Infinite diameter column

FIGURE 22.9 Reduced plate height versus reduced velocity. Measured data V, toluene O, PS 2200 , PS 43,900 A, PS 77S.000. Theoretical lines solid lines, Giddings, infinite diameter column dotted line, Knox, infinite diameter column dashed line Knox walled column. (Reprinted from J. Chromatogr., 634, IS4, Copyright 1993, with permission from Elsevier Science.)... 

Operating conditions vary widely, from low pressure to high pressure, short columns to long columns, narrow columns to infinite diameter columns, analytical samples to prep samples, and so on. 

II Given these conditions, what would be the minimum diameter of a 25 cm column, packed with 5 /an particles, if the column is to show infinite diameter behaviour ... 

In practice, the injected solute will occupy a finite volume, and the injection may not be properly centralised either. Both of these have the effect of making dc greater, or L smaller, for infinite diameter behaviour, than the values calculated from Eq. 2.3e. If these effects are allowed for, it can be shown that columns of 25 cm or less, with injections of 10 fil or less, show infinite diameter behaviour when their diameters are greater then about 4 mm. 

Lederman et al (Ref 20) studied the detonation behavior of AMATEX-30, nominally 40/30/30 TNT/RDX/AN, at an average density of 1.645g/cc. Their results of the diameter effect (in terms of R, the charge radius) are summarized in Fig 2. Detonation failed to propagate in column diameters of 10mm. As shown, the infinite diameter D is 7.318km/sec, as compared to 7.031km/sec for Amatex 20 (40/20/40 TNT/RDX/AN). They also examined the effect of AN particle size on D. Their results for Amatex 20 are shown in Table 4... 

The second extreme we can imagine is to maintain finite flows for the feed and products but increase the internal flows for L and V to infinite values. This second case cannot really occur, as we would need a column with an infinite diameter. It is a limiting case. Both ways to think of infinite reflux are useful. In the latter case the column is still thought of as producing its products. 

The internal diameter of the column affects several chromatographic aspects. In the beginnings of modern liquid chromatography there was much discussion of the infinite diameter effect (20-22). Due to slow radial mass transfer, for certain combinations of particle diameter and column diameter, solute injected directly onto the center of a column will traverse the length of the column without ever approaching the column walls. For poorly packed columns this significantly increases column efficiency, by eliminating wall effects. However, for well-packed columns the effect is rather small. The practical utilization of this phenomenon also requires specialized injection apparatus and decreased column sample capacity. For these reasons, this concept is now little discussed. 

If the columns are used in an overloaded condition, the infinite diameter phenomenon does not apply. 

Furthermore, as diffusion can also take place radially, migration of solute molecules towards the column walls can occur. This could lead to appreciable band broadening on account of, first, the slower flow at the walls of the column, and second, solute molecule interaction with the walls, causing retardation of the zone. However, provided the sample is applied as a narrow concentrated band and the solvent has suitable viscosity, the rate of radial diffusion is not sufficient to become a problem, and under these conditions the column is described as operating in the infinite diameter mode. 

Column head. If one feeds a column with a diameter larger than 10 mm, a good distribution of the sample over the cross-section is essential. Using point--injection, the column will be centrally overloaded by infinite-diameter and often noticeable tailing is observed. If one wishes to obtain a high loading, one has to spread the sample homogeneously over the whole cross-section, as demonstrated in Fig. 2. 

For preparative applications, however, the infinite diameter mode is not so desirable as it reduces the effective capacity of the column. Here, complete utilization of the whole packed bed is required and so it is necessary to ensure uniform presentation of the sample across the whole cross section of the column, together with uniform flow. Although this will result in some peak broadening, due to the wall effect, this is reduced as the column diameter increases. 

A wastewater stream of 0.038 m3/s, containing 10 ppm (by weight) of benzene, is to be stripped with air in a packed column operating at 298 K and 2 atm to reduce the benzene concentration to 0.005 ppm. The packing specified is 50-mm plastic Pall rings. The airflow rate to be used is five times the minimum. Henry s law constant for benzene in water at this temperature is 0.6 kPa-m3/mol (Davis and Cornwell, 1998). Calculate the tower diameter if the gas-pressure drop is not to exceed 500 Pa/m of packed height. Estimate the corresponding mass-transfer coefficients. The diffusivity of benzene vapor in air at 298 K and 1 atm is 0.096 cm2/s the diffusivity of liquid benzene in water at infinite dilution at 298 K is 1.02 x 10 5 cm2/s (Cussler, 1997). 

The value of is very nearly equal to the free-fall velocity of a single particle in an infinite fluid, wo(oo) except when the ratio of particle size, d, to column diameter, D, is large, and, in general. 

There is an engineering trade-off between the number of trays and the reflux ratio. An infinite number of columns can be designed that produce exactly the same products, but have different heights, different diameters, and different energy consumptions. Selecting the optimum column involves issues of both steady-state economics and dynamic controllability. 

Figure 29. Binary diffusion coefficients at infinite dilution DJJ from SFC experiments for naphthalene and biphenyl in cEirbon dioxide at 309 tnd 331 K as a fimction of density, according to Klask [66] (void column, ca. 40 m long, ca. 0.4 mm internal diameter flow velocity ca. 0.5 cm s UV detector).

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