Chromatography eddy diffusion

The term A is related to the flow profile of the mobile phase as it traverses the stationary phase. The size of the stationary phase particles, their dimensional distribution, and the uniformity of the packing are responsible for a preferential path and add mainly to the improper exchange of solute between the two phases. This phenomenon is the result of Eddy diffusion or turbulent diffusion, considered to be non-important in liquid chromatography or absent by definition in capillary columns, and WCOT (wall coated open tubular) in gas phase chromatography (Golay s equation without term A, cf. 2.5). 

In the frontal analysis experiment described in Section 5.3.2, the transport model of chromatography was used to fit the experimental data [40]. Neglecting axial and eddy diffusion, band broadening was accounted for by one single mass transfer rate coefficient. The mass transfer rate coefficients estimated were small and strongly dependent on the temperature and solute concentration, particularly the rate coefficients corresponding to the imprinted L-enantiomer (Fig. 5.12). Above a concentration of ca. 0.1 g/L the mass transfer rate coefficients of the two enantiomers are similar. 

The contribution of eddy diffusion and other factors to band broadening in liquid chromatography can be quantitatively described by the following equation, which relates the column plate height H to the linear velocity of the solute, ju ... 

In the modeling of chromatography, the contributions of aU the phenomena that contribute to axial mixing are lumped into a single axial dispersion coefficient. Two main mechanisms contribute to axial dispersion molecular diffusion in the interparticle pores and eddy diffusion. In a first approximation, their contributions are additive, and the axial dispersion coefficient, Di, is given by... 

In contrast to the equilibrium-dispersive model, which is based upon the assumptions that constant thermod3mamic equilibrium is achieved between stationary and mobile phases and that the influence of axial dispersion and of the various contributions to band broadening of kinetic origin can be accounted for by using an apparent dispersion coefficient of appropriate magnitude, the lumped kinetic model of chromatography is based upon the use of a kinetic equation, so the diffusion coefficient in Eq. 6.22 accounts merely for axial dispersion (i.e., axial and eddy diffusions). The mass balance equation is then written... 

Apparent dispersion coefficient, Dapi The apparent dispersion coefficient lumps all the contributions to axial dispersion arising from axial molecular diffusion, tortuosity, eddy diffusion, and from a finite rate of mass transfer, adsorption-desorption, or other phenomena, such as reactions, in which the eluites may be involved. It is used in the equilibrium-dispersive model of chromatography to ac-coimt for the finite efficiency of the column (Eq. 2.53 and 10.11). See equilibrium-dispersive model. 

Eddy diffusion arises from movement of the mobile phase (liquid in liquid chromatography and gas in gas chromatography) in a packed column in tortuous channels. The flow-paths available are tortuous and zig-zag, some of these being narrow ones and others wider ones. This is so on account of irregularities in the packing material (e.g. non-uniformity of particle size) and different qualities of the packing of the column. The zig-zag path taken by a part of the mobile phase makes some molecules of a particular solute take longer paths and they lag behind the bulk of the molecules of that solute, while some molecules of the same solute which are present in another part of the mobile phase take shorter paths and move ahead of the mainstream of the molecules of that particular solute. Also, the mobile phase moves more slowly in narrow flow paths and more rapidly in wider ones so that further inequalities are introduced in the transport of molecules of a particular... 

The significance of the three terms A, B, and C in packed-column gas chromatography is illustrated in Figure 19.4, which is a plot of H determined as a function of carrier gas velocity. Here, A represents eddy diffusion and is due to the variety of tortuous (variable-length) pathways available between the particles in the column and is independent of the gas- or mobile-phase velocity. The heterogeneity in axial velocities (eddy diffusion) is related to particle size and geometry of packing by ... 

As we will see in Chapter 20, capillary columns are the most widely used in gas chromatography because of their high efficiency due to large numbers of plates. These columns have no packing, and so the eddy diffusion term in the van Deempter equation disappears. For open tubular columns, the modification of the van Deempter equation, called the Golay equation, applies ... 

In 1957 Marcel Golay published a paper entitled Vapor Phase Chromatography and the Telegrapher s Equation [Anal. Chem., 29 (1957) 928]. His equation predicted increased number of plates in a narrow open-tubular column with the stationary phase supported on the inner wall. Band broadening due to multiple paths (eddy diffusion) would be eliminated. And in narrow columns, the rate of mass transfer is increased since molecules have small distances to diffuse. Higher flow... 

HPLC is the liquid chromatography analog of GC. The secret to its success is small uniform particles to give small eddy diffusion and rapid mass transfer. 

---