Ignoring cross-diffusion, diffusive mass fluxes down chemical potential gradients can be described by the equation (I am working from de Groot and Mazur's 1984 text on non-equilibrium thermodynamics):(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{\partial C_k}{\partial t} = L_{kk}\frac{\partial (\mu_k-\mu_n)}{\partial x}[/itex]

where [itex]C_k[/itex] is the concentration of species [itex]k[/itex], [itex]L_{kk}[/itex] is a phenomenological coefficient, [itex]\mu_k[/itex] is the chemical potential of species k, [itex]\mu_n[/itex] is the chemical potential of a different species, and [itex]x[/itex] is distance.

However, if the chemical potential of a species is high (relative to others) when its concentration approaches zero, this equation will predict that a flux will continue to remove the component, resulting in negative concentrations. Mass conservation is "preserved" because the concentration of a different component will then be greater than 1, but this is obviously still incorrect.

How can this behavior be corrected? Must you simply enforce non-negative concentrations ad hoc, or is there a more obvious method.

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# Diffusion down chemical potential gradients

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