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.

Analytical and numerical solutions of two-dimensional general rate models for liquid chromatographic columns packed with core–shell particles

“…The remaining solution procedure is similar to one presented in our previous article [41] and is, therefore, omitted here. Thus, the general Hankel-Laplace domains solution is given as…”

“…Recently, we have also derived analytical solutions and temporal moments of linear 2D-models for cylindrical columns packed with fully-porous particles [38][39][40][41]. Very recently, Qamar et al [22,42] have investigated linear and nonlinear 1D-models for core-shell particles.…”

“…These results are in agreement with the results inFigure 3 (c). For the effects of P e ρ on fully porous particles, see Qamar et al[41].Figures 9 (a)-(d)shows plots of the local moment on the radial coordinate this time for ρ core = 0, 0.5 and 0.8. It can be seen that the values of the moments are decreasing as the value of ρ core is increased from 0 to 0.8.Figure 9(e) shows the results of the plotted plate heights HETP (c.f.…”

Analysis of two‐dimensional models for liquid chromatographic reactors of cylindrical geometry

“…Our research group has solved analytically the linear one-dimensional (1D) and two-dimensional (2D) models of nonreactive and reactive chromatography. [11][12][13][14][15][16] The current work extends our previous analysis on 1D-GRM 17 to the analysis of linear two-component reactive 2D-GRM considering both axial and radial concentration gradients. Analytical solutions of the model for irreversible and reversible reactions are derived by applying the Hankel transformation, the Laplace transformation, the eigendecomposition technique, and the conventional solution technique for ordinary differential equations (ODEs).…”

Evaluation of the van Deemter equation in terms of open‐ended flow to chromatography

“…Frequently, chromatographic parameters are evaluated with double-logarithmic plots [14,[27][28][29][30]; however, this method runs the risk of suppressing information that may be gained from minor details in the experimental data, which are important for understanding the mechanisms of chromatography [26]. Many details of the chromatographic process have been included in theories such as the moment analysis of rectangular concentration profiles injected into columns [21,31]. However, to what extent a rectangular concentration profile or pulse-like concentration profile [32] maintains its shape during elution through the column should be investigated in greater detail [26].…”