived from the linear Boltzmann kinetic equation. Our approach, based on spectral theory, structural properties of eigenvectors, and the theory of slow manifolds, allows us to define a unique, optimal reduction in phase space close to equilibrium. The hydrodynamically constrained system induces a modification of entropy that ensures pure dissipation on the hydrodynamic manifold, which is interpreted as a nonlocal variant of Korteweg's theory of viscosity-capillarity balance. The rigorous hydrodynamic equations are exemplified on the Knudsen minimum paradox in a channel flow.
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