Separating mixtures and solutions: Chromatography Mixtures and Solutions.
Model: Chromatography. Introduction Chromatography encompasses an important group of methods to...
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Transcript of Model: Chromatography. Introduction Chromatography encompasses an important group of methods to...
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.