Bound-free gas transport coefficients via the time correlation formulation based on an atomic picture

1999 ◽  
Vol 110 (17) ◽  
pp. 8533-8542 ◽  
Author(s):  
R. F. Snider ◽  
Saman Alavi
Keyword(s):  
Gas Transport ◽  
Transport Coefficients ◽  
Time Correlation ◽  
Free Gas

Nanoscale Free Gas Transport in Shale Rocks: A Hard-Sphere Based Model

2017 ◽  
Author(s):  
Jinze Xu ◽  
Keliu Wu ◽  
Sheng Yang ◽  
Jili Cao ◽  
Zhangxin Chen
Keyword(s):  
Hard Sphere ◽  
Gas Transport ◽  
Free Gas

Time Correlation Functions

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Correlation Functions ◽  
Thermal Environment ◽  
Structural Information ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Relevant Information ◽  
Time Correlation ◽  
Time Correlation Functions ◽  
Dynamical Information

In the previous chapter we have seen how spatial correlation functions express useful structural information about our system. This chapter focuses on time correlation functions that, as will be seen, convey important dynamical information. Time correlation functions will repeatedly appear in our future discussions of reduced descriptions of physical systems. A typical task is to derive dynamical equations for the time evolution of an interesting subsystem, in which only relevant information about the surrounding thermal environment (bath) is included. We will see that dynamic aspects of this relevant information usually enter via time correlation functions involving bath variables. Another type of reduction aims to derive equations for the evolution of macroscopic variables by averaging out microscopic information. This leads to kinetic equations that involve rates and transport coefficients, which are also expressed as time correlation functions of microscopic variables. Such functions are therefore instrumental in all discussions that relate macroscopic dynamics to microscopic equations of motion. It is important to keep in mind that dynamical properties are not exclusively relevant only to nonequilibrium system. One may naively think that dynamics is unimportant at equilibrium because in this state there is no evolution on the average. Indeed in such systems all times are equivalent, in analogy to the fact that in spatially homogeneous systems all positions are equivalent. On the other hand, just as in the previous chapter we analyzed equilibrium structures by examining correlations between particles located at different spatial points, also here we can gain dynamical information by looking at the correlations between events that occur at different temporal points. Time correlation functions are our main tools for conveying this information in stationary systems. These are systems at thermodynamic equilibrium or at steady state with steady fluxes present.

Modeling of Gas Transport Driven by Density Gradients of Free Gas within a Coal Matrix: Perspective of Isothermal Adsorption

2020 ◽  
Vol 34 (11) ◽  
pp. 13728-13739
Author(s):  
Wei Liu ◽  
Yueping Qin ◽  
Wei Zhao ◽  
Deyao Wu ◽  
Jia Liu ◽  
...  
Keyword(s):  
Gas Transport ◽  
Density Gradients ◽  
Isothermal Adsorption ◽  
Free Gas ◽  
Coal Matrix

Turbulent Transport Equations and Kubo Formulae for Eddy Transport Coefficients

1971 ◽  
Vol 26 (11) ◽  
pp. 1782-1791
Author(s):  
S. Grossmann
Keyword(s):  
Eddy Viscosity ◽  
Turbulent Transport ◽  
Transport Coefficients ◽  
Time Integration ◽  
Time Correlation ◽  
Heat Conducting ◽  
Eddy Transport ◽  
Cascade Method ◽  
Factor C ◽  
Heat Conducting Fluids

Kubo type time correlation formulae for turbulent transport coefficients in incompressible but heat conducting fluids are derived, especially for eddy viscosity, eddy heat conductivity, and pressure. The connection to the cascade method as well as its equivalence to the methods of closure of hierarchy are established. Lagrangean time integration is used. If the retarded Green’s function has exponential time behaviour the damping constant Γq can be calculated explicitely. In this approximation in the inertial range one finds the Kolmogoroff k-5/3 spectrum including its numerical factor (C=1.53). This induces a frequency spectrum ∼ ω -2.

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