Loschmidt tube

Another device used to study diffusion and to measure diffusion coefficients is the Loschmidt tube illustrated in Figure 5.6. Two tubes containing fluids with different concentrations are brought together at time t = 0 and the fluids allowed to interdiffuse. After some time the tubes are separated and the compositions measured. 

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... 

Arnold and Toor (1967) investigated diffusional interaction effects in a Loschmidt tube of the kind described above. The system they used was methane (l)-argon (2)-hydrogen (3). The diffusion tube had a length of = 60 m . At the temperature (34°C) and... 

Figure 5.7. Composition-time history in Loschmidt tube diffusion experiment. Experimental data from Arnold (1965).

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. 

SOLUTION As in the preceding example, none of the simple effective diffusivity formulas are applicable to the situation in the Loschmidt tube. We will proceed with the effective diffusivity formula of Wilke that gives... 

Figure 6.4. Comparison between Loschmidt tube experiments of Arnold and Toor (1967) and the composition trajectories predicted by the linearized theory and effective diffusivity methods.

In an isobaric closed system like the diffusion cell or Loschmidt tube (see Chapter 5), any... 

The Loschmidt tube is simply a tube with an impermeable partition separating the two sections of the tube (Figure 8.3-1). Initially, the partition is in the position that gases in the two sections do not mix with each other. Here we shall assume that the total pressure is the same in both sections of the tube, and the initial compositions are different in the two parts of the tube. At time t = 0, the partition is removed and the diffusion process is started. 

Multiplying the above equation by Ac, where A is the cross-sectional area of the Loschmidt tube and c (the total molar concentration), we obtain what is known as the overall mass balance equation ... 

Methane/Argon/Hydrogen diffusion in the Loschmidt tube... 

The constitutive Maxwell-Stefan flux equations are the same as those presented in the last section (Section 8.3) because in this case to maintain the constant pressure of the closed system the sum of all fluxes must be zero, the same requirement as that in the Loschmidt tube. The flux equations are given by eqs. (8.3-7) with the matrix B given by eq. (8.3-6). 

For the purpose of programming this problem in MATLAB language, we define the following concentration matrices for the two sections of the Loschmidt tube. 

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