Watershed point

The watershed point of component i is the displacer concentration (C = w ) corresponding to the intersection of the displacer isotherm and the initial tangent to the isotherm of that component. This concept was first identified by Glueckauf [6,7]. This critical concentration is given by Eq. 9.7. No displacement of component i is possible if the displacer concentration is below its watershed point (Figure 9.5a). Under conditions where C = w, the tail of the first component will end at the front of the second component band. As the displacer concentration falls below the watershed point, the rear boimdary of the first component separates completely from the isotachic train. In this case, which is not exceptional, one or a few early eluting components appear as independent elution bands before the isotachic train. This may be impossible to avoid—for example, if the solubility of the displacer in the carrier is insufficient. 

Figure 9.5 Displacement at the watershed point of the first component, (a) Single- component isotherms with C = (b) Profiles of the zones in the ideal isotachic train.

We have seen (Figure 12.3b) that, even when the displacer concentration is above the watershed point (f.e., when the operating line is below the initial tangent of the isotherm of the first component, see Eq. 9.7 and Figiues 9.3 and 9.5), the classical isotachic train is not necessarily achieved. Figures 12.2 and 12.3 illustrate how the sample size and the displacer concentration can be manipulated to... 

See definition Chapter 9, Section 9.1.3 and Figure 9.5. The watershed point is a displacer concentration. 

Figure 12.4 Top Illustration of the watershed point. Same experimental conditions as in Figxue 12.1b, except Q and sample size, (a) Displacement chromatogram with a displacer concentration at the watershed point of the first component, Q = 85 mg/mL. Sample sizes 50, 50, and 100 mg. (b) Same conditions as in (a), except sample sizes 50, 25, and 50 mg. Bottom Illustration of the watershed point. Same experimental conditions as in Figures 12.1b and a above, except Q and sample size, (c) Illustration of the isotherms and the operating fine for (b). (d) Displacement chromatogram with a displacer concentration at the watershed point of the second component, Q = 46.4 mg/mL. Sample sizes 50,25, and 50 mg.

Finally, we note that the fact that the displacement chromatogram is carried out at the watershed point of the first component guarantees that the profile of its band will be that of an overloaded elution band, just resolved from tine isotachic band of the second component when the isotachic train is formed. As illustrated in Figure 12.4b, changing the amount of the other components in the sample, hence the width of their zones, does not affect the resolution of this overloaded elution profile with the band of the second component. Similarly, increasing the column length or the displacer concentration would not affect the resolution of the bands rmder isotachic conditions. The only way to affect the heights of the zone and, to some extent, the width of the mixed zones is to increase the concentration of the displacer. 

Watershed Point Concentration of the displacer at which the displacement of a component becomes impossible because the velocity of the displacer front is lower than the velocity of a zero concentration of that component. 

A pure thermal wave is always a shock and from Eq. (9.36) it is clear that its velocity is given by o/(l + [(1 - f)/i.]CjC ) while the velocity of the mass transfer front is given by o/ l +[(1 - e)/e]d(j dc. For the thermal wave to precede the concentration front (adsorption) therefore requires dq /dc o > Cs / Cf while for a pure thermal wave lagging the concentration front to be formed during desorption (dq /dc Q < CjCy. At the watershed point Tn), dq /dc o = CJC and the velocity of the limiting proportionate-pattern wave is the same as that of the thermal shock. A more detailed discussion of the conditions of thermal wave formation and the practical importance of this type of behavior has been given by Basmadjian. ... 

Finally, a closer examination of Figure 7.14 shows that at E values below unity, the plots veer off and asymptotically approach a constant value of R. This implies that we cannot, under these conditions, attain arbitrarily low effluent concentrations, no matter how high we set the level of solvent or adsorbent flow rate or indeed the number of stages. The value of E = 1 consequently represents an important watershed point, below which it becomes impractical or impossible to attain a desired goal. The reasons for this behavior are addressed more fully in Illustration 8.2. 

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