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.