Columns capacity parameter

The relative steepness or sharpness improves as the volume of the resin bed increases and also as the exchange rate increases. In order to use generalized mathematical results, these two factors must be combined into a dimensionless column capacity parameter 2, which is entirely analogous to the number of transfer units, NTU or N, as defined by Chilton and Colburn for differentially continuous separations (C3). 

Number of Reaction Units, Column-Capacity Parameter, or Bed-Thickness Modulus, Nb, or s. The general treatment of ion-exchange rates is based upon a surface reaction-kinetic driving force which approximates either an external or an internal material-transfer driving force. By... 

N R number of reaction units see Eq. (54) r equilibrium parameter s column-capacity parameter for fixed-bed operation, based on reaction-kinetics calculation t solution-capacity parameter for fixed-bed operation, based on reaction-kinetics calculation x ratio of fluid-phase concentration of a component to that of all components, c/C0 (xa, etc.) y ratio of particle-phase concentration of a component to total for solid at saturation with the feed, q/Q... 

Vapor Capacity Parameters. The diameter of a distiUation column is determined by the capacity of the column to handle the required flows of vapor and Hquid. The vapor capacity parameter is... 

The term in equation 42 is called a Souders-Brown capacity parameter and is based on the tendency of the upflowing vapor to entrain Hquid with it to the plate above. The term E in equation 43 is called an E-factor. and E to be meaningful the cross-sectional area to which they apply must be specified. The capacity parameter is usually based on the total column cross section minus the area blocked for vapor flow by the downcomer(s). Eor the E-factor, typical operating ranges for sieve plate columns are... 

The absolute pressure may have a significant effect on the vapor—Hquid equiHbrium. Generally, the lower the absolute pressure the more favorable the equiHbrium. This effect has been discussed for the styrene—ethylbenzene system (30). In a given column, increasing the pressure can increase the column capacity by increasing the capacity parameter (see eqs. 42 and 43). Selection of the economic pressure can be faciHtated by guidelines (89) that take into consideration the pressure effects on capacity and relative volatiHty. Low pressures are required for distillation involving heat-sensitive material. 

Capacity parameters (C) i.e. those parameters which affect the phase ratio film thickness, surface area, column diameter (open columns), porosity (packed columns). 

The capacity parameters allow a variation of the capacity factor (and hence the resolution) independent of the selectivity. However, all these parameters are difficult to vary, since they almost always require new columns to be used. Moreover, the range of variation offered by these parameters is too limited for them to be generally useful in optimization schemes (see also section 4.2.3). 

Capacity parameters are not often used as primary optimization parameters in chromatography. Therefore, they are only included in table 3.10 in those cases in which they are used with some frequency. It should be noted, however, that changing one of the capacity factors usually involves the use of a completely different column and is therefore unattractive. Although changing the capacity parameters affects retention in an essentially predictable way, changing the column (packing material, film thickness, etc.) may give rise to unexpected second order phenomena. This is a second reason for which capacity parameters should not be recommended as primary optimization parameters. 

In the second place, the parameters listed in table 4.2 cannot always be varied independently and, moreover, will have side effects on yet other parameters. All the capacity parameters affect the phase ratio (V/ V. If all other parameters are kept constant, then the film thickness and the surface area will affect Ks, the porosity will affect Vm and the diameter of open columns will affect both Vm and Vs. However, it is often impossible to keep all other parameters constant. For instance, it would be very difficult to vary the porosity without changing the surface area. An example of the effect of variations in the capacity parameters on other parameters is the decrease in the number of theoretical plates in the column that usually accompanies an increase in the stationary phase film thickness in GLC. 

In packed columns, there are two parameters which may be varied independently in order to optimize the column characteristics, i.e. the diameter of the column and the diameter of the particles. In open columns, only the column diameter may be varied. Additionally, the phase ratio may be varied by changing one of the capacity parameters (see section 3.5). For packed columns these parameters include the surface area of the packing material, the column porosity and the stationary phase film thickness. For open columns only the latter parameter is relevant. 

The suitability of the GPDC interpolation charts as a basis for interpolation is not accidental. Packing pressure drops correlate extremely well with GPDC coordinates, i.e., the fiow parameter and the capacity parameter. The dependence does not always follow the correlation contours, but always appears to exist. Further, the correlation coordinates are essentially a performance diagram, i.e., a plot of a vapor load against liquid load, a tool commonly used for analysing column performance. 

At low HSA concentrations the model fits well the whole breakthrough curve (Fig. 5). Two parameters are necessary to describe the model, the column capacity Qx and the number of transfer units n. The overall adsorption process is described by an apparent association rate constant that includes the transport to the active sites and the biospecific interaction (Eq. (6)]. 

Table 2 lists the two parameters n and Qx necessary to describe the model as determined with columns differing by the density of immobilized polyclonal antibody. As previously described, from the variation of the column capacity one can evaluate the contribution to the transport to the binding sites (I/nmt = 0.040) and calculate the effective adsorption rate constant ka. The results agree with those obtained from frontal analysis. The value of the apparent adsorption rate constant k is close to the value of Aa for experiments carried out both at high flow rates and with an immunoadsorbent column of low capacity 22). In this case, the rate-controlling step is the biospecific interaction. 

HPLC is ideally suited to examine adsorption kinetics in the working conditions of column immunoassays. In this technique, high flow rates and minimized column volumes are required to perform rapid on-line immunodetections. The column capacities and residence times in the column are parameters that influence the efficiency of the immunoreactor. Kinetic studies using the chromatographic format will be useful to understand the process better and optimize the methodology. 

As the chromatographic process in CCC is based on the partition of a solute between the mobile and stationary phases, the value is the most important parameter in CCC. A Ad value of around 1.0 is most desirable in CCC, wherein a solute with Ad =1.0 elutes with its retention volume equivalent to the total column capacity. In the above two-phase solvent systems, the Ad values of monomers (catechin and/or epicatechin) were greater than 1.0, and those of the ACTs are always smaller than 1.0, suggesting that monomers are more hydrophobic than their oligomers present in ACTs. Among these four solvent systems, we selected a simple binary system of methyl acetate/water for the separation of procyanidin oligomers from ACTs by CCC. 

Packed-bed enzyme reactors, those employing enzymes immobilized onto a particulate phase that is subsequently packed into a column, may be characterized by their column capacity, C, and the degree of reaction P. The parameter C is defined in Eq. 4.23,... 

Different column design parameters like depth of exchange zone, adsorption rate, adsorption capacity, and so on were calculated. It was found that the adsorption capacity and adsorption rate constant were increased and the minimum column bed depth required was reduced when the rice husk is treated with phosphate, when compared with that of RRH. 

Figure 11.5 Comparison between the results of the calculations of the individual band profiles of a 3 1 binary mixfure using the CXZFE method and two finite difference methods (Eqs, 10.78 and 10.80). Solid fine profile calculated with the OCFE method, with Sz = 0.050 cm, St = 0.15 s. Dotted line profile calculated with the forward-backward method (Eq. 10.78), Sz = 0.0050 cm and St = 0.33 s. Dash-dotted line profile calculated with the backward-forward method (Eq. 10.80), Sz = 0.0050 cm and St = 0.033 s. Calculation parameters column length 15 cm. Phase ratio 0.25. Mobile phase flow velocity 0.15 cm/s. Column capacity factors (Cg j = 4, fcpj = 5. Np = 3. 3 1 binary mixture. Langmuir competitive isotherms parameters = 20, fl2 = 16/ = 5 62 = 4 Input profile ...

From Figure 12.53, both limiting capacity and pressnre drop may be predicted. The abscissa term is the flow parameter [Equation (13.29)], nsed also for plate columns. The ordinate term is a capacity parameter CP, modified from the capacity parameter for plate colnmns [Eqnation (13.30)] ... 

In any one case both rate controlling processes may contribute to the overall exchange kinetics. Equations (15) and (16) show that the degree of column utilisation and the breakthrough capacity can be expected to increase when zeolite grain size and the flow rate are decreased, although, clearly, column design parameters must be taken into account. 

In spite of very diverse successful practical applications, the mechanism of com-plexation and the relationship between structure and selectivity are still at best only partly solved and remain open for discussion. Thermodynamic studies could supply some valuable information facilitating an understanding of the physicochemical basis of the complexation processes. The GC modified with CyDs is one of a variety of experimental methods employed in the determination of thermodynamic quantities for the formation of CyD inclusion complexes (see Chapters 8-10). The thermodynamic parameters for separation of the enantiomers were determined for various derivatives of CyDs dissolved in various stationary phases [63-65] or as a Uquid derivatized form [66]. Interesting observations were made by Armstrong et al. [66]. The authors postulated two different retention mechanisms. The first involved classical formation of the inclusion complex with high thermodynamic values of AH, AAH, and AAS and a relatively low column capacity and the second loose, probably external, multiple association with the CyD characterized by lower AH, AAH, and AAS values. The thermodynamic parameters of complexation processes obtained from liquid and gas chromatography measurements are collected in Table 5.2. It is clear from those data that for all the compounds presented the complexation processes are enthalpy-driven since in all cases AH is more negative than TAS. 

In the development of the above series of equations, Zuiderweg has used the work of many prior investigators and relied heavily on the data recently released by Fiactionadon Research, Inc. (FRI), as repotted by Sakata and Yanagi on the performance of two types of commercial perforated tray. Zui-derweg also presents correlations that define the flow regime transitions, pressure drop, entiainment, column capacity, and other operating parameters of sieve trays. 

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