The Thickness of Shock Layers in Liquid Chromatography

Abstract

At high concentrations, one boundary (the front if the isotherm is convex upward) of the elution band of a single component becomes very steep. Similarly, in frontal analysis, the same boundary is self-sharpening. These steep boundaries are called shock layers. They result from the steady-state equilibrium between a nonlinear thermodynamics of phase equilibrium on the one hand, which tends to create a concentration discontinuity, and axial dispersion and a finite rate of mass transfer on the other hand, which tend to relax the concentration gradient. We show that the width of experimental breakthrough curves recorded in frontal analysis agrees well with the prediction of the shock layer theory of Rhee and Amundson in the high concentration range. It is a function of the coefficients of the column HETP equation and the height of the concentration step and is independent of the column length, after the steady state is achieved. In the low concentration range, a discrepancy is observed when the column length is short and the migration distance is insufficient to achieve constant pattern behavior.

Application of the Shock Layer Theory to the Determination of the Mass Transfer Rate Coefficient and Its Concentration Dependence for Proteins on Anion Exchange Columns

“…It has been shown (Zhu and Guiochon, 1993; Zhu et al, 1993) that, the shock layer being an asymptotic solution, the corresponding profile, and hence the theoretical value of the SLT, is achieved only when the BC migrates under steady‐state conditions. While this is in principle achieved only after an infinitely long migration distance, experiments show that a rather short column may be sufficient in practice, when the concentration step is high enough and the nonlinear effects are strong (Zhu et al, 1993). In the present experiments the asymptotic solution was reached in all cases since the lowest concentration step was already relatively high (the value of b 1 C always exceeds 1, see Table 1 and Figure 5).…”

“…It is a powerful tool for the investigation of the mass transfer resistance in chromatographic column. The shock layer concept provides a new approach for the study of the column performance in nonlinear chromatography which could be as helpful as the column efficiency is in linear chromatography (Zhu and Guiochon, 1993; Zhu et al, 1993). Simple experiments permit the accurate determination of the shock layer thickness (SLT).…”

Anion-Exchange Displacement Centrifugal Partition Chromatography

“…By adding an acid or a base in the stationary phase as a retainer, Ito introduced the pH-zone-refining mode . For the first time in CCC and CPC, isotachic rectangularly shaped blocks of analytes separated by steep boundaries, the so-called shock layers, were observed . This protocol is restricted to solutes showing a dramatic difference in polarity and, therefore, in solubility between their neutral and ionized forms.…”

Effect of anti-Langmuir adsorption on spreading in porous media

“…This can lead to either contraction of the concentration front known as shock layer or expansion of the concentration front known as rarefaction, depending on the initial concentration profile of the solute [10,20,21]. For the Langmuir adsorption there are a few theoretical studies [19,[22][23][24] that examine the influence of adsorption on spreading of the solute. However, the anti-Langmuir adsorption isotherm is not yet reported in the theoretical community.…”