Modelling counter-current chromatography: a chemical engineering perspective

Area of Science:

• Chromatography
• Separation Science
• Chemical Engineering

Background:

• Conventional chromatography assumes solutes only move in the mobile phase.
• Counter-current chromatography involves intense mixing of both phases.
• Longitudinal dispersion in the stationary phase is a factor in counter-current systems.

Purpose of the Study:

• To propose a cell model for chromatographic processes that includes longitudinal mixing in both stationary and mobile phases.
• To provide an equation for determining the number of perfectly mixed cells based on phase mixing rates.
• To analyze parameter determination and relationships within the proposed model.

Main Methods:

• Development of a cell model for chromatographic processes.
• Derivation of an equation for the number of perfectly mixed cells (n).
• Comparison of the discontinuous cell model with continuous diffusion under equilibrium conditions.

Main Results:

• A novel equation for 'n' was derived: n = LF/(2ADc)/(1 + Sf(lambda - 1)).
• The equation incorporates mixing rates (Ds, Dm) and other chromatographic parameters (F, L, Ac, KD).
• The model accounts for longitudinal dispersion in both mobile and stationary phases.

Conclusions:

• The proposed cell model offers a more comprehensive understanding of solute transport in counter-current chromatography.
• The derived equation provides a quantitative method to assess the impact of longitudinal mixing.
• Further discussion on parameter determination and their interrelationships is provided.