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Development of a Unifying Framework for the Restrictions in Multi-component Diffusion Close to Equilibrium

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Abstract

In this work a unifying framework is developed for multi-component diffusion close to equilibrium by proposing additional restrictions for the Fickian diffusion coefficients such as the Onsager reciprocal relations. Moreover, it is shown that these additional restrictions can explain the discrepancy, reported in the literature, of calculating negative concentrations in Fickian ternary free diffusion observed even if the second thermodynamic law constraints and the phase stability criteria are satisfied. It is believed that this work could be used to further investigate multi-component diffusion.

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Abbreviations

B ij :

Auxiliary parameters

c i :

Molar concentration

c T :

Total molar concentration

D ij :

Fickian diffusion coefficients

\( \bar{D}_{ij} \) :

Binary Maxwell–Stefan diffusion coefficient

\( D_{i}^{\text{T}} \) :

Multi-component thermal diffusion coefficient of the i-th substance

F i :

External forces per mole

G ij :

Auxiliary parameters

\( J_{i}^{ \ne } \) :

Molar flux of the i-th substance relative to an arbitrary velocity

\( J_{i}^{*} \) :

Molar flux of the i-th substance relative to the velocity of the center of mass

L :

Thickness of the solution

L ij :

Conductivity coefficients

M i :

Molecular weight of the i-th substance

P h :

Hydrostatic pressure

R :

Universal gas constant

R ij :

Resistance (friction) coefficients for diffusion

S :

Rate of entropy production per unit volume

T :

Absolute temperature

t :

Time

u i :

Volume fraction of the i-th substance

V i :

Partial molar volume of the i-th substance

v i :

Velocity of the i-th substance

v ≠ :

Arbitrary reference velocity

w i :

Weighting factors whose sum is equal to unity

X i :

Thermodynamic driving force for diffusion

X ′ i :

Transformed thermodynamic driving force for diffusion

x i :

Mole fraction of the i-th substance

z :

Axial length, m

a i :

Activity of the i-th substance

\( \gamma_{i} \) :

Activity coefficient of the i-th substance

δ ij :

Kronecker delta

\( \mu_{i} \) :

Chemical potential of the i-th substance

\( \Uppsi \) :

Dissipation function

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  1. Department of Chemistry, Aristotle University of Thessaloniki, P.O. Box 454, Plagiari Thes, 57500, Epanomi, Greece

    George D. Verros & George K. Xentes

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  1. George D. Verros
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Correspondence to George D. Verros.

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Verros, G.D., Xentes, G.K. Development of a Unifying Framework for the Restrictions in Multi-component Diffusion Close to Equilibrium. J Solution Chem 43, 59–70 (2014). https://doi.org/10.1007/s10953-013-0018-6

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