Abstract:
Analytical and Numerical Solutions of Two-Dimensional Non-Equilibrium
Models of Liquid Chromatography
Column liquid chromatography is the most widely used physicochemical technique for the
separation, identification, quantification and purification of constituents of complex mixtures.
It has significant contributions in petrochemical, fine chemical, pharmaceutical and
biotechnical industries. This dissertation is concerned with the analytical and numerical
solutions of non-reactive and reactive non-equilibrium models of liquid chromatography in
cylindrical geometry. The models are described by systems of convection-dominated partial
differential equations coupled with some algebraic and differential equations. Both linear
and nonlinear models are investigated. The models incorporate cylindrical pulse injections
of finite width through inner cylindrical core or outer annular ring at the column inlet,
two different sets of boundary conditions, liquid and solid phase reactions, and sorption kinetic
process. The Hankel and Laplace transformations are successively applied to obtain
analytical solutions of the models. The analytical expressions of statistical time dependent
moments are obtained from the Hankel and Laplace transformed solutions. These
moments can be utilized for further analyze the solute transport behavior. In the case of
nonlinear models, a semi-discrete high resolution finite volume scheme (HR-FVS) is applied
to get physically realistic solutions. Several case studies are carried out to analyze
the effects of mass transfer kinetics on the process. The derived semi-analytical solutions
are also compared with the numerical results of the suggested HR-FVS. Good agreements
in the results verify the correctness of analytical solutions and accuracy of the proposed
numerical algorithm. The derived solutions provide a useful tool for sensitivity analysis,
process optimization, analyzing numerical algorithms, studying and quantifying the effects
axial and radial dispersion coefficients, and for estimating the model parameters from a
laboratory-scale experiments.
