High-performance liquid chromatographic 2D-reversible reactive modelling: Analytical and numerical study

This study presents a comprehensive analytical and numerical investigation of a two-dimensional equilibrium-dispersive (2D-EDM) chromatographic model describing reversible reactions between two solutes, ω₁ and ω₂. The system is formulated for a cylindrical geometry representative of high-performance liquid chromatography (HPLC), comprising two concentric regions corresponding to the inner and outer phases. The axial domain extends from the inlet (z=0) to the outlet (z=Lorz→∞), while radial effects arising from inner-phase injection are explicitly incorporated. To address the geometric complexity and transient transport behavior, the governing equations are solved using Laplace and Hankel transforms. The model enables systematic evaluation of the influence of flow velocity, axial dispersion, radial position, Peclet number, and boundary conditions (Dirichlet and Neumann) on solute concentration profiles. Analytical solutions are validated through numerical Laplace inversion techniques, demonstrating strong agreement and numerical robustness. The results reveal the pronounced sensitivity of elution dynamics to hydrodynamic and boundary parameters. Dirichlet boundary conditions promote faster elution, whereas Neumann boundary conditions enhance retention. Overall, the proposed framework provides mechanistic insight into mass transport and reaction dynamics in concentric chromatographic systems and offers a rigorous tool for optimizing separation efficiency and operational performance in advanced HPLC applications.