The Two Bulb Diffusion Cell

The molar density c is 39.5 mol/m. Hence, the fluxes through the tube are 

The flux of hydrogen (component 1) is not too different from the flux estimated using the linearized equations in Example 5.3.1. However, the effective diffusivity method predicts a very small flux of nitrogen (component 2), a result quite different from the predictions of the linearized theory. This, of course, is because the effective diffusivity method ignores the contribution due to the driving forces of the other components. We will investigate the consequences of this prediction in Example 6.4.1.  

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. 

With the molar fluxes given by Eqs. 6.3.1 we may write the differential mass balances for the two bulb cell, Eq. 5.4.1 as 

The material balance relation (Eq. 5.4.2) is used to eliminate the mole fractions dr, 

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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. 

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). 

Let us now proceed to see if the Wilke effective diffusivity method is able to model the diffusional process in the two bulb diffusion cell experiment of Duncan and Toor (1962). For convenience, we repeat the following information from Example 5.4.1. The two bulbs in the apparatus built by Duncan and Toor had volumes of 77.99 and 78.63 cm3, respectively. The capillary tube joining them was 85.9 mm long and 2.08 mm in diameter. The entire device... 

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... 

Since thermodynamic nonidealities are of the essence for phase separation in liquid-liquid systems, and such nonidealities contribute to multicomponent interaction effects, it may be expected that liquid-liquid extraction would offer an important test of the theories presented in this book. Here, we present some experimental evidence to show the significance of interaction effects in liquid-liquid extraction. The evidence we present is largely based on experiments carried out in a modified Lewis batch extraction cell (Standart et al., 1975 Sethy and Cullinan, 1975 Cullinan and Ram, 1976 Krishna et al., 1985). The analysis we present here is due to Ej-ishna et al. (1985). The experimental system that will be used to demonstrate multicomponent interaction effects is glycerol(l)-water(2)-acetone(l) this system is of Type I. The analysis presented below is the liquid-liquid analog of the two bulb gas diffusion experiment considered in Section 5.4. 

Example 1.5.3 Consider the thermal diffusion separation of a gas mixture of H2 and N2 initially present with a hydrogen mole fraction Xif in a two-bulb cell. The volumes of the two bulbs are Vi and V2. Let the uniform temperature of the two-bulb cell be changed so that the bulb of volume V] now has a temperature Ti while the other one is at T2 (Ti > T2) (Figure 1.1.3, example 111). Assuming that this is a case of close separation such that Xn Xj/ we obtain... 

To see which reference velocity is easiest to use, we consider the diffusion apparatus shown in Fig. 3.1 -2. This apparatus consists of two bulbs, each of which contains a gas or liquid solution of different composition. The two bulbs are connected by a long, thin capillary containing a stopcock. At time zero, the stopcoek is opened after an experimentally desired time, the stopcock is closed. The solutions in the two bulbs are then analyzed, and the concentrations are used to calculate the diffusion coefficient. The equations used in these calculations are identical with those used for the diaphragm cell. 

Example 1.4.1 Close separation in thermal dijfusion of an isotopic mixture Isotopic mixtures are difficult to separate since isotopes are very similar to one another. One method sometimes adopted is thermal diffusion. Consider a two-bulb cell as shown in example III of Figure 1.1.3, with one bulb at 300 °C and the other at 23 °C. Initially, both bulbs at the same temperature, 23 °C, contained an equimolar mixture of and C H4. After the temperature of bulb 1 was raised to 300 ° C, the mole fractions of C H4 in bulbs 1 and 2 were found to be 0.5006 and 0.4994, respectively. The separation factor ai2 for C H4 as species 1, with the hot bulb as region 1, is given by... 

We have observed that countercurrent separation devices achieve considerable separation under driving forces such as chemical potential gradient and the external force of a centrifugal force field. As illustrated in equations (3.1.44) and (3.1.50), there is another type of force, the thermal diffusion force. The separation achieved thereby in a closed two-bulb cell has been illustrated in Section 4.2.5.I. We have already illustrated conceptually how thermal diffusion can achieve separation in a countercurrent column via Figures 8.1.1(a)-(h). For UF isotope separation, however, the radial separation factor in a two-bulb cell is much smaller than for other isotope separation processes. In a countercurrent column, this value is reduced by about 50%. As a result, thermal diffusion columns are not used at all for any practical/large-scale separation. More details on thermal diffusion columns are available in Pratt (1967, chap, viii) and Benedict et al. (1981, pp. 906-915), where one can find information on the primary references. 

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