Rate model, chromatography

CHROMDIFF - Dispersion Rate Model for Chromatography Columns System... 

As explained in Section 4.4.4, the movement of components through a chromatography column can be modelled by a two-phase rate model, which is able to handle multicomponents with nonlinear equilibria. In Fig. 1 the column with seg-... 

The general rate model of chromatography is the most complex of all the models used in this field. In this model, it is assumed that the mobile phase percolates through the interstitial volume between stationary phase particles, diffusion takes place from this stream into the particles and inside the pores of the stationary phase particles, where the mobile phase is stagnant, and adsorption-desorption takes place between the stagnant mobile phase within the pores and the adsorbent surface. 

In order to estimate resolution among peaks eluted from a chromatography column, those factors that affect N must first be elucidated. By definition, a low value of Hs will result in a large number of theoretical plates for a given column length. As discussed in Chapter 11, Equation 11.20 obtained by the rate model shows the effects of axial mixing of the mobile phase fluid and mass transfer of solutes on Hs. 

General rate model Chromatographic separation of solutes with complex mass transfer and adsorption behavior (e.g. bio separations or ion exchange chromatography)... 

Equation 6.138 defines a formal connection between the effective mass transport and the film transport, the pore diffusion and the adsorption rate coefficient. It illustrates that keff is a lumped parameter", composed of several transport effects connected in series. This also gives reasons for the use lumped rate models as it proves that the impact of the lumped parameters on the most important peak characteristics, retention time and peak width, is identical to the effect described by general rate model parameters in linearized chromatography. 

The detailed study of the mass transfer kinetics is necessary in certain problems of chromatography in which the column efficiency is low or moderate. Complex models are then useful. The most important ones are the General Rate Model [52,62] and the FOR model (see next Section) [63]. To study the mass transfer kinetics, these models need to consider separately the mass balance of the feed components in the two different fractions of the mobile phase the one that percolates through the bed of the solid phase (column packed with fine particles or monolithic column) and the one that is stagnant inside the pores of the packing material. 

This set of equations (Eqs. 2.25 to 2.35) constitutes the general rate model of chromatography. 

The transport approach has been used very early, and most extensively, to calculate the chromatographic response to a given input function (injection condition). This approach is based on the use of an equation of motion. In this method, we search for the mathematical solution of the set of partial differential equations describing the chromatographic process, or rather the differential mass balance of the solute in a slice of column and its kinetics of mass transfer in the column. Various mathematical models have been developed to describe the chromatographic process. The most important of these models are the equilibrium-dispersive (ED) model, the lumped kinetic model, and the general rate model (GRM) of chromatography. We discuss these three models successively. 

---