International Journal of Thermophysics

, Volume 36, Issue 10–11, pp 3116–3132 | Cite as

Systematic Study of Mass Transfer in a Loschmidt Cell for Binary Gas Mixtures

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

Abstract

The present paper reports on efforts to explain discrepancies which were found in concentration-dependent binary diffusion coefficient data determined with a Loschmidt cell combined with holographic interferometry using pure gases prior to the diffusion process. While the binary diffusion coefficient data which are determined in the upper half-cell decrease with the mole fraction of the heavier component, those determined in the lower half-cell increase. The reason for such discrepancies, which can also be found in other literature data obtained with interferometric gas analysis methods, is not clear. Therefore, systematic experimental and theoretical investigations on the Loschmidt experiment and the applied evaluation procedure were performed. Furthermore, the influence of different driving forces on the particle flux was examined. Although the reason for the discrepancies between the measurement data determined in each half-cell could not been clarified, various reasons that have been debated in the literature could be excluded. Moreover, experiments using a gas mixture in one of the half-cells suggested that the evaluation procedure is most likely to be the reason for the observed discrepancies.

Keywords

Binary diffusion coefficient Concentration dependence Holographic interferometry Loschmidt cell 

Symbols

\(b_{i}\)

Acceleration of component i due to external forces (\(\text {m}{\cdot }\text {s}^{-2}\))

\(D_{12}\)

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

g

Acceleration due to gravity (\(\text {m}{\cdot }\text {s}^{-2}\))

\(J_{1}\)

Molar diffusion flux of component 1 (\(\text {mol}{\cdot }\text {m}^{-2}{\cdot }\text {s}^{-1}\))

\(\tilde{J}_1\)

Total molar flux of component 1 (\(\text {mol}{\cdot }\text {m}^{-2}{\cdot }\text {s}^{-1}\))

\(k_\mathrm{T}\)

Thermal diffusion ratio

L

Height of the Loschmidt cell (m)

l

Depth of the Loschmidt cell (m)

M

Molar mass (\(\text {kg}{\cdot }\text {mol}^{-1}\))

\(\Delta M\)

Molar mass difference between components 1 and 2 (\(\text {kg}{\cdot }\text {mol}^{-1}\))

\(M_{\mathrm{i}}\)

Molar mass of component i (\(\text {kg}{\cdot }\text {mol}^{-1}\))

\(m_{\mathrm{i}}\)

Molecular mass of component i (kg)

\(n_{1}\)

Amount of substance 1 (mol)

p

Pressure (Pa)

\(r_{1}\)

Source or sink of component 1 (\(\text {mol}{\cdot }\text {s}^{-1}{\cdot }\text {m}^{-3}\))

s

Width of the Loschmidt cell (m)

T

Temperature (K)

t

Time (s)

\(V_\mathrm{l}\)

Volume of lower half-cell (\(\text {m}^{3}\))

\(V_{\mathrm{u}}\)

Volume of upper half-cell (\(\text {m}^{3}\))

v

Molar convective or molar averaged velocity (\(\text {m}{\cdot }\text {s}^{-1}\))

\(x_\mathrm{i}\)

Mole fraction of component i

z

Vertical coordinate (m)

\(\rho _1\)

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

\(\Delta \rho _1\)

Partial molar density difference of component 1 between the half-cells (\(\text {mol}{\cdot }\text {m}^{-3}\))

\(\rho _{\mathrm{1,0l}}\)

Molar density of component 1 prior to diffusion in lower half-cell (\(\text {mol}{\cdot }\text {m}^{-3}\))

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

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

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

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

\(\rho _{\mathrm{m,i}}\)

Mass density of component i (\(\text {kg}{\cdot }\text {m}^{-3}\))

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

Mass density of the mixture (\(\text {kg}{\cdot }\text {m}^{-3}\))

\(\tau \)

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 2 as well as BI 1389/2-1 and 2).

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Copyright information

© Springer Science+Business Media New York 2015

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-NurembergErlangenGermany
  2. 2.Institute of Engineering Thermodynamics (LTT)Friedrich-Alexander-University Erlangen-NurembergErlangenGermany
  3. 3.Institute of ChemistryUniversity of RostockRostockGermany

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