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Consider change in composition at x1
as front advances. From the Diffusion Equation:
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As the profile
is steady in the moving frame (x'=x-vDt),
the new composition at x=x1 must be the
same as the old value vDt
behind |
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Substituting for DC(x1)
and expressing in the moving frame |
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The profile in the liquid must conform to this
equation. The solution will depend on boundary conditions. Here we have CL(x'=0)=CL*
and the condition equating the solute rejected at the front to that diffusing away into
liquid. |
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Using these two equations to evaluate the two
integration constants, the solution is |
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If the value of CL* (and hence CS*)
is identified, then a specific solution can be given. For example, if CL*=C0/k
(CS*=C0), then |
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