International Journal of Thermophysics

, Volume 34, Issue 1, pp 47–63 | Cite as

Measurement of Binary Diffusion Coefficients for Neon–Argon Gas Mixtures Using a Loschmidt Cell Combined with Holographic Interferometry

  • T. Kugler
  • B. Jäger
  • E. Bich
  • M. H. Rausch
  • A. P. Fröba
Article

Abstract

The paper reports on experimental binary diffusion coefficient data of neon–argon gas mixtures. Measurements were performed in the temperature range between 293.15 K and 333.15 K and for pressures between 1 bar and 10 bar over almost the whole composition range using a Loschmidt diffusion cell combined with holographic interferometry. The thermostated Loschmidt cell is divided into two half-cells, which can be separated and connected by a sliding plate. Prior to the measurements, two different pure gases are filled into the two half-cells. After starting the diffusion process, the temporal change of the partial molar densities, or rather of the refractive index of the gases, is detected in both half-cells using two holographic interferometers. With this apparatus, the temperature, pressure, and concentration dependence of the binary diffusion coefficient can be determined. The relative uncertainty of a diffusion measurement is between 0.4 % and 1.4 % depending on the pressure. The experimental data are compared with data from the literature and with new theoretical data based on quantum-mechanical ab initio calculations combined with the kinetic theory of gases. Due to a systematic error, the concentration dependence determined in the upper half-cell shows deviations from the theoretical values and from most of the literature data. The concentration, temperature, and pressure dependence obtained from the data from the lower half-cell, however, are in very good agreement with available data. The product of the binary gas diffusion coefficient and the molar density of the gas mixture shows no significant dependence on pressure for the studied neon–argon noble gas system.

Keywords

Argon Binary diffusion coefficient Holographic interferometry Loschmidt cell Neon Quantum-mechanical ab initio calculations 

List of symbols

\(A_\mathrm{R1}\)

First refractivity virial coefficient of component 1 (\(\text{ m}^{3}\cdot \text{ mol}^{-1}\))

\(A_\mathrm{R2}\)

First refractivity virial coefficient of component 2 (\(\text{ m}^{3}\cdot \text{ mol}^{-1}\))

\(B_{11}\)

Second pressure virial coefficient of component 1 (\(\text{ m}^{3}\cdot \text{ mol}^{-1}\))

\(B_{22}\)

Second pressure virial coefficient of component 2 (\(\text{ m}^{3}\cdot \text{ mol}^{-1}\))

\(B_{12}\)

Mixed second pressure virial coefficient (\(\text{ m}^{3}\cdot \text{ mol}^{-1}\))

\(B_\mathrm{R11}\)

Second refractivity virial coefficient of component 1 (\(\text{ m}^{6}\cdot \text{ mol}^{-2}\))

\(B_{\mathrm{R}22}\)

Second refractivity virial coefficient of component 2 (\(\text{ m}^{6}\cdot \text{ mol}^{-2}\))

\(B_{\mathrm{R}12}\)

Second refractivity virial coefficient of the mixture (\(\text{ m}^{6}\cdot \text{ mol}^{-2}\))

\(C_{111}\)

Third pressure virial coefficient of component 1 (\(\text{ m}^{6}\cdot \text{ mol}^{-2}\))

\(C_{222}\)

Third pressure virial coefficient of component 2 (\(\text{ m}^{6}\cdot \text{ mol}^{-2}\))

\(C_{112},\, C_{122}\)

Mixed third pressure virial coefficients (\(\text{ m}^{6}\cdot \text{ mol}^{-2}\))

\(D_{12}\)

Binary diffusion coefficient (\(\text{ m}^{2}\cdot \text{ s}^{-1}\))

\(k\)

Order of interference fringes

\(L\)

Height (m)

\(l\)

Depth (m)

\(\Delta L_\mathrm{opt}(z,t)\)

Optical path length difference (m)

\(\Delta n\)

Refractive index difference

\(n_{1,0}\)

Refractive index of component 1 prior to diffusion

\(n_{2,0}\)

Refractive index of component 2 prior to diffusion

\(n_\mathrm{mix}\)

Refractive index of the mixture

\(p\)

Pressure (Pa)

\(T\)

Temperature (K)

\(t\)

Time (s)

\(x\)

Mole fraction

\(x_{2}\)

Mole fraction of component 2

\(z\)

Local coordinate (m)

\(\lambda \)

Wavelength (m)

\(\rho _{1}\)

Partial molar density of component 1 (\(\text{ mol}\cdot \text{ m}^{-3}\))

\(\rho _{2}\)

Partial molar density of component 2 (\(\text{ mol}\cdot \text{ m}^{-3}\))

\(\rho _{2,0}\)

Molar density of component 2 prior to diffusion in lower half (\(\text{ mol}\cdot \text{ m}^{-3}\))

\(\rho _\mathrm{mix}\)

Molar density of the mixture (\(\text{ mol}\cdot \text{ m}^{-3}\))

\(\tau \)

Characteristic diffusion time (s)

Notes

Acknowledgments

This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) by funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) within the German Initiative for Excellence and via the project “diffusion coefficient” (grants FR 1709/10-1 and BI 1389/2-1). The authors thank the working group of Professor E. Vogel from the Institute of Chemistry at the University of Rostock for the transfer of and the introduction to the diffusion apparatus, which allowed the continuation of the experimental investigations in Erlangen.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • T. Kugler
    • 1
    • 2
  • B. Jäger
    • 3
  • E. Bich
    • 3
  • M. H. Rausch
    • 1
    • 2
  • A. P. Fröba
    • 1
    • 2
  1. 1.Erlangen Graduate School in Advanced Optical Technologies (SAOT)Friedrich-Alexander-University Erlangen-Nürnberg ErlangenGermany
  2. 2.Institute of Engineering Thermodynamics (LTT)Friedrich-Alexander-University Erlangen-Nürnberg ErlangenGermany
  3. 3.Institute of ChemistryUniversity of Rostock RostockGermany

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