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Abstract
There are some hydrodynamic equations that, while their parent kinetic equation satisfies fundamental mechanical properties, appear themselves to violate mechanical or thermodynamic properties. This article aims to shed some light on the source of this problem. Starting with diffusive volume hydrodynamic models, the microscopic temporal and spatial scales are first separated at the kinetic level from the macroscopic scales at the hydrodynamic level. Then we consider Klimontovich’s spatial stochastic version of the Boltzmann kinetic equation, and show that, for small local Knudsen numbers, the stochastic term vanishes and the kinetic equation becomes the Boltzmann equation. The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a sub-domain of the continuum range which the conventional Knudsen number classification does not account for appropriately. In this sub-domain, it is possible to obtain a fully mechanically-consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics.
Original language | English |
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Article number | 041202 |
Number of pages | 7 |
Journal | Physical Review E |
Volume | 85 |
Issue number | 4 |
DOIs | |
Publication status | Published - 17 Apr 2012 |
Keywords
- Stochastic kinetic equatio n
- Boltzmann equation
- Rarefied Gas
- Non-continuum flow
- Volume and mass diffusion
- Navier-Stokes equations
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Dive into the research topics of 'Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number'. Together they form a unique fingerprint.Projects
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Non-Equilibrium Fluid Dynamics for Micro/Nano Engineering Systems
Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/01/11 → 16/02/16
Project: Research