Model: Chromatography

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.

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.

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.

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.

2

2

11xc

Dxc

vtc

dcdn i

effii

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.

ii

iiii

cK

cKnn

10

20

1 ii

ii

i

i

cK

Kn

dc

dn

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.

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.

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.