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Separation Process Engineering: Includes Mass Transfer Analysis, Third Edition by Phillip C. Wankat

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15.2.3 Unsteady Binary Fickian Diffusion with No Convection (Optional)

We can also study unsteady diffusion in dilute systems. The classic unsteady-state diffusion problem is diffusion with no convection in the direction of diffusion in an infinitely thick slab. The entire slab is initially at concentration Cinitial, and at t = 0, the z = 0 face of the slab is set to C = C0 At the far end of the slab, z → ∞, the concentration is CA,∞ = Cinitial for all times; thus, the slab is so thick that the far end is unaffected by the diffusion into the slab. We will see shortly that with ordinary liquid diffusion coefficients, the slab really does not need to be too thick to keep the far end at the initial concentration. For a segment of thickness Δz, the ...

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