Analysis of linear two-dimensional general rate model for chromatographic columns of cylindrical geometry

- An analysis of a two-dimensional model of a chromatographic column is presented.
- The finite Hankel and Laplace transforms are jointly applied to solve the model.
- Analytical solutions quantify the influence of solute transport in radial direction.
- Different sets of boundary conditions are considered.
- For further analyses, temporal moments up to the fourth order are derived.

This work is concerned with the analytical solutions and moment analysis of a linear two-dimensional general rate model (2D-GRM) describing the transport of a solute through a chromatographic column of cylindrical geometry. Analytical solutions are derived through successive implementation of finite Hankel and Laplace transformations for two different sets of boundary conditions. The process is further analyzed by deriving analytical temporal moments from the Laplace domain solutions. Radial gradients are typically neglected in liquid chromatography studies which are particularly important in the case of non-perfect injections. Several test problems of single-solute transport are considered. The derived analytical results are validated against the numerical solutions of a high resolution finite volume scheme. The derived analytical results can play an important role in further development of liquid chromatography.