1. Model: Chromatography

2. Introduction
Chromatography encompasses an important group of methods to separate closely related components of complex mixtures.
In this model, the separation in High Performance Liquid Chromatography (HPLC) is simulated.

3. Problem Definition
In HPLC, the sample is introduced as a zone in a liquid mobile phase by an injector.
The mobile phase containing the sample zone is pumped through a column containing a solid stationary phase.

4. Problem Definition
The mobile and stationary phase is chosen so that the components of the sample to varying degrees are distributed between the two phases.
Components that strongly adsorb to the stationary phase move slowly with the flow of the mobile phase.
Components that are weakly adsorbed move more rapidly.

5. Problem Definition – Domain Equation
A mass balance for the system is given by:
Where ci is the conventation of component i, ni the concentration on the stationary phase, v the mobile phase flow and  the phase ratio of the column.

6. Problem Definition – Domain Equation
The adsorption isotherm for both components is assumed to follow a Langmuir adsorption isotherm.
where Ki is the adsorption constant for component i and n0i is the monolayer capacity of the stationary phase for component i.

7. Results
The concentration of components 1 and 2 in the column during the migration through the column at times 0, 80 and 160 s.
The originally bell shaped concentration profiles is deformed and skewed as it moves in the column.
Species 1 moves faster than species 2.

8. Results
A close-up of the concentration profile of component 2 during the entrance into the column. Solid line corresponds to the mobile phase concentration, the dashed line to the stationary phase concentration, and the dash-dotted line to the sum of mobile and stationary phase concentrations.

9. Results
The chromatogram registered by the detector. The dashed line shows the concentration of species 2, c2, as function of time and the solid line shows c1.