Van Deem ter

The height equivalent to a theoretical plate (HETP) for a chromatographic column is approximated by the van Deem ter equation (107) ... 

The expanded version of the van Deem ter equation is used to help understand the relationships between the packing parameters and the gas flow. 

The basically correct equation appears to be that of Giddings but, over the range of mobile phase velocities normally employed i.e., velocities in the neighborhood of the optimum velocity), the Van Deem ter equation is the simplest and most appropriate to use. 

The Van Deem ter equation appears to be a special case of the Giddings equation. The form of the Van Deemter equation and, in particular, the individual functions contained in it are well substantiated by experiment. The Knox equation is obtained... 

Smit JJ, Schinkel AH, Oude Elferink RP, Groen AK, Wagenaar E, van Deem-ter L et al. Homozygous disruption of the murine mdr2 P-glycoprotein gene leads to a complete absence of phospholipid from bile and to liver disease. Cell 1993 75(3)451-462. 

In the presence of similar molecules and impurities, that molecule will also have to compete for the interactive sites on the surface of the stationary phase. The first scientist to assess the composite effects of mass transport in a chromatographic column from a chemical engineering perspective was JJ van Deem ter 241 in the early 1950s. In doing so he derived a more dynamic equation for the HETP which, in simplified form, can be represented as ... 

The A term, which was known as the eddy diffusion effect, does not exist in Hawkes s equation as a separate term. The effect is better called a multipath term it is flow-dependent, contrary to the original van Deem-ter equation, and is included in the C term. An exact equation would be very complicated and is inappropriate because of the negligible contri-... 

It is seen that an excellent fit is obtained with the Van Deem ter equation with an Index of determination, for that particular fit, of 0.999885 However, the results from testing all the data to each of the dispersion equations need to be known in order to Identify the equation that, overall, shows the best fit. 

Figure 5.3 Van Deem ter plots of plate height, H, against average linear velocity, U, of the mobile phase, (a) The contribution of each term to the composite curve, (b) Plots for WCOT GC column using N2, He, H2 carrier gas and N2 for packed column GC.

Equation 21.8 is a slightly modified version of the Van Deem ter equation, Equation 22.10, used in gas chromatography. Because of the so-called coupling between the A term (eddy diffusion) and the Cu, term of Equation 22.10, a different relationship between H and v is observed in LC than in GC. The fundamental difference between GC and LC is the great difference in sample diffusion rates in liquids and in gases Dm is 10 -10 times greater in GC. Thus, the contribution in LC is much smaller than in GC, whereas the /fmp term is larger. 

Schinkel AH, Wagenaar E, van Deem ter L, Mol CA and Borst P. Absence of themdrla P-Glycoprotein in mice affects tissue distribution and pharmacokinetics of dexametha-sone, digoxin, and cyclosporin A. J Clin Invest 1995 96 1698-1705. 

Note that Eq. (4.25) examines column efficiency as a complex function of linear mobile-phase velocity. It is the linear velocity that conducts analytes of interest through a chromatographic column to the detector. Any comparison of van Deem ter cnrves snch as that shown in Fig. 4.5 must use linear velocity because the influence of the colnmn radins is eliminated.. Tennings has artieulated an interesting relationship between linear and volumetrie flow rates, F, and ineorporating the column radins, rc, according to (24)... 

A number of HETP equations were developed other than that of Van Deem ter. Giddings developed an alternative form that eliminated the condition predicted by the Van Deemter equation that there was a finite dispersion at zero velocity. However, the Giddings equation reduced to the Van Deemter equation at velocities approaching the optimum velocity. Due to extra-column dispersion, the magnitude of which was originally unknown, experimental data were found not to fit the Van Deemter... 

The bubbling bed model proposed by Kunii and Levenspiel (1969) can be considered a modified version of the two-phase model where, in addition to the bubble and the emulsion phases, a cloud-wake phase is also considered. The model represents a group of models often referred to as backmixing or dense phase flow reversal models (see also Van Deem ter, 1961 Latham et al., 1968 Fryer and Potter, 1972). A key difference between this model and the rest of the two-phase models is that the interphase mass transfer considers two distinct resistances, one from the bubble phase to the cloud-wake phase, and the other from the cloud-wake phase to the emulsion phase. 

With this equation, and the simplifications mentioned above, we can now estimate how the peak capacity changes as we vary the gradient parameters. Thus far, we have assumed that the plate count remains constant. However, what we would like to do is vary the flow rate at a constant run time. This means that the plate count will change as well. To introduce this variation, we use the van Deem ter equation ... 

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