Multicomponent separation capability

We will now study the multicomponent separation capability of a discontinuous profile (shown in Figure 3.2.2 by the dashed line). The particular discontinuous profile we have chosen has a maximum value of at all values of 0 < z < Z, but at z = Z, abruptly drops to tbe value of zero and stays at that level beyond l It is thus a step function. Such a profile can be obtained in practice by having = 0 or F = 0 and maintaining two different phases or solvents in the two regions 0 < z < Z and Iz governing equation for the concentration distribution of species 1 is then obtained from equation (3.2.10) as the simpler... 

We observe then that no more than two species may be imperfectly separated when ( h) is zero, and that only one pure species may be obtained with a poor recovery. To determine what will happen in the other solvent in the region z > Z, it is better to start imagining what will happen if the initial solute mixture pulse were introduced at z = Z (Figure 3.2.5B). If we can assume that a different sequence of profiies of species will be observed in each solvent vessel, then one can get at the most two pure species, one in each vessei from the furthest region from the solute introduction point. It is clear that this type of discontinuous potential profile can at the most separate two pure species and thus inherently lacks multicomponent separation capability. When the diffosion proi ess ceases in such a system after an adequate time has elapsed, the species are going to distribute themselves between the two solvents in a... 

Consider, in addition, the nature of the force beli used in separation. Since there is adsorption and/or desorption of solutes between the mobile fluid and the stationary solid phases, the potential profile under consideration for each solute is discontinuous, a simple step function (see Figure 3.2.2) there are no external forces. According to Section 3.2, such a system in a closed vessel without any flow does not have any multicomponent separation capability. Multicomponent separation capability is, however, achieved in elution chromatography by having bulk flow perpendicular to the direction of the discontinuous chemical potential profile. The velocity here functions exactly like the quantity (- ) in equation (3.2.37). 

At the beginning of each of Sections 8.1, 8.2 and 8.3, a brief description of the overall flow patterns of the two phases/regions in various separation technologies/pro-cesses will be provided. This description will be followed by a brief consideration of the multicomponent separation capability of the particular bulk flow vs. force(s) configuration. Then detailed treatments of individual separation... 

In the following part of this section, we provide simple mathematical descriptions of a few common features of two-phase/two-region countercurrent devices, specifically some general considerations on equations of change, operating lines and multicomponent separation capability. Sections 8.1.2, 8.1.3, 8.1.4, 8.1.5 and 8.1.6 cover two-phase systems of gas-Uquid absorption, distillation, solvent extraction, melt crystallization and adsorption/SMB. Sections 8.1.7, 8.1.8 and 8.1.9 consider the countercurrent membrane processes of dialysis (and electrodialysis), liquid membrane separation and gas permeation. Tbe subsequent sections cover very briefly the processes in gas centrifuge and thermal diffusion. 

In the following developments, we rely on the results of Section 6.2.1.1 and identify the equations of change of concentration of a species i in a countercurrent two-region/two-phase system we focus on two-phase systems. Next we consider the equations for operating lines in such devices. The multicomponent separation capability of sucb systems is treated next in tbe context of a two-pbase system. 

Multicomponent separation capability in a device with a countercurrent flow system... 

We now focus on the multicomponent separation capability of a countercurrent flow configuration in a two-phase system. For two phases y = 1, 2 moving with superficial velocities of vifj and V2fj in the z-direction, an overall balance of species i in both phasesy = 1,2 is obtained from equation (6.2.34) as... 

We treat three aspects here governing equations of change, operating lines and multicomponent separation capability. The equations of change are considered first... 

A few less common perpendicular flow techniques are not used to generate multicomponent separations, although they are inherently capable of doing so. These techniques include the thermogravitational column [21] and electrodecantation [22]. Here the extended path serves to enhance the selectivity generated by the field and to allow the collection of two enriched or separated fractions at the two extremes of the flow coordinate. 

In comparing separation techniques, we generally find a striking difference in methods based on continuous (c) chemical potential profiles and those involving discontinuous (d or cd) profiles. There is, for example, a glaring contrast in instrumentation, applications, experimental techniques, and the capability for multicomponent separations between the two basic static systems, Sc (e.g., electrophoresis) and Sd (e.g., extraction). Similarly, there... 

For ail species moving in a given direction in a coiumn, the solution of this equation wiii indicate that, at that coiumn exit, aii such species wiii appear/exist therefore multicomponent separation is not possibie. Oniy a binary separation is possible with one species moving in the opposite direction in the column and therefore available as a pure species. This is the primary reason why we will see that a countercurrent colutnn used for steady state processes such as distillation, absorption, extraction, crystallization, etc., separates a binary mixture only. For temany mixture separation, two columns are needed. Three columns are employed to separate a four-component mixture (see Chapter 9 for various schematics). However, if a feed sample injection is made, as in elution chromatography, into a mobile phase in countercurrent flow vis-k-vis another mobile phase, transient multicomponent separation would appear to be feasible. If pulse injection of one phctse containing feed is introduced countercurrent to the other phase, it may be possible to achieve a multi-component separation capability (as is tme for cocmrent flow, considered in Section 8.2). 

All these methods give similar results but their sensitivities and resolutions are different. For example, UV-Vis spectrophotometry gives good results if a single colorant or mixture of colorants (with different absorption spectra) were previously separated by SPE, ion pair formation, and a good previous extraction. Due to their added-value capability, HPLC and CE became the ideal techniques for the analysis of multicomponent mixtures of natural and synthetic colorants found in drinks. To make correct evaluations in complex dye mixtures, a chemometric multicomponent analysis (PLS, nonlinear regression) is necessary to discriminate colorant contributions from other food constituents (sugars, phenolics, etc.). 

The need to limit the maximum temperature rise has resulted in two main types of apparatus, illustrated in Fig. 20-25. The first consists of multicomponent ribbon separation units—apparatus capable of separating small quantities of mixtures which may contain few or many species. In general, such units operate with high voltages, low... 

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