scholarly journals Generalizations of Boltzmann's Equation

1974 ◽  
Vol 27 (6) ◽  
pp. 773 ◽  
Author(s):  
GR Anstis
Keyword(s):  
Diffusion Coefficient ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
The Self ◽  
One Dimensional ◽  
Point Particles ◽  
Self Diffusion ◽  
Self Diffusion Coefficient ◽  
Boltzmann's Equation ◽  
Boltzmann’S Equation

A scheme is proposed for systematically generalizing Boltzmann's equation in order to describe the non-equilibrium behaviour of an arbitrarily dense gas. The method avoids the divergences that arise from considering the dynamics of groups of isolated particles by introducing appropriate damping terms. Transport coefficients are obtained from the kinetic equations by using the autocorrelation formulae. For a one-dimensional gas of impenetrable point particles, approximations to the coefficient of self-diffusion may be obtained readily from the proposed generalization. A first correction to Boltzmann's equation yields the self-diffusion coefficient to within 1 % of its exact value.

Self-Diffusion Coefficient and Viscosity in Fluids

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Lawrence Novak
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Transport Coefficient ◽  
Transport Coefficients ◽  
Dynamics Simulation ◽  
Residual Entropy ◽  
Transport Reaction ◽  
Self Diffusion ◽  
Coefficient Corrélation ◽  
Self Diffusion Coefficient

Rate-based models suitable for equipment or transport-reaction modeling require a capability for predicting transport coefficients over a sufficient range of temperature and pressure. This paper demonstrates a relatively simple novel approach to correlate and estimate transport coefficients for pure components over the entire fluid region.The use of Chapman-Enskog transport coefficients for reducing self-diffusion coefficient and viscosity to dimensionless form results in relatively simple mathematical relationships between component dimensionless transport coefficients and residual entropy over the entire fluid region. Dimensionless self-diffusion coefficients and viscosities were calculated from extensive molecular dynamics simulation data and experimental data on argon, methane, ethylene, ethane, propane, and n-decane. These dimensionless transport coefficients were plotted against dimensionless residual entropy calculated from highly accurate reference equations of state.Based on experimental data, the new scaling model introduced here shows promise as: (1) an equation of state-based transport coefficient correlation over the entire fluid region (liquid, gas, and critical fluid), (2) a component transport coefficient correlation for testing transport data consistency, and (3) a component transport coefficient correlation for interpolation and extrapolation of self-diffusion coefficient and viscosity.

Investigation on the Diffusion Behavior of Mo-Ni Interface

2010 ◽  
Vol 152-153 ◽  
pp. 1607-1610 ◽  
Author(s):  
Wei Chan Cao ◽  
Shu Hua Liang ◽  
Yue Xin Xue ◽  
Xian Hui Wang
Keyword(s):  
Solid Solution ◽  
Diffusion Coefficient ◽  
Electron Microscope ◽  
Intermetallic Compound ◽  
Diffusion Layer ◽  
Interdiffusion Coefficient ◽  
The Self ◽  
Diffusion Behavior ◽  
Self Diffusion ◽  
Self Diffusion Coefficient

In order to gain a deep insight into the mechanism of Ni-doped Mo activated sintering process, the diffusion behavior of Mo-Ni interface was studied utilizing a Mo-Ni diffusion couple. The phase structure and composition on the diffusion layer were characterized and analyzed by means of scanning electron microscope and transmission electron microscope, the self diffusion coefficient and interdiffusion coefficient were calculated. The results show that a diffusion layer is formed between Mo and Ni after sintering at 1223k for 1h, which is comprised of a δ-NiMo intermetallic compound and a limit solid solution containing small amounts of nickel. The self diffusion coefficient and interdiffusion coefficient are 2.068×10-18cm2/s and 4.5×10-12cm2/s, respectively. It is suggested that the diffusion rate of Mo in δ-NiMo intermetallic compound and a limit solid solution containing small amounts of nickel is 106 times bigger than that of self diffusion, and the intermetallic compound layer provides a short diffusion path for Mo activated sintering.

Self-Diffusion in Molten Lithium Nitrate

1992 ◽  
Vol 47 (10) ◽  
pp. 1047-1050 ◽  
Author(s):  
C. Herdlicka ◽  
J. Richter ◽  
M. D. Zeidler
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Spin Echo ◽  
The Self ◽  
Lithium Nitrate ◽  
Equimolar Ratio ◽  
Self Diffusion ◽  
Field Gradients ◽  
Molten Lithium ◽  
Self Diffusion Coefficient

AbstractSelf-diffusion coefficients of 7Li+ ions have been measured in molten LiNO3 with several compositions of 6Li+ and 7Li+ over a temperature range from 537 to 615 K. The NMR spin-echo method with pulsed field gradients was applied. It was found that the self-diffusion coefficient depends on the isotopic composition and shows a maximum at equimolar ratio. At temperatures above 600 K this behaviour disappears.

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