, Volume 80, Issue 3, pp 383–400 | Cite as

Analysis of Two-Component Non-Equilibrium Model of Linear Reactive Chromatography

  • Shamsul QamarEmail author
  • Sameena Bibi
  • Noreen Akram
  • Andreas Seidel-Morgenstern


This article presents semi-analytical solutions and analytical temporal moments of a two-component linear reactive lumped kinetic model incorporating irreversible (\(A\rightarrow B\)) and reversible (\(A\leftrightarrows B\)) reactions in a fixed-bed liquid chromatographic column. Both solid and liquid phase reactions and two sets of boundary conditions are considered. The current model equations contain a coupled system of two partial differential equations (PDEs) and two ordinary differential equations (ODEs). The solution methodology successively employs the Laplace transform and linear transformation steps to uncouple the governing set of coupled differential equations. The resulting system of uncoupled ODEs is solved by applying an elementary solution technique. The numerical Laplace inversion is employed to transform back the solutions in the actual time domain. To further analyze the effects of different kinetic parameters, statistical temporal moments are derived from the Laplace-transformed solutions. The current solutions extend and generalize our recent solutions for single-solute transport models of non-reactive liquid chromatography. For verification, the analytical results are compared with the numerical solutions of a high-resolution finite volume scheme. Several case studies of practical interest are considered. Good agreements in the results validate the correctness of semi-analytical solutions and the accuracy of proposed numerical algorithm.


Liquid chromatography Non-equilibrium transport Irreversible and reversible reactions Mass transfer Analytical solutions Moment analysis 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Shamsul Qamar
    • 1
    • 3
    Email author
  • Sameena Bibi
    • 2
  • Noreen Akram
    • 1
  • Andreas Seidel-Morgenstern
    • 3
  1. 1.Department of MathematicsCOMSATS Institute of Information TechnologyIslamabadPakistan
  2. 2.Department of MathematicsAir UniversityIslamabadPakistan
  3. 3.Max Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany

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