• Title/Summary/Keyword: longitudinal diffusion coefficient

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A Monte-Carlo method and Boltzmann Equation analysis on the electron swarm parameter in SiH$_4$+Ar mixtures gas. ($SiH_4+Ar$ 혼합기체의 전자군 파라미터에 대한 볼츠만 방정식 및 몬테 칼로법 해석)

  • 김대연;하성철
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1999.05a
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    • pp.387-390
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    • 1999
  • Electron swarm parameterdthe drift velocity and longitudinal diffusion coefficienthn $SiH_4-Ar$ mixtures containing 0.5% and 5% monosilane were measured using over the range of E/N from 0.01 to 300 Td at room temperature. Electron swarm parameters in argon were drastically changed by adding a small amount of monosilane. The electron drift velocity in both mixtures showed unusual behaviour against E/N. It had negative slope in the medium range of E/N, yet the slope was not smooth but contained a small hump. The longitudinal diffusion coefficient also showed a corresponding feature in its dependence on E/N. A two-tern approximation of the Boltzmann equation analysis and Monte Carlo simulation have been used to study electron transport coefficients.

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Determination of Diffusion Coefficients of Boron from Borate Rods in Wood Using Boltzmann's Transformation

  • Ra, Jong-Bum
    • Journal of the Korean Wood Science and Technology
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    • v.31 no.3
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    • pp.24-29
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    • 2003
  • This research was performed to investigate the diffusivity of borate rods in radiata pine (Pinus radiata D. Don) conditioned to 40 percent moisture content (MC). The deepest penetration of boron were observed in the longitudinal direction, followed by the radial and the tangential directions. The boron loading on the wood face adjacent to the borate rod tended to increase with diffusion time in all directions. To mathematically quantify boron diffusion, the diffusion coefficient of boron was determined using Boltzmann's transformation by assuming that it was a function of concentration only. The values of the longitudinal diffusion coefficients were between 1.3×10-8 cm2/sec and 9.2×10-8 cm2/sec. The radial diffusion coefficients were between 1.4×10-8 cm2/sec and 9.5×10-8 cm2/sec, and the tangential diffusion coefficients were between 5.2×10-9 cm2/sec and 1.3×10-8 cm2/sec. The differences of diffusion coefficients between the longitudinal direction and the radial direction were slight, although their concentration profiles were markedly different. This indicates that the amount of boron loading on the wood face adjacent the borate rod is one of the most important factor for boron penetration in wood with low MC.

Development of Longitudinal Dispersion Coefficient Based on Theoretical Equation for Transverse Distribution of Stream-Wise Velocity in Open Channel : Part II. Longitudinal Dispersion Coefficient (개수로에서 흐름방향 유속의 횡분포 이론식에 기반한 종분산계수 개발 : II. 종분산계수)

  • Baek, Kyong Oh
    • Journal of Korea Water Resources Association
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    • v.48 no.4
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    • pp.299-308
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    • 2015
  • The aim of this study is that a theoretical formula for estimating the one-dimensional longitudinal dispersion coefficient is derived based on a transverse distribution equation for the depth averaged stream-wise velocity in open channel. In "Part I. Theoretical equation for stream-wise velocity" which is the former volume of this article, the velocity distribution equation is derived analytically based on the Shiono-Knight Method (SKM). And then incorporating the velocity distribution equation into a triple integral formula which was proposed by Fischer (1968), the one-dimensional longitudinal dispersion coefficient can be derived theoretically in "Part II. Longitudinal dispersion coefficient" which is the latter volume of this article. The proposed equations for the velocity distribution and the longitudinal dispersion coefficient are verified by using observed data set. As a result, the non-dimensional longitudinal dispersion coefficient is inversely proportional to square of the Manning's roughness coefficient and the non-dimensional transverse dispersion coefficient, and is directly proportional to square of the aspect ratio (channel width to depth).

The Study of Electron Transport coefficients in $SiH_4$-Ar Mixtures by Using Boltzmann Equation Analysis and Monte-Carlo Simulation (볼츠만방정식과 몬테칼로법에 의한 $SiH_4$-Ar 혼합가스의 전자수송계수에 관한 연구)

  • 하성철;전병훈
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.14 no.2
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    • pp.169-174
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    • 2001
  • The electron transport coefficients(the electron drift velocity, W, and the longitudinal and transverse diffusion coefficient, D$_{L}$ and D$_{T}$) in SiH$_4$-Ar mixtures containing 0.5% and 5.0% monosilane were calculated over the E/N range from 0.01 to 300 Td and over the gas pressure range 0.5, 1.0 and 1.5 Torr by the time-of-flight(TOF) method of the Boltzmann equation(BE.) and Monte-Carlo simulation(MCS). The electron energy distribution function in each SiH$_4$-Ar mixtures at E/N=10 Td and L=0.2 cm, which in equilibrium region in the mean electron enregy were compared.red.

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The study of electron transport coefficients in pure Xe by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 Xe분자가스의 전자수송계수의 해석)

  • Ma, Su-Young;Jeon, Byung-Hoon;Kim, Song-Gang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.174-177
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    • 2001
  • The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure Xe were calculated over the wide E/N range from 0.01 to 500 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of Xe molecular gas.

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The study of electron transport coefficients in pure Ne by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 Ne분자가스의 전자수송계수의 해석)

  • Jeon, Byung-Hoon;Gang, Myung-Hee;Kim, Song-Gang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.182-185
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    • 2001
  • The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure Ne were calculated over the wide E/N range from 0.01 to 300 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of Ne molecular gas.

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The study of electron transport coefficients in pure $CO_2$ by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 $CO_2$분자가스의 전자수송계수의 해석)

  • Jeon, Byung-Hoon;Kim, Ji-Yeon;Kim, Song-Gang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.164-167
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    • 2001
  • The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure $CO_2$ were calculated over the wide E/N range from 0.01 to 500 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of $CO_2$ molecular gas. And for propriety of two-term approximation of Boltzmann equation analysis, the calculated results compared with the electron transport coefficients measured by Nakamura.

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The study of electron transport coefficients in pure $CF_4$ by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 $CF_4$분자가스의 전자수송계수의 해석)

  • Jeon, Byung-Hoon;Ha, Sung-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.29-32
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    • 2001
  • We measured the electron transport coefficients(the electron drift velocity, W, and the longitudinal diffusion coefficient, $D_L$) in pure $CF_4$ over the E/N range from 0.04 Td to 250 Td by the double shutter drift tube. And these electron transport coefficients in pure $CF_4$ were calculated over the E/N range from 0.01 to 250 Td at 1 Torr by using the two-term approximation of the Boltzmann equation.

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Determination of the Inelastic cross Sections for $C_{3}F_{8}$ Molecule by electron Swarm Study

  • Jeon, Byung-Hoon;Ha, Sung-Chul;Yang, Jeong-Mo
    • Transactions on Electrical and Electronic Materials
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    • v.2 no.1
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    • pp.7-11
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    • 2001
  • We measured the electron transport coefficients, the electron drift velocity, W, and the longitudinal diffusion coefficient, $D_{L}$, over the E/N range from 0.03 to 100 Td and gas pressure range from 0.133 to 122 kPa in the 0.526% and 5.05% $C_{3}F_{8}$-Ar mixtures by the double shutter drift tube with variable drift distance. And we calculated these electron transport coefficients by using multi-term approximation of Boltzmann equation analysis. We determined the electron collision cross sections set for $C_{3}F_{8}$ molecule by the comparison of measurement and calculation. Our special attention in the present study was focused upon the inelastic collision cross sections of the $C_{3}F_{8}$ molecule.

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Determination of an Inelastic Collision Cross Sections for C3F8 Molecule by Electron Swarm Method (전자군 방법에 의한 C3F8분자가스의 비탄성충돌단면적의 결정)

  • Jeon Byung-Hoon
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.19 no.3
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    • pp.301-306
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    • 2006
  • The electron drift velocity W and the product of the longitudinal diffusion coefficient and the gas number density $ND_{L}$ in the $0.525\;\%$ and $5.05\;\%$ $C_{3}F_8-Ar$ mixtures were measured by using the double shutter drift tube with variable drift distance over the E/N range from 0.03 to 100 Td and gas pressure range from 1 to 915 torr. And we determined the electron collision cross sections set for the $C_{3}F_8$ molecule by STEP 1 of electron swarm method using a multi-term Boltzmann equation analysis. Our special attention in the present study was focused upon the vibrational excitation and new excitations cross sections of the $C_{3}F_8$ molecule.