Maxwell-Stefan approach Capillary

So far we have analysed the two systems using the Maxwell-Stefan approach the steady state analysis of the Stefan tube and the transient analysis of the Loschmidt s tube, and they are conveniently used to study the diffusion characteristic of the system. Here, we consider another example which is also useful in the determination of diffusion characteristics. This system is the two bulb method, in which a small capillary tube or a bundle of capillaries is bounded by two well-mixed reservoirs as shown in Figure 7.2-3. 

We have presented in this chapter a systematic approach of Maxwell-Stefan approach in dealing with flow in homogeneous media as well as inside a capillary or porous media. The approach using the concept of friction is elegant, and it puts the various flow mechanisms under the same framework. For large pore space, the Maxwell-Stefan approach is comprehensive, and it is able to describe experimental results, such as the uphill diffusion, which the traditional Pick s law approach can... 

The description of the separation of multicomponent mixtures requires a more complex approach, for example by using Maxwell-Stefan methodology. However, the real membrane often assumes a more complex structure, in which, beside the microporous zeolite layer, the mesoporosity of the intra-crystalline-defects and of the underlying support can play an important role, especially when the capillary condensation phenomenon can occur, as in the case of the permeation of vapour. Kondo and Kita (Kondo and Kita, 2010) attempted an interpretation of the dehydration process by including narrow non-zeolitic pores into the support. The water molecules in the feed selectively adsorbed in zeolite pores are then transported to the non-zeolitic pore, where they are released in the permeate side of the membrane. 

To illustrate the solution procedure of this Stefan-Maxwell approach, we apply it to the experimental results of Duncan and Toor (1962). The two well-mixed bulbs used have volumes of 7.8 x 10 and 7.86 x 10 m, respectively, and the capillary tube has a length and a diameter of 0.086 m and 0.00208 m, respectively. The operating conditions are 35 and 101.3 kPa. Duncan and Toor (1962) used a ternary system of hydrogen, nitrogen and carbon dioxide in their experiment. We use the following numerical values to denote the three components used in their experiment 1-hydrogen 2-nitrogen and 3-carbon dioxide. 

Stefan-Maxwell Approach for Bulk-Knudsen Diffusion in Complex System of Capillaries... 

We have seen in Section 8.6 that the analysis using the Stefan-Maxwell approach is readily carried out for the case of a simple capillary, namely a uniformly sized capillary. In this section we will extend the analysis to more complex pore networks and will consider the three cases ... 

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