Two-bulb cell

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... 

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... 

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... 

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. 

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. ... 

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. 

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 ]... 

Segovia, S., Valencia, A., Cales Jose, M., and Guillamon, A, 1986, Effects of sex steroids on the development of two granule cell populations in the rat accessory ol ctoty bulb, Dev. Brain Res. 30 283-286. 

It appears that the two receptor cell layers in the vomeronasal epithelium relate directly to the rostral/caudal division of the accessory olfactory bulb. In mice and rats, apical and basal receptor cell layers differ in their pattern of projections to the accessory olfactory bulb. The apical, Gaj2-expressing cells project to the rostral half of the accessory olfactory bulb, and the basal, Ga -expressing cells project to the caudal half (Jia Halpern, 1996). The boundary between these two areas matches that described in the lectin- and antibody-labeling studies. Further, the output cells of the accessory olfactory bulb appear to arborize predominantly or exclusively within either the rostral or the caudal portion, suggesting that the two halves of the accessory olfactory bulb may form separate functional pathways carrying information solely or mainly from each of the two receptor families (Jia, Goldman Halpern, 1997). 

For example, consider the voltaic cell in Figure 16.9. In this cell, a solid strip of Zn is placed into a Zn(N03)2 solution to form a half-cell. Similarly, a solid strip of Cu is placed into a Cu(N03)2 solution to form a second half-cell. Then the two half-cells are coimected by attaching a wire from the Zn, through a lightbulb or other electrical device, to the copper. The natural tendency of Zn to oxidize and Cu to reduce results in the flow of electrons through the wire. The flowing electrons constitute an electrical current that lights the bulb. 

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