Two-bulb diffusion cell

The two bulb diffusion cell is a simple device that can be used to measure diffusion coefficients in binary gas mixtures. Figure 5.3 is a schematic of the apparatus. Two vessels containing gas mixtures with different compositions are connected by a capillary tube. At the start of the experiment (at t = 0), the valve is opened and the gases in the two bulbs allowed to diffuse along the capillary tube. Samples from each bulb are taken after some time and this information is used to calculate the binary diffusion coefficient. 

A set of multicomponent diffusion experiments in a two bulb diffusion cell apparatus was carried out by Duncan and Toor (1962) in an investigation of diffusional interaction effects. The two bulbs in their apparatus had volumes of 77.99 and 78.63 cm, respectively. The capillary tube joining them was 85.9 mm long and 2.08 mm in diameter. The entire device was placed in a water bath at 35.2°C. The system used by Duncan and Toor was the ternary hydrogen (l)-nitrogen (2)-carbon dioxide (3). The initial concentration in each cell is... 

Figure 5.4. Composition-time history in two bulb diffusion cell. Experimental data from Duncan (1960).

We have carried out similar computations covering the entire duration of three similar experiments that were carried out by Duncan and Toor (1962). The results of these calculations are shown in the triangular diagram, Figure 5.5, along with the data of Duncan (1960). We see that for all three experiments theoretical profiles are in good agreement with the data. This experiment (and others like it) provides support for the theoretical considerations of earlier chapters and the successful prediction of the concentration time history in the two bulb diffusion cell is a valuable test of the linearized theory of multicomponent diffusion. ... 

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. 

Let us illustrate the calculation of the effective diffusivity and the molar fluxes for the conditions existing at the start of the two bulb diffusion cell experiment of Duncan and Toor discussed in Examples 5.3.1 and 5.4.1. The components are hydrogen (1), nitrogen (2), and carbon dioxide (3) and the values of the diffusion coefficients of the three binary pairs at 35.2° C and 1-atm pressure were... 

SOLUTION Strictly speaking none of the limiting cases of the two general expressions (Eqs. 6.1.10-6.1.14) applies to the two bulb diffusion cell. Nevertheless, we will proceed to calculate > and the molar fluxes through the capillary tube using Wilke s method (Eq. 6.1.14). 

We derived expressions for the concentration time history in the two bulb diffusion cell in Section 5.4. Here we present the corresponding problem solved using an effective diffusivity formulation. 

Example 6.4.1 Diffusion in a Two Bulb Diffusion Cell A Test of the Effective Diffusivity... 

A set of multicomponent diffusion experiments in a two bulb diffusion cell apparatus was carried out by Duncan and Toor (1962) in an investigation of diffusional interaction effects. In Experiment 1 the initial concentration in each cell is... 

Volume of bulb in two-bulb diffusion cell (Chapter 5) [m ]... 

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