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Anisotropic diffusion

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hi,
I have been going through 'Separation through the dialysis' and found that the diffusion process was chosen there is anisotropic diffusion for which diagonal matrix was selected. I am just wondering that when to chose isotropic or anisotropic diffusion. Another thing is, Partition coefficient is the ratio of concentrations for both phases at equilibrium, but which one goes to the denominator or vice-versa, I am confused about that.

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