Prediction of Gradients

Be courageous, when you have about 10 peaks and a relatively clean sample, then proceed as follows short column, high flow, short, steep gradient starting at about 30 -40% . 

We can use our gradient system to make this eluent mixture. The horizontal line in all chromatograms shown in this chapter represents the set value of the methanol content, the rather uneven line the measured pressure. Both parameters should always be displayed as error indicators. 

Now we have made an isocratic overview run and can see the four peaks with increasing retention times in the above-mentioned order. Knowing the mobile time (formerly called dead time) of q = 0.75 min (small peak, calculation see below) we can also calculate the retention factor k, which generally should be not 

The retention time t is the primary variable in chromatography, from which we deduce whether an analyte is present or not. The retention times t are dependent on the column dimensions. When under the same conditions a column with three times the length L is used, then the retention times and /q increase by a factor of 3. A column with half the internal diameter d, that is, a quarter of the cross-section, reduces at the same flow rate the retention times and t by a factor of 4. 

To convert the retention times into the dimensionless retention factors k the mobile time /g is needed, which is calculated from the mobile volume Vq and the flow F [7]. The mobile volume can be estimated from the internal volume of the column and a characteristic factor for the packing. 

---

I) prediction of gradient retention time r, as functitm of gradient conditions [Eqs. (8) and (54)] (2) prediction of band width Oi as a function of gradient conditions [Eqs. (8), (9), and (51)] (3) predictions of solute conformation during separation (Action IV, ). Unless care is taken in the design... 

Figure 2.21. The dependence of the surface tension on the relative molecular mass for alkanes at 150 °C. The circles are the data and the crosses give the predictions of gradient theory. The lines are fits to the power law of equation (2.4.2), with the exponent taking the values 2/3 (solid line) and unity (dashed line). Data are from Sauer and Dee (1994).

Chapter 3 is devoted to the gradient elution. Stavros Kromidas, Frank Steiner, and Stefan Lamotte discuss about aspects of gradient optimization in a dense form in the first part and offer simple to-do rules. In the second part, Hans-Joachim Kuss shows that predictions of gradients runs with excel can be very unerring and that the often used linear model represents a simplified approximation. 

Eatemi, M.H. Abraham, M.H. Poole, C.E. Combination of artificial neural network technique and linear free energy relationship parameters in the prediction of gradient retention times in hquid chromatography. J. Chromatogr. A, 2008,1190, 241-252. 

Golkiewicz, W. (1981a). Use of data obtained from RP-18 plates for the prediction of gradient programs in reversed phase liquid chromatography. Chromatographia 14 629-632. 

TABLE 16-14 Expressions for Predictions of Chromatographic Peak Properties in Linear Gradient Elution Chromatography under Trace Conditions with a Small Feed Injection and Inlet Gradient Described by op = opo + pt (Adapted from Refs. A and B). 

The average geothermal gradient used in most areas of the United States for initial predictions of subsurface temperatures is a value of0.016°F/ft [32]. 

Consideration will now be given to the various flow regimes which may exist and how they may be represented on a Flow Pattern Map to the calculation and prediction of hold-up of the two phases during flow and to the calculation of pressure gradients for gas-liquid flow in pipes. In addition, when gas-liquid mixtures flow at high velocities serious erosion problems can arise and it is necessary for the designer to restrict flow velocities to avoid serious damage to equipment. 

Kencmnoton, J. M. Hydrotransporl 5, (BHRA Fluid Engineering, Hanover, Germany) (May 1978) Paper D7. Prediction of pressure gradient in dense phase conveying. 

Finally, a comparison of the two-phase frictional pressure gradient data with the predictions of the Lockhart-Martinelli correlation using different C-values is shown in Fig. 5.32, including C = 5, C = 0.66, C calculated from the Lee and Lee model (2001), and C = 0.24. The conventional value of C = 5 again significantly over-... 

Fig. 5.32 Predictions of two-phase friction pressure gradient data by a Lockhart-Martinelli correlation with different C-values. Reprinted from Kawahara et al. (2002) with permission...

---