dorsal/arxiv
View SchemaDriven cavity flow: from molecular dynamics to continuum hydrodynamics
| Authors | Tiezheng Qian, Xiao-Ping Wang |
|---|---|
| Categories | |
| ArXiv ID | physics/0403047 |
| URL | https://arxiv.org/abs/physics/0403047 |
| Journal | SIAM Multiscale Modeling and Simulation 3, 749 (2005) |
Abstract
Molecular dynamics (MD) simulations have been carried out to investigate the slip of fluid in the lid driven cavity flow where the no-slip boundary condition causes unphysical stress divergence. The MD results not only show the existence of fluid slip but also verify the validity of the Navier slip boundary condition. To better understand the fluid slip in this problem, a continuum hydrodynamic model has been formulated based upon the MD verification of the Navier boundary condition and the Newtonian stress. Our model has no adjustable parameter because all the material parameters (density, viscosity, and slip length) are directly determined from MD simulations. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from MD simulations, from the molecular-scale structure to the global flow. The main discovery is as follows. In the immediate vicinity of the corners where moving and fixed solid surfaces intersect, there is a core partial-slip region where the slippage is large at the moving solid surface and decays away from the intersection quickly. In particular, the structure of this core region is nearly independent of the system size. On the other hand, for sufficiently large system, an additional partial-slip region appears where the slippage varies as $1/r$ with $r$ denoting the distance from the corner along the moving solid surface. The existence of this wide power-law region is in accordance with the asymptotic $1/r$ variation of stress and the Navier boundary condition.
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"abstract": "Molecular dynamics (MD) simulations have been carried out to investigate the\nslip of fluid in the lid driven cavity flow where the no-slip boundary\ncondition causes unphysical stress divergence. The MD results not only show the\nexistence of fluid slip but also verify the validity of the Navier slip\nboundary condition. To better understand the fluid slip in this problem, a\ncontinuum hydrodynamic model has been formulated based upon the MD verification\nof the Navier boundary condition and the Newtonian stress. Our model has no\nadjustable parameter because all the material parameters (density, viscosity,\nand slip length) are directly determined from MD simulations. Steady-state\nvelocity fields from continuum calculations are in quantitative agreement with\nthose from MD simulations, from the molecular-scale structure to the global\nflow. The main discovery is as follows. In the immediate vicinity of the\ncorners where moving and fixed solid surfaces intersect, there is a core\npartial-slip region where the slippage is large at the moving solid surface and\ndecays away from the intersection quickly. In particular, the structure of this\ncore region is nearly independent of the system size. On the other hand, for\nsufficiently large system, an additional partial-slip region appears where the\nslippage varies as $1/r$ with $r$ denoting the distance from the corner along\nthe moving solid surface. The existence of this wide power-law region is in\naccordance with the asymptotic $1/r$ variation of stress and the Navier\nboundary condition.",
"arxiv_id": "physics/0403047",
"authors": [
"Tiezheng Qian",
"Xiao-Ping Wang"
],
"categories": [
"physics.flu-dyn",
"cond-mat.soft",
"physics.comp-ph"
],
"journal_ref": "SIAM Multiscale Modeling and Simulation 3, 749 (2005)",
"title": "Driven cavity flow: from molecular dynamics to continuum hydrodynamics",
"url": "https://arxiv.org/abs/physics/0403047"
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