Theoretical separation efficiency

Column ID (mm) Sample capacity (ng) Separation efficiency (theoretical plates/m)a Carrier gas flow rate, optimum (cc/min)... 

Theoretical Formulation of the Separative Efficiency. The separative efficiency E of a countercurrent gas centrifuge maybe considered to be the product of four factors, all but one of which can be evaluated on the basis of theoretical considerations. In this formulation the separative efficiency is defined by... 

Design data for separation of the particular or similar mixture in a packea column are not available. Design procedures are better estabhshed for tray-type columns than for packed columns. This is particularly so with respect to separation efficiency since tray efficiency can be estimated more accurately than packed height equivalent to a theoretical stage (HETP). 

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

Botz et al. (29) also demonstrated, by scanning electron microscopy, that application of overpressure increases the density of the layer, which could be one reason for the higher separation efficiency. These results showed that Empore silica TLC sheets enable extremely rapid separations (5-20 min) in one-dimensional OPLC, and gave good resolution. Theoretically, for a 3-D OPLC separations development times of 15-60 min would be required. The separation cube of sheets could be especially useful for micropreparative separations (30). 

The main limitation of TLC is its restricted separation efficiency. The separating efficiency (in terms of plates per metre) decreases rapidly over long development distances. That is, highest efficiencies are only achievable within a development distance of approximately 4-7 cm. Therefore, the total number of theoretical plates achievable on an HPTLC plate is limited (about 5000) and inferior to long LC or GC columns. Consequently, complex separations of many compounds are usually not achievable by means of HPTLC. This method is most useful for quantitating only a few components in simple or complex sample matrices. The efficiencies can also be reduced if the plate is overloaded, in an attempt to detect very trace components in a sample. 

The basic theory of batch distillation is given in Volume 2, Chapter 11 and in several other texts Hart (1997), Perry et al. (1997) and Walas (1990). In the simple theoretical analysis of batch distillation columns the liquid hold-up in the column is usually ignored. This hold-up can have a significant effect on the separating efficiency and should be taken into account when designing batch distillation columns. The practical design of batch distillation columns is covered by Hengstebeck (1976), Ellerbe (1997) and Hart (1997). 

The elimination of turbulent mixing in the flow chamber and the short residence time of the reaction mixture in the detection chamber provided a high separation efficiency of 100,000 theoretical plates for labeled amino acids, obtaining good resolution in comparison with previous CL detectors [79, 82], For the isoluminol thiocarbamyl derivative of valine, a detection limit of 500 amol was reported however, it was not possible to separate all 20 isoluminol-deriva-tized amino acids. 

For the simulation of SMB-separations efficient software packages,based on the Triangle-Theory, are commercially available. The number of columns, the column dimensions, the theoretical number of plates in the columns, the feed concentration, the bi-Langmuir adsorption isotherm parameters and the number of cycles need to be defined by the user. Then the separation is simulated and values for the flow rate ratios, the flow rates, the switching time and the quality of the separation, purity and yield, are calculated. Based on these values an actual separation can be performed. However, some optimization/further development is usually necessary, since the simulations are based on an ideal model and the derived parameters and results therefore can only be taken as indications for the test runs. 

Kameyama, Fukuda and Dokiya (1980, 1981) reported separation experiments of H2-H2S mixtures with porous glass (mean pore diameter 4.5 nm) and an alumina membrane (mean pore diameter 100 nm) up to temperatures of 800°C. They used the separation of H2 from the mixture to shift the equilibrium in the decomposition reaction of H2S. H2S, however, diffused partly along the surface, especially at the lower temperature range, thereby decreasing the separation efficiency. No attempt was made to describe the transport. Shindo et al. (1983, 1984) reported data on the separation of He-C02 mixtures by means of a porous glass membrane over the temperature range 296-947 K. A theoretical analysis was made, studying the... 

The vertical IPs of CO deserve special attention because carbon monoxide is a reference compound for the application of photoelectron spectroscopy (PES) to the study of adsorption of gases on metallic surfaces. Hence, the IP of free CO is well-known and has been very accurately measured [62]. A number of very efficient theoretical methods specially devoted to the calculation of ionization energies can be found in the literature. Most of these are related to the so-called random phase approximation (RPA) [63]. The most common formulations result in the equation-of-motion coupled-cluster (EOM-CC) equations [59] and the one-particle Green s function equations [64,65] or similar formalisms [65,66]. These are powerful ways of dealing with IP calculations because the ionization energies are directly obtained as roots of the equations, and the repolarization or relaxation of the MOs upon ionization is implicitly taken into account [59]. In the present work we remain close to the Cl procedures so that a separate calculation is required for each state of the cation and of the ground state of the neutral to obtain the IP values. 

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 ... 

In summary, the efficiency TV of a TLC plate is variable. The height equivalent to a theoretical plate has a minimum value, as in HPLC. However, it is not possible, unlike in HPLC, to vary the flow rate of the mobile phase in order to increase separation efficiency. 

In preparative GC one is not primarily concerned with resolution or theoretical plates. The basic reasons for the technique is its high separation efficiency and high speed. 

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