Theory of tracer diffusion measurements in liquid systems

Simo Liukkonen, Pentti Passiniemi, Z. Noszticzius, Jussi Rastas

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The differential equation of non-steady state tracer diffusion has been solved for liquid systems with general initial and boundary conditions. On the basis of the solution the measurement of the tracer diffusion coefficient can be reduced, regardless of the geometry of the cell, to the determination of the eigenvalues, of which the first one only is necessary after a certain time. An obvious distinction can be made between relative and absolute measuring methods. The planning of new experiments is possible if the roles of the initial condition and the counting efficiency are appreciated. As a special example of a three dimensional diffusion cell, a slightly conical open-ended capillary has been analysed. To obtain 0.1% accuracy with the 0.8 mm diameter capillary, a variation of only 0.001 mm in the diameter can be allowed. The space dependent tracer diffusion coefficient has also been treated. The tracer diffusion current density and the corresponding differential equation of continuity, which take into account the unequal equilibrium distribution of the tracer concentration in the system, have been derived. The solution of the differential equation for this continuous multiphase system has been obtained in an analogous manner to that of the single phase. Here again after a certain time the first eigenvalue can be determined experimentally. However, the eigenvalue may include only a certain part of the tracer diffusion coefficient which is independent on the positional coordinates. In this case the form D = D0f(r) is used for the tracer diffusion coefficient with the constant D0.

Original languageEnglish
Pages (from-to)2836-2843
Number of pages8
JournalJournal of the Chemical Society, Faraday Transactions 1: Physical chemistry in Condensed Phases
Volume72
DOIs
Publication statusPublished - 1976

Fingerprint

tracers
Liquids
liquids
diffusion coefficient
Differential equations
differential equations
eigenvalues
cells
continuity
planning
counting
Current density
Boundary conditions
boundary conditions
current density
Planning
Geometry
geometry
Experiments

ASJC Scopus subject areas

  • Chemistry(all)

Cite this

Theory of tracer diffusion measurements in liquid systems. / Liukkonen, Simo; Passiniemi, Pentti; Noszticzius, Z.; Rastas, Jussi.

In: Journal of the Chemical Society, Faraday Transactions 1: Physical chemistry in Condensed Phases, Vol. 72, 1976, p. 2836-2843.

Research output: Contribution to journalArticle

@article{cc958973dbc34c5f970c69128043eede,
title = "Theory of tracer diffusion measurements in liquid systems",
abstract = "The differential equation of non-steady state tracer diffusion has been solved for liquid systems with general initial and boundary conditions. On the basis of the solution the measurement of the tracer diffusion coefficient can be reduced, regardless of the geometry of the cell, to the determination of the eigenvalues, of which the first one only is necessary after a certain time. An obvious distinction can be made between relative and absolute measuring methods. The planning of new experiments is possible if the roles of the initial condition and the counting efficiency are appreciated. As a special example of a three dimensional diffusion cell, a slightly conical open-ended capillary has been analysed. To obtain 0.1{\%} accuracy with the 0.8 mm diameter capillary, a variation of only 0.001 mm in the diameter can be allowed. The space dependent tracer diffusion coefficient has also been treated. The tracer diffusion current density and the corresponding differential equation of continuity, which take into account the unequal equilibrium distribution of the tracer concentration in the system, have been derived. The solution of the differential equation for this continuous multiphase system has been obtained in an analogous manner to that of the single phase. Here again after a certain time the first eigenvalue can be determined experimentally. However, the eigenvalue may include only a certain part of the tracer diffusion coefficient which is independent on the positional coordinates. In this case the form D = D0f(r) is used for the tracer diffusion coefficient with the constant D0.",
author = "Simo Liukkonen and Pentti Passiniemi and Z. Noszticzius and Jussi Rastas",
year = "1976",
doi = "10.1039/F19767202836",
language = "English",
volume = "72",
pages = "2836--2843",
journal = "Physical Chemistry Chemical Physics",
issn = "1463-9076",
publisher = "Royal Society of Chemistry",

}

TY - JOUR

T1 - Theory of tracer diffusion measurements in liquid systems

AU - Liukkonen, Simo

AU - Passiniemi, Pentti

AU - Noszticzius, Z.

AU - Rastas, Jussi

PY - 1976

Y1 - 1976

N2 - The differential equation of non-steady state tracer diffusion has been solved for liquid systems with general initial and boundary conditions. On the basis of the solution the measurement of the tracer diffusion coefficient can be reduced, regardless of the geometry of the cell, to the determination of the eigenvalues, of which the first one only is necessary after a certain time. An obvious distinction can be made between relative and absolute measuring methods. The planning of new experiments is possible if the roles of the initial condition and the counting efficiency are appreciated. As a special example of a three dimensional diffusion cell, a slightly conical open-ended capillary has been analysed. To obtain 0.1% accuracy with the 0.8 mm diameter capillary, a variation of only 0.001 mm in the diameter can be allowed. The space dependent tracer diffusion coefficient has also been treated. The tracer diffusion current density and the corresponding differential equation of continuity, which take into account the unequal equilibrium distribution of the tracer concentration in the system, have been derived. The solution of the differential equation for this continuous multiphase system has been obtained in an analogous manner to that of the single phase. Here again after a certain time the first eigenvalue can be determined experimentally. However, the eigenvalue may include only a certain part of the tracer diffusion coefficient which is independent on the positional coordinates. In this case the form D = D0f(r) is used for the tracer diffusion coefficient with the constant D0.

AB - The differential equation of non-steady state tracer diffusion has been solved for liquid systems with general initial and boundary conditions. On the basis of the solution the measurement of the tracer diffusion coefficient can be reduced, regardless of the geometry of the cell, to the determination of the eigenvalues, of which the first one only is necessary after a certain time. An obvious distinction can be made between relative and absolute measuring methods. The planning of new experiments is possible if the roles of the initial condition and the counting efficiency are appreciated. As a special example of a three dimensional diffusion cell, a slightly conical open-ended capillary has been analysed. To obtain 0.1% accuracy with the 0.8 mm diameter capillary, a variation of only 0.001 mm in the diameter can be allowed. The space dependent tracer diffusion coefficient has also been treated. The tracer diffusion current density and the corresponding differential equation of continuity, which take into account the unequal equilibrium distribution of the tracer concentration in the system, have been derived. The solution of the differential equation for this continuous multiphase system has been obtained in an analogous manner to that of the single phase. Here again after a certain time the first eigenvalue can be determined experimentally. However, the eigenvalue may include only a certain part of the tracer diffusion coefficient which is independent on the positional coordinates. In this case the form D = D0f(r) is used for the tracer diffusion coefficient with the constant D0.

UR - http://www.scopus.com/inward/record.url?scp=0038290229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038290229&partnerID=8YFLogxK

U2 - 10.1039/F19767202836

DO - 10.1039/F19767202836

M3 - Article

AN - SCOPUS:0038290229

VL - 72

SP - 2836

EP - 2843

JO - Physical Chemistry Chemical Physics

JF - Physical Chemistry Chemical Physics

SN - 1463-9076

ER -