Extra column dispersion sources

Having established that a finite volume of sample causes peak dispersion and that it is highly desirable to limit that dispersion to a level that does not impair the performance of the column, the maximum sample volume that can be tolerated can be evaluated by employing the principle of the summation of variances. Let a volume (Vi) be injected onto a column. This sample volume (Vi) will be dispersed on the front of the column in the form of a rectangular distribution. The eluted peak will have an overall variance that consists of that produced by the column and other parts of the mobile phase conduit system plus that due to the dispersion from the finite sample volume. For convenience, the dispersion contributed by parts of the mobile phase system, other than the column (except for that from the finite sample volume), will be considered negligible. In most well-designed chromatographic systems, this will be true, particularly for well-packed GC and LC columns. However, for open tubular columns in GC, and possibly microbore columns in LC, where peak volumes can be extremely small, this may not necessarily be true, and other extra-column dispersion sources may need to be taken into account. It is now possible to apply the principle of the summation of variances to the effect of sample volume. 

The Golay equation [9] for open tubular columns has been discussed in the previous chapter. It differs from the other equations by the absence of a multi-path term that can only be present in packed columns. The Golay equation can also be used to examine the dispersion that takes place in connecting tubes, detector cells and other sources of extra-column dispersion. Extra-column dispersion will be considered in another chapter but the use of the Golay equation for this purpose will be briefly considered here. Reiterating the Golay equation from the previous chapter. 

There are four major sources of extra-column dispersion which can be theoretically examined and/or experimentally measured in terms of their variance contribution to the total extra-column variance. They are as follows ... 

It follows that the allocation of all the permitted extra column dispersion to sample volume dispersion, as defined by Klinkenberg (4) and suggested on page (54), is not permissible. Other sources of dispersion must be taken into account and take a share of the permitted 10% increase in column variance. 

Unfortunately, the magnitude of the variance contribution from each source will be different and the ultimate minimum size of each is often dictated by the limitations in the physical construction of of the different parts of the apparatus and consequently not controllable. It follows that equipartition of the permitted extra column dispersion is not possible. It will be seen later that the the maximum sample volume provides the maximum chromatographic mass and concentration sensitivity. Consequently, all other sources of dispersion must be kept to the absolute minimum to allow as large a sample volume as possible to be placed on the column without exceeding the permitted limit. At the same time it must be stressed, that all the permitted extra column dispersion can not be allotted solely to the sample volume. 

Dispersion in column frits was originally thought to be large and thus, made a significant contribution to the overall extra column variance. It was not until the introduction of low-dispersion unions that it was found that most of the dispersion that was thought to occur in the frits, actually occurred in the unions that contained the frits. Scott and Simpson (11) measured the dispersion that occurred in some commercially available column frits and demonstrated that their contribution to dispersion to be insignificant compared with other sources of extra column dispersion. 

The major sources of extra column dispersion are as follows ... 

However, when assessing the length of tube that can be tolerated, it must be remembered that the 10% increase in variance that can be tolerated before resolution is seriously denigrated involves all sources of extra-column dispersion, not just for a connecting tube. In practice, the connecting tube should be made as short as possible and the radius as small as... 

It is seen from equation (20) that the minimum detectable mass, or mass sensitivity of a chromatographic system, where the column has been designed to have the optimum radius for the detector employed, is directly proportional to the extra column dispersion and the detector concentration sensitivity. It follows that detector dispersion is as important as detector sensitivity in its influence on the overall chromatographic mass sensitivity where the chromatographic system has been optimized with respect to the radius of the column. The effect of extra column dispersion and in particular, detector dispersion on the overall mass sensitivity of the chromatogaphic system is not generally appreciated or completely understood. As the total extra column dispersion is the integral of a variety of sources, the distribution and nature of the various sources of dispersion will now be considered in some detail. 

Instrument dispersion can be reduced by optimizing injector and detector systems and reducing diameter of connection capillaries. The individual sources of volumetric extra-column broadening specified in equation (17-26)... 

It follows that the total permitted extra column variance, i.e. 10% of the column variance (o2) as suggested by Khnkenberg (4), has to be shared between each source of dispersion. 

Generally, extra-column band-broadening could be expressed as the sum of the main dispersion sources ... 

In a recent study Jakobsen et al. [71] examined the capabilities and limitations of a dynamic 2D axi-symmetric two-fluid model for simulating cylindrical bubble column reactor flows. In their in-house code all the relevant force terms consisting of the steady drag, bulk lift, added mass, turbulence dispersion and wall lift were considered. Sensitivity studies disregarding one of the secondary forces like lift, added mass and turbulent dispersion at the time in otherwise equivalent simulations were performed. Additional simulations were run with three different turbulence closures for the liquid phase, and no shear stress terms for the gas phase. A standard k — e model [95] was used to examine the effect of shear induced turbulence, case (a). In an alternative case (b), both shear- and bubble induced turbulence were accounted for by linearly superposing the turbulent viscosities obtained from the A — e model and the model of Sato and Sekoguchi [138]. A third approach, case (c), is similar to case (b) in that both shear and bubble induce turbulence contributions are considered. However, in this model formulation, case (c), the bubble induced turbulence contribution was included through an extra source term in the turbulence model equations [64, 67, 71]. The relevant theory is summarized in Sect. 8.4.4. 

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