Craig plate model

The difference between the two plate models has been discussed by Klinkenberg and Sjenitzer [16]. In both models, we have a series of identical mixers, each containing the same amoimt of mobile and stationary phases. In the Martin and Synge model, by contrast with the Craig model, the mobile phase flows continuously. The result is that we have two different distributions, but both of them tends toward the same limit (Eq. 6.5) when the number of stages increases indefinitely. 

To explain the mechanism of migration and separation of compounds on the column, the oldest model, known as Craig s theoretical plate model is a static approach now judged to be obsolete, but which once offered a simple description of the separation of constituents. 

These models assume that the chromatographic column can be divided into a series of a finite number of identical plates. Each plate contains volumes and of the mobile and stationary phases, respectively. The sample is introduced as a solution of known concentration in the mobile phase used to fill the required number of plates. Plate models are essentially empirical, and cannot be related to first principles. Depending upon whether one assumes continuous or batch operation. two plate models can be considered The Craig model and the Martin and Synge model. 

Seshadri and Deming [44] have used the Craig model to calculate band profiles in chromatographic systems. However, they selected an unrealistic isotherm, (Ji = ( j + biCj)Ci, i.e., an isotherm which, for each component i, is linear in respect to its concentration, but with a retention factor that is a linear function of the other component concentration. There is little physical basis for this model, and this prevented them from deriving any useful conclusions. More recently, Eble et al. [45] have used the Craig model to calculate band profiles in isocratic elution and to develop general correlations between the sample size on the one hand and the apparent retention factor and the column efficiency on the other. Experimental data confirm the approximate validity of the relationships obtained [24,25] (Eig-ure 10.3). The use of such empirical relationships allowed an estimation of the band shape on a personal computer for column efficiencies not exceeding a few hxmdred theoretical plates. 

As the plate number N increases, just as in the case of the Craig model the profile tends rapidly toward a Gaussian profile ... 

Note that, although both models lead to the same profile, the resulting relationships between number of plates in the column and standard deviation differ. The conventional plate number as defined in chromatography is equal to N for the Martin and Synge model, and to N (l+ k o)lk o for the Craig model. In any discussion of column efficiency it is convenient to consider the height equivalent to a theoretical plate (or HETP). 

Bobby G. Craig refined explosively driven plate technology and discovered the time-dependent nature of the detonation wave. The experimental data he generated, in the 1960s and 1970s, furnished the basis of much of the detonation physics and modeling described in this book. 

These simulation processes are quite rapid, requiring only a few minutes processing time for moderate numbers of plates. The time required is a function of the square of the plate number using a 80486 based 66 MHz personal computer a single solute simulation based on the mass balance model for 2000 plates takes a little over 30 s the Craig calculation takes somewhat longer. The result of such a simulation is shown in Fig. 2-5 the results from the use of Eqs. (5-7) for the same conditions are also shown. This indicates that the simple equations are reasonably good at such predictions. Simulations are valuable since the results are very close to those which... 

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