dorsal/arxiv
View SchemaGeneralized Boltzmann Equation: Slip-No -Slip Dynamic Transition in Flows of Strongly Non-Linear Fluids
| Authors | Victor Yakhot, Hudong Chen, Ilia Staroselsky, John Wanderer, Raoyang Zhang |
|---|---|
| Categories | |
| ArXiv ID | physics/0411105 |
| URL | https://arxiv.org/abs/physics/0411105 |
Abstract
The Navier-Stokes equations, are understood as the result of the low-order expansion in powers of dimensionless rate of strain $\eta_{ij}=\tau_{0}S_{ij}$, where $\tau_{0}$ is the microscopic relaxation time of a close-to- thermodynamic equilibrium fluid. In strongly sheared non-equilibrium fluids where $|\eta_{ij}|\geq 1$, the hydrodynamic description breaks down. According to Bogolubov's conjecture, strongly non-equlibrium systems are characterized by an hierarchy of relaxation times corresponding to various stages of the relaxation process. A "hydro-kinetic" equation with the relaxation time involving both molecular and hydrodynamic components proposed in this paper, reflects qualitative aspects of Bogolubov's hierarchy. It is shown that, applied to wall flows, this equation leads to qualitatively correct results in an extremely wide range of parameter $\eta$-variation. Among other features, it predicts the onset of slip velocity at the wall as an instability of the corresponding hydrodynamic approximation.
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"abstract": "The Navier-Stokes equations, are understood as the result of the low-order\nexpansion in powers of dimensionless rate of strain $\\eta_{ij}=\\tau_{0}S_{ij}$,\nwhere $\\tau_{0}$ is the microscopic relaxation time of a close-to-\nthermodynamic equilibrium fluid. In strongly sheared non-equilibrium fluids\nwhere $|\\eta_{ij}|\\geq 1$, the hydrodynamic description breaks down.\n According to Bogolubov\u0027s conjecture, strongly non-equlibrium systems are\ncharacterized by an hierarchy of relaxation times corresponding to various\nstages of the relaxation process. A \"hydro-kinetic\" equation with the\nrelaxation time involving both molecular and hydrodynamic components proposed\nin this paper, reflects qualitative aspects of Bogolubov\u0027s hierarchy. It is\nshown that, applied to wall flows, this equation leads to qualitatively correct\nresults in an extremely wide range of parameter $\\eta$-variation. Among other\nfeatures, it predicts the onset of slip velocity at the wall as an instability\nof the corresponding hydrodynamic approximation.",
"arxiv_id": "physics/0411105",
"authors": [
"Victor Yakhot",
"Hudong Chen",
"Ilia Staroselsky",
"John Wanderer",
"Raoyang Zhang"
],
"categories": [
"physics.flu-dyn"
],
"title": "Generalized Boltzmann Equation: Slip-No -Slip Dynamic Transition in Flows of Strongly Non-Linear Fluids",
"url": "https://arxiv.org/abs/physics/0411105"
},
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