Definition of separation efficiency

As observed, it is impossible to require the relevancy to the intuitive definition of separation efficiency and traditional mixing performance indices that are shown in Table 2.1. In this chapter, a new separation efficiency will be defined by making use of the information entropy on the basis that there is no discrepancy between the viewpoint of the definitions of the evaluation indices for mixing and separation operations/equipment. 

Besides, it is possible to apply the same consideration in the following discussion to the case of a flow system when the region is replaced by an outlet. (The discussion from this point until Eq. (3.11) is identical to that from Eq. (2.32) to Eq. (2.40) in the previous Chapter.) 

Under these conditions, the uncertainty regarding the component of the element that is selected is considered. Since the ratio of the volume of the /-component to the total volume of all components is VJVT, this ratio becomes the probability that the selected element is the /-component. Therefore, the amount of information that is obtained by the news that gives the information that the selected element is the /-component is expressed as 

The probability that the news described above is given is VJVT. Therefore, the amount of uncertainty regarding the component of the element that is selected is expressed by the information entropy as 

In practical operations, it is natural that the region into which each component is fed is already known. There is also a relationship between each component and each region after the beginning of the separation operation. Therefore, the amount of uncertainty described above (Eq. (3.6)) should decrease if the position from where the element is selected is known. Next, the uncertainty regarding the component of the element that is selected when the element is taken from the j-region is discussed. 

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The definition of separation efficiency known from chromatography, expressed as height equivalent to a theoretical plate (F1ETP), can be applied in the same way to CZE ... 

If we wish to consider both the separation of the solids and that of the liquid with equal emphasis, entropy gives us an ideal tool. The efficiency of the overall separation can thus be evaluated as a fraction or percentage decrease in the entropy of the system, taking the initial entropy of the suspension (from equation 18.34) as being 100%. This definition of separation efficiency has been called the entropy index and has been used widely in the Russian scientific literature ". ... 

To use the formula in Equation 38.2, it is necessary to define at what stage the two peaks representing the two masses are actually separate (Figure 38.4). The depth of the valley between the two peaks serves this purpose, with valley definitions of 5, 10, or 50%. A 5% valley definition is a much stricter criterion of separation efficiency than the 50% definition. 

Fig. 1. Definition of the efficiency of a separation procedure in a radioimmunoassy. In a perfect assay all the labeled antigen would distribute between the free and bound fractions. In practice, some of the free is classified as bound (assay blank, nonspecific binding), and some of the free will be nonimmunoreactive. The greater the total amount of tracer ligand that reacts in the system, the better the assay. From Chard. ...

It can be seen that equation 3.40 satisfies the basic requirements for a definition of net efficiency in that it gives zero for conditions of no separation when Ej = and one for complete separation of solids when Ej =. ... 

The use of entropy in particle technology is not restricted to evaluations of separation efficiency. A unit-less definition of entropy virtually identical with that in equation 18.6 but in terms of probability of events, as used in information theory and proposed by Shannon , has been applied in geology to histograms and cumulative curves by Sharp and Fan to define a sorting index for particle size analysis. Sharp applied the information entropy to... 

When this is combined with the definition of minimum separation work, an approximation for distillation efficiency for an ideal binary can be obtained ... 

Karlsson and Novotny [12] introduced the concept of nanoliquid chromatography in 1988. The authors reported that the separation efficiency of slurry packed liquid chromatography microcolumns (44 xm, id) was very high. Since then, many advance have been reported in this modality of chromatography and it has been used as a complementary and/or competitive separation method to conventional chromatography. Unfortunately, to date no correct and specific definition of this technique has been proposed, probably due to the use of varied column sizes (10 to 140 xm). Some definitions of nanoliquid chromatography are found in the literature based on column diameter and mobile... 

In its broadest terms the discussion of HPLC detection for chiral species must include the analysis of mixtures with achiral substances as well as the quality testing of, for example, the enantiomeric purity of a chemically pure drug form. The distinction between the definitions of chemical purity versus optical purity can not be overemphasized. In an efficient chiral HPLC system the latter problem is trivial, and if retention times are significantly different then any conventional detector such as RI, electrochemical, absorption, etc., could be used. Co-elutions are a major experimental concern in separations of mixtures and at this juncture it is not only prudent but absolutely necessary to involve a chiroptical detector to preferentially identify the chiral analyte. 

This equation shows that N increases with Xlcr, the ratio of the migration distance in which separation can occur to the zone width parameter zone overlap. The overall goodness of a separation obviously increases with this ratio, so N is clearly a valid index of separation power, as substantiated more fully elsewhere [8,15]. In chromatography, N is often taken as a measure of column efficiency, a definition that can be extended to other zonal separation methods as well. 

The definition of a more efficient enzymatic system could be based on the separation of the catalytic cycle of the enzyme and the degradation step by the Mn3+ reactive species in MnP systems. The Mn3+-chelates present several advantages in their use as oxidants. They are more tolerant to protein denaturing conditions such as extremes of temperature, pH, oxidants, organic solvents, detergents, and proteases, and they are smaller than proteins therefore, they can penetrate microporous barriers inaccessible to proteins. The optimization of the production of the Mn3+-chelate will have to be compatible with the minimal consumption and deactivation of the enzyme. 

Microbiological or immunochemical detection systems offer the advantage to screen, rapidly and at low cost, a large number of food samples for potential residues, but cannot provide definitive information on the identity of violative residues found in suspected samples. For samples found positive by the screening assays, residues can be tentatively identified and quantified by means of the combined force of an efficient liquid chromatographic (LC) separation and a selective physicochemical detection system such as UV, fluorescence, or electrochemical detection. The potential of pre- or postcolumn derivatiza-tion can further enhance the selectivity and sensitivity of the analysis. Nevertheless, unequivocal identification by these methods is not possible unless a more efficient detection system is applied. 

The determination of quantum efficiency of the photochemical reactions has not been attempted because it is difficult to separate definitely the effects of the type I and type II reactions. However, on the assumption that the type n dominates in copolymer photolyses and that tile type I dominates in the photolyses of blends, the results appear to be in accord with expectations based on the photochemistry of related simple molecules. 

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