On the modified Stefan–Maxwell equation for isothermal multicomponent gaseous diffusion

Abstract

Understanding multicomponent gaseous diffusion in porous media is crucial to describing the transport of fuel and reaction products in the anode of a solid oxide fuel cell, for which this work was originally pursued. The Stefan–Maxwell approach provides a general theoretical framework so that measured or predicted binary diffusion coefficients may be utilized for multicomponent diffusion (for which Fick's law is invalid). This approach has since been extended to account for a porous solid structure resulting in what is usually referred to as the “modified Stefan–Maxwell equation”, which is the subject of the present work. Using a virtual experiment involving ternary diffusion and the modified Stefan–Maxwell equation, it is shown that multicomponent diffusion in the Knudsen regime (in which wall drag is significant) produces a gradient in total pressure, which then drives the diffusion of gaseous components for which there are no mole fraction gradients. To the author's knowledge, this peculiar phenomenon has not been verified by a real experiment. The analysis also shows that bulk diffusion in the present virtual experiment is equimolar, which contradicts the common assertion that Graham's relation is valid even in conditions where bulk diffusion is dominant. Finally, the present work shows the importance of the term involving the total pressure gradient in the modified Stefan–Maxwell equation. In the literature, the gradient in total pressure is often mistakenly associated only with permeation. This paper demonstrates that it is an essential part of the driving force for diffusion and its omission leads to an erroneous prediction in the present virtual experiment. A detailed derivation of the modified Stefan–Maxwell equation is also provided, underscoring the relevance of the total pressure gradient term.