Horvath and Lin equation

In (1976) Horvath and Lin [8,9] introduced yet another equation to describe the value of(H) as a function of the linear mobile phase velocity (u). Again, it would appear... 

Horvath and Lin s equation is very similar to that of Huber and Hulsman, only differing in the magnitude of the power function of (u) in their (A) and (D) terms. These workers were also trying to address the problem of a zero (A) term at zero velocity and the fact that some form of turbulence between particles aided in the solute transfer across the voids between the particles. 

Finally, Horvath and Lin [9,10] developed an equation very similar to the one introduced by Huber and Hulsman ... 

Giddings [29], Huber [49], and Horvath and Lin [50] have used alternate models to accoimt for the relationships between the rate of variation of the solute concentration in the stationary phase, its mobile phase concentration, and the various parameters characterizing the chromatographic system used. This explains the differences in the plate height equations they derived, as we see in the next section. 

In order to include the coupling between the rugged laminar flow in a porous medium and the molecular diffusion, Horvath and Lin [50] used a model in which each particle is supposed to be surrounded by a stagnant film of thickness 5. Axial dispersion occurs only in the fluid outside this stagnant film, whose thickness decreases with increasing velocity. In order to obtain an expression for S, they used the Pfeffer and Happel "free-surface" cell model [52] for the mass transfer in a bed of spherical particles. According to the Pfeffer equation, at high values of the reduced velocity the Sherwood number, and therefore the film mass transfer coefficient, is proportional to... 

Figure 6.13 Comparison of the plots of the reduced axial plate height vs. the reduced flow velocity obtained (a) by PFGNMR and (b) using a conventional chromatographic method. Column packed with 50 m particles of porous C18 silica. The lines shown are the best fits of the experimental data (symbols) to the correlations suggested by Giddings (x = 1), Huber (x = 0.5), and Horvath and Lin (x = 0.33). In either case, the best fit of the data to the Knox equation coincides with that to the Horvath and Lin correlation. Reproduced with permission from U. Tallarek, E. Bayer, G. Guiochon, J. Am. Chem. Soc., 120 (1998) 1494 (Fig. 6). 1998 American Chemical Society.

To separate slow kinetics due to mobile-immobile transfer, binding-release or intraparticle diffusion fi-om dispersion in the mobile phase, it is necessary to have an independent estimate of D for the organic solutes (as defined by equation 1). Horvath and Lin (11) analyzed hydrodynamic dispersion of organic solutes versus ionic tracers in liquid chromatography using an empirical approach ... 

The only difference between the two equations is the description of the resist-ance-to-mass-transfer effect, which Horvath and Lin interpret to depend on the square of the cubic root of the flow velocity instead of a quadratic root dependence. 

Van Deemter first proposed an equation that described the column performance as a function of the linear velocity (10). Since then several plate height and rate models were derived for liquid chromatography by numerous researchers. The most accepted equations were introduced by Giddings, Snyder, Huber and Hulsman, Kennedy and Knox, Horvath and Lin, and Yang (11-16). 

Horvath, Cs. Lin, H.J. Band spreading in liquid chromatography General plate height equation and a method for the evaluation of the individual plate height contributions. J. Chromatogr. 1978, 149, 43. 

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