Optimization of the column efficiency and production rate for displacement chromatography : an application of the shock layer theory

Although there has been constant efforts to solve the contradicted experimental reports about the optimum linear velocity for the minimum overlap in the mixed zone of the isotactic train in displacement chromatography, all the attempts are not successful since they are based on the not realistic ideal mode. For a given system the only way to find out the optimum value used to be by repeating the separations under different linear velocities experimentally or numerically.

For a long time, the shock layer theory developed by Rhee and Amundson for single and multi-component frontal analysis has been ignored and more surprisingly, has never been applied to the optimization of displacement chromatography. In this dissertation, the shock layer theory is applied to the multi-component shock layer or the mixed zone between successive bands in a fully developed isotactic train in displacement chromatography. The shock layer thickness were measured from the experimental chromatograms for single component frontal analysis and from the numerically generated chromatograms for displacement chromatography. The shock layer thickness data found agree very well with the predictions from the shock layer thickness equations derived based on the kinetic model.

In the particular case of components following the Langmuir competitive isotherm, the shock layer theory is successfully used to derive the analytical equations given the optimum linear velocity, u^sopt, for the minimum Shock layer thickness in both single frontal and displacement chromatography. The optimum linear velocity is not only a function of the coefficients of the axial dispersion and the mass transfer resistance terms, and the retention factor (k’₀), as in linear chromatography, but also a function of the plateau concentration and the second Langmuir parameter of the isotherm, b of the feed component in single component frontal analysis and of the displacer in displacement chromatography. This discovery explains the apparent contradictions found in the literature regarding the influence of the mobile phase flow velocity on the degree of separation between bands achieved in displacement chromatography, and clarify certain controversies. There also exists the optimum linear velocity for the maximum production rate, u^popt. In agreement with previous experimental results, those optimum flow values are different for the different feed components.

Based on the shock layer thickness equation, the equation to calculated the product contained in the mixed zone in displacement chromatography is derived. The derivation of the recovery yield is also possible. The shock layer thickness increases rapidly and the production rate decreases sharply when α - 1 tends towards 0. components. Also, those derived equations are used to explain the influences of the displacer and feed component retention factors and concentrations to the optimum linear velocities, u^soptand u^popt, and the optimization of the production rate of displacement chromatography. The shock layer theory permits an easy access to the optimization of these parameters.