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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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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.

Physical Review. E

|December 18, 2024

Summary

This summary is machine-generated.

This study rigorously derives exact hydrodynamic equations from the Boltzmann kinetic equation, revealing a modified entropy for pure dissipation and applying it to channel flow phenomena.

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Area of Science:

Fluid dynamics
Statistical mechanics
Kinetic theory

Background:

Deriving accurate hydrodynamic equations from kinetic theory is challenging.
Existing models often lack rigorous justification or are limited in scope.
Understanding dissipation and non-local effects is crucial for complex fluid behaviors.

Purpose of the Study:

To rigorously derive exact closure for hydrodynamic variables from the linear Boltzmann equation.
To develop a unique, optimal reduction in phase space near equilibrium.
To investigate the implications for entropy modification and dissipation in hydrodynamic systems.

Main Methods:

Spectral theory and analysis of eigenvector properties.
Theory of slow manifolds for phase space reduction.
Modification of entropy within a hydrodynamically constrained system.

Main Results:

A unique, optimal reduction in phase space near equilibrium was defined.
A modified entropy ensuring pure dissipation on the hydrodynamic manifold was established.
The derived equations were exemplified using the Knudsen minimum paradox in channel flow.

Conclusions:

The study provides a rigorous foundation for hydrodynamic equations derived from kinetic theory.
The findings offer a nonlocal variant of Korteweg's theory, linking viscosity and capillarity.
The approach successfully explains complex phenomena like the Knudsen minimum paradox.