Packed Column Design Equations

The design equations can be used in a simple computer program to report the basic data and print the column and analytical specifications for any particular analysis carried out on a specified liquid chromatograph. The program is written In the Microsoft Quick Basic language that can be used on 

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As in the chapter on packed column design, the characteristics of many of the equations discussed in this chapter will be examined employing realistic chromatographic conditions and the typical conditions chosen for an open tubular column are given in table 1. 

Figure 8.1.46(d) illustrates a few curves from a more detailed plot by Michaels (1966) with A as a parameter. As Qii is decreased for a given blood flow rate Qf, th decreases, since Cid increases, leading to a reduced solute transfer rate. At any given Qf/Qd, Vi increases as A increases, since the solute transfer rate is increased. There is an additional interpretation of the parameter A. From an analysis of the packed countercurrent column design equation (8.1.54a), we know... 

Other correlations based partially on theoretical considerations but made to fit existing data also exist (71—75). A number of researchers have also attempted to separate from a by measuring the latter, sometimes in terms of the wetted area (76—78). Finally, a number of correlations for the mass transfer coefficient itself exist. These ate based on a mote fundamental theory of mass transfer in packed columns (79—82). Although certain predictions were verified by experimental evidence, these models often cannot serve as design basis because the equations contain the interfacial area as an independent variable. 

It appears that the equation introduced by Van Deemter is still the simplest and the most reliable for use in general column design. Nevertheless, all the equations helped to further understand the processes that occur in the column. In particular, in addition to describing dispersion, the Kennedy and Knox equation can also be employed to assess the efficiency of the packing procedure used in the preparation of a chromatography column. 

In a similar manner to the design process for packed columns, the physical characteristics and the performance specifications can be calculated theoretically for open tubular columns. The same protocol will be observed and again, the procedure involves the use of a number of equations that have been previously derived and/or discussed. However, it will be seen that as a result of the geometric simplicity of the open tubular column, there are no packing factors and no multi-path term and so the equations that result are far less complex and easier to manipulate and to understand. 

Application of the Design Equations to Packed Liquid Chromatography Columns and Open Tubular Gas Chromatography Columns... 

It should be noted that the constants of the equation were arrived at by a curve fitting procedure and not derived theoretically from a basic dispersion model as a consequence the Knox equation has limited use in column design. It Is, however, extremely valuable in accessing the quality of the packing. This can be seen from the diagram shown in figure 2. 

The curves represent a plot of Log.(/V),(Reduced Plate height)against Log.(v), (Reduced Velocity). The lower the Log.(/7) curve versus the Log.(v) curve the better the column is packed. At low velocities the (B) term dominates and at high velocities the (C) term dominates as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, Log (.ft) Is about 0.35. The minimum value for (H) as predicted by the Van Deemter equation has also been shown to be about two particle diameters. The optimum reduced velocity is in the range of 3 to 5 that is Log.(v ) takes values between 0.3 and 0.5. The Knox equation is a simple and effective method of examining the quality of a given column but, as stated before, is not nearly so useful In column design due to the empirical nature of the constants. 

It now possible to summarize the design equations for a packed column which are given as follows. 

By using exactly the same procedures as those used in the design of packed columns the same equations can be derived for the column length and the analysis time. Namely,... 

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