Loschmidt tube multicomponent diffusion

An analysis of multicomponent diffusion in a Loschmidt tube was presented by Arnold and Toor (1967). The salient results of their work are summarized below. 

The equation governing unsteady-state, one-dimensional, multicomponent diffusion in the Loschmidt tube is... 

Example 5.5.1 Multicomponent Diffusion in the Loschmidt Tube Another Test... 

Equation 6.2.3 has exactly the same form as Eq. 5.1.3 for binary systems. This means that we may immediately write down the solution to a multicomponent diffusion problem if we know the solution to the corresponding binary diffusion problem simply by replacing the binary diffusivity by the effective diffusivity. We illustrate the use of the effective diffusivity by reexamining the three applications of the linearized theory from Chapter 5 diffusion in the two bulb diffusion cell, in the Loschmidt tube, and in the batch extraction cell. 

Our task here is to derive an expression that describes how the composition of a multicomponent mixture changes with time in a Loschmidt diffusion apparatus of the kind described in Section 5.5. The composition profile for a binary system is given by Eqs. 5.5.5 and 5.5.6) the solution to the binarylike multicomponent problem is given by the same expressions on replacing the binary diffusivity in those equations by the effective diffusivity. The average composition in the bottom tube after time Z, for example, is given by... 

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