A Combined diffusion coefficient for gas mixture

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The discussion focuses on simulating gas mixtures, specifically Fe vapor in Argon, and calculating the mole fractions and diffusion fluxes involved. The participant references two academic papers to support their calculations and understanding of diffusion behavior. They note that Fe vapor diffuses from areas of high concentration to low concentration and from high to low temperature. A point of confusion arises regarding the temperature diffusion coefficient's sign change, raising the question of whether Argon diffuses from low to high temperature. Clarification on this aspect is sought from the referenced literature on transport phenomena.
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Is the diffusion direction from high concentration to low concentration and from high temperature to low temperature?
Hi. I am starting to do a gas mixture simulation. I learn the fundamentals from a paper. (doi: 10.1088/0022-3727/43/2/022001)
For a gas mixture (Fe vapor in Argon), the mole fraction of Fe vapor is calculated by,
1698340196300.png
and the diffusion flux JFe is given by,
1698340272926.png

x_ar is the mole fraction of Argon; T is the temperature; P is the pressure; E is the electric field.
It seems like Fe vapor diffuses from high concentration of Fe vapor to low concentration (grad x_Ar) and from high temperature to low temperature (- grad T).

If we calculates the mole fraction of Argon not Fe vapor, this paper (doi: 10.1007/BF01459700) says these coefficients follow this rule,
1698340760935.png

I don't understand why the temperature diffusion coefficient change the sign? Does it mean the argon diffuses from low temperature to high temperature?
 
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See Transport Phenomena by Bird, Stewart, and Lightfoot.
 
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