Chromatography Column

Chromatography is one of the most important tools for both analysis of chemical mixtures and purification. Chromatography columns come in vastly different sizes, but the basic principle behind them remains the same: that different molecular interactions will cause different substances to flow through the column at different speeds, effectively separating them from each other. This model studies one such type of interaction. The free BioChem Modelica library is needed to run this example; it can be downloaded here.

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The Model

A chromatography column can be described as having two phases, the mobile phase and the stationary phase. Substances will move between the two phases, subject to an equilibrium. Substances in the mobile phase will also move toward the bottom of the column. Partial differential equations describe the substance concentrations of the two phases at each point in the column. Using the method of lines, the spatial points can be discretized and the resulting DAE solved numerically.
The model partial differential equations are discretized in Mathematica and automatically converted to Modelica code.

Automatic Code Generation

Mathematica can generate and export Modelica code that can be directly simulated in SystemModeler.

The example shows the chromatography column being used to analyze a simple biochemical reaction modeled using the free Modelica library BioChem. If the eluant of the column was continuously monitored using a spectrophotometer, distinct peaks would signal the elution of a particular substance. Simulating the system makes it so that the elution profile can be analyzed to see how each substance contributes to the profile.
Plot of how each of the substances contributes to the elution profile.

Interact with the System

With the simulation results imported into Mathematica, the inside of the chromatography column can be visualized. The interactive visualizations can be deployed and distributed using the Computable Document Format, CDF.
Substance separation inside of the column and a representation of how each substance contributes to the output signal from the spectrophotometer.

Interact with the Results

Results from SystemModeler can be imported into Mathematica, where further analysis can be performed.

Discretize Partial Differential Equations

Using the method of lines, the spatial coordinates are discretized, while the time derivatives are kept continuous.

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