Separation factor local

FIG. 16-35 EluHon curves under trace conditions with a constant separation factor isotherm for different feed loadings and N = 80. Solid lines, rate model dashed line, local equilihrium theory for Xp= 0.4. 

The application of the z-transform and of the coherence theory to the study of displacement chromatography were initially presented by Helfferich [35] and later described in detail by Helfferich and Klein [9]. These methods were used by Frenz and Horvath [14]. The coherence theory assumes local equilibrium between the mobile and the stationary phase gleets the influence of the mass transfer resistances and of axial dispersion (i.e., it uses the ideal model) and assumes also that the separation factors for all successive pairs of components of the system are constant. With these assumptions and using a nonlinear transform of the variables, the so-called li-transform, it is possible to derive a simple set of algebraic equations through which the displacement process can be described. In these critical publications, Helfferich [9,35] and Frenz and Horvath [14] used a convention that is opposite to ours regarding the definition of the elution order of the feed components. In this section as in the corresponding subsection of Chapter 4, we will assume with them that the most retained solute (i.e., the displacer) is component 1 and that component n is the least retained feed component, so that... 

The disposal of pig manure poses problems comparable to those of the vegetable waste water. Pre-filtering is even more important here because of the very coarse nature of some of the manure components. As manure from pigs has solids contents as low as 5 to 11%, the main goal is the reduction of the amount to be transported from areas with a manure-surplus to regions with a fertiliser shortage. Very important too, but in the economical sense, is the possibility for disposal of the concentrate of the separation process. Local factors like fertilising limits and the nearby availability of fields that can be fertilised are decisive. 

Eluent selectivity is the ability of different mobile phases to change the separation factor a of two or more compounds present in the sample. It has nothing to do with eluent strength but is another means that allows a separation to be influenced. Adsorption chromatographic selectivity has two different aspects, localization and basicity. 

For a two-component mixture, the relationship between y and x may be expressed in terms of a local separation factor a, defined as... 

Such a simple cascade, with an infinite number of stages each performing an infinitesimal amount of separation, is equivalent to type A differential st e separation. Equation (12.51) is equivalent to the form of the Rayleigh equation (12.35), when one recognizes that w in the simple cascade is equivalent to the heads separation factor 0 in differential stage enrichment, and a in the simple cascade is equivalent to the local separation factor a. ... 

The separation factor in the gas centrifuge thus depends on the difference between molecular wei ts, whereas in gaseous diffusion it depends on their ratio. Table 14.13 gives local separation factors for mixtures of and UFs (Am = 3) for the same speeds and radial... 

Table 14.13 Local separation factors for UFs- UF4 in a centrifugal field...

Pressure ratio p(r)/Pg Va of for speed Local separation factors for speed Ufl of ... 

The radial separation factor, expressed as a — 1, is nearly independent of Ug over this range, instead of varying as u as would be the case for a uniform mass velocity profile, and is much smaller than the local separation factor between the center and outer radius of the centrifuge, given in Table 14.13. 

As noted in Section 2 the d- and fi-isomers of optically active molecules exhibit somewhat different order parameters in liquid crystals possessing a local screw sense (such as cholesteryl derivatives). Accordingly d- and C-isomers should separate on cholesteric substrates. For 3,3,3-trichloropropylene oxide the difference in the order parameter is of the two isomers is AS z = 0.00015 (cf Section 2) for a compensated nematic mixture of cholesteryl derivatives. On the basis of Equ. (42) one would expect a separation factor of a 1.002. Up to the present the separation of optically active isomers on cholesteric substrates has not been achieved. 

We will now develop an analytical solution for a binary feed gas mixture of species A and B by assuming that the local separation factor uab is independent of the membrane separator length/location. This approach (Stem and Walawender, 1969) is tui adaptation of the Naylor and Backer (1955) approach employed for gaseous diffusion with porous barriers. Rewrite equation (7.2.8) for i = A as... 

This is an implicit expression for XAp in terms of Xazl> 0 and Oab- The actual separation factor, ab, is to be determined from the ideal separation factor ab, the pressure ratio y(=Pp/Py) and the exit composition for the concentrate Xa2l (since ab is assumed to be independent of the local variation of Xa2 from Xa/ to xa2z, at the exit) via relation (6.3.202b), where Xa2 can be used instead of Xa ... 

In a distillation column, such a relation may be used for approximate calculations in a particular section of the column where the equilibrium curve may be considered straight with the operating line being straight. Specifically, if the Bjvfv value is available, Eo may be determined so that the number of actual trays for that section may be determined. One way to determine the local value of ttii is to use the separation factor relation (Equation (4.1.24)) ... 

A possible approach to overcome this problem could be to split the estimation of the probability of occurrence extracting criminal energy and political influences on the probability of lEMI attacks as well as availability and cost of lEMI weapons as separate factors. The remaining part of the failure probability is then associated with objective technical conditions comprising local accessibility and electro-technical properties. Based on available EMC research results, the electro-technical vulnerability could be modelled. With this model and a standardized questionnaire, filled in by the Cl providers, comparable risk priority numbers should be obtained. 

In contrast to previous treatments [12,13], Eq. (13) emphasizes the effect of the degree of coverage on the overall resistance by a separate factor 1 - 9.) For a rigid object (such as, c.g., a colloidal particle), U z) can simply be taken to be the (Helmholtz) energy of interaction at separation z. However, a polymer is flexible and can adjust its shape to the local field. We should, therefore, average over all allowed conformations of a polymer molecule that has an arbitrary segment at the distance of closest approach z. In other words, one has to evaluate the partition function Q(z) of a chain at a distance z fi-om the surface, in the imposed field of the surface ... 

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