scholarly journals Statistical–mechanical, Molecular Theory of Boundary Conditions for Liquid Flow at Nanostructured Surfaces and in Confined Geometries

2012 ◽  
Vol 44 ◽  
pp. 386-387
Author(s):  
A. Kovalenko
Keyword(s):  
Boundary Conditions ◽  
Liquid Flow ◽  
Molecular Theory ◽  
Confined Geometries ◽  
Nanostructured Surfaces ◽  
Statistical Mechanical

scholarly journals Extreme boundary conditions and random tilings

2021 ◽  
Author(s):  
Jean-Marie Stéphan
Keyword(s):  
Boundary Conditions ◽  
Quantum Particle ◽  
Condensed Matter ◽  
Two Dimensions ◽  
Basic Knowledge ◽  
Dimer Model ◽  
Long Range Correlations ◽  
Statistical Mechanical ◽  
Local Densities ◽  
Random Tilings

Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as illustrated by the famous 'arctic circle theorem' for dimer coverings in two dimensions. In these notes, I discuss such examples in the context of critical phenomena, and their relation to 1+1d quantum particle models. All those turn out to share a common feature: they are inhomogeneous, in the sense that local densities now depend on position in the bulk. I explain how such problems may be understood using variational (or hydrodynamic) arguments, how to treat long range correlations, and how non trivial edge behavior can occur. While all this is done on the example of the dimer model, the results presented here have much greater generality. In that sense the dimer model serves as an opportunity to discuss broader methods and results. [These notes require only a basic knowledge of statistical mechanics.]

Kinetic Theory and Boundary Conditions for Fluids

1973 ◽  
Vol 25 (6) ◽  
pp. 1183-1215 ◽  
Author(s):  
Jon Schnute ◽  
Marvin Shinbrot
Keyword(s):  
Kinetic Theory ◽  
Boundary Conditions ◽  
Molecular Theory ◽  
Rigorous Derivation ◽  
The One

SummaryA rigorous derivation of the molecular theory of a confined, deterministic gas is given. Then, a molecular reflection law is presented with the property that the corresponding fluid does not slip at the boundary. It is also shown that, within a certain reasonable class of reflection laws, the one we give is the only one that leads to no-slip.

Single-phase filtration in the porous medium saturated with anomalous thermoviscous liquid

2008 ◽  
Vol 6 ◽  
pp. 184-192
Author(s):  
S.F. Khizbullina
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Liquid Flow ◽  
Velocity Vector ◽  
Single Phase ◽  
Polymer Gel ◽  
Characteristic Distribution ◽  
Type Boundary

In work the single-phase filtration of anomalous thermoviscous liquid on an example of thermoreversible polymer gel, named МЕТКА, is simulated numerically. Features of a filtration liquid flow at her injection into porous medium are investigated. Characteristic distribution pictures of fields of temperature, viscosity and velocity vector components are constructed when using first-type and third-type boundary conditions.

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