title: Analysis of linear two-dimensional general rate model for chromatographic columns of cylindrical geometry.
abstract: 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.
authors.affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, Pakistan; Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.
authors.forename: Shamsul
authors.initials: S
authors.lastname: Qamar
authors.affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, Pakistan.
authors.forename: David U
authors.initials: DU
authors.lastname: Uche
authors.affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, Pakistan; Department of Mathematics, HITEC University, Taxila Cantt, Pakistan.
authors.forename: Farman U
authors.initials: FU
authors.lastname: Khan
authors.affiliation: Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.
authors.forename: Andreas
authors.initials: A
authors.lastname: Seidel-Morgenstern
mesh_terms: D000465:Algorithms; D002853:Chromatography, Liquid / Q000379:methods*; D007700:Kinetics; D008962:Models, Theoretical
keywords: Analytical solutions; Cylindrical column; General rate model; Liquid chromatography; Mass transfer; Moment analysis