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Numerical approximation of a general rate model of liquid chromatography considering solvent and thermal gradients.

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Title: Numerical approximation of a general rate model of liquid chromatography considering solvent and thermal gradients.
Authors: Shehzad, Amir1 (AUTHOR), Perveen, Sadia1 (AUTHOR) sadia.ahsan@au.edu.pk, Fatima, Andleeb2 (AUTHOR), Qamar, Shamsul2 (AUTHOR)
Source: Journal of Liquid Chromatography & Related Technologies. Mar-May2026, Vol. 49 Issue 5-8, p208-228. 21p.
Subjects: Gradient elution (Chromatography), Rate equation model, Adsorption isotherms, Thermal gradient measurment, Transport equation, Numerical analysis, Liquid chromatography
Abstract: In liquid chromatography simultaneous gradients of solute and temperature can be applied to control adsorption of solute on the stationary phase by simultaneously changing the composition of the mobile phase and the temperature. These parallel variations alter adsorption equilibria and solute migration rates. The work extends a general rate model to incorporate such parallel gradients, enabling the simulation of two-mode gradient elution. The model consists of coupled nonlinear convection-diffusion equations which describe the simultaneous transport of mass, energy, and solvent composition within a chromatographic column. By introducing time-dependent gradients of temperature and solvent composition, it accurately represents advanced elution protocols. The integrated retention model combines the theory of linear solvent strengths with modified van't Hoff behavior, defining Henry's constants and the non-linearity coefficients as functions of solvent composition and temperature. The governing equations are solved with a high-resolution finite-volume scheme, effectively capturing temperature-dependent retention, nonlinear adsorption, and sharp concentration fronts. The effects of positive, negative, and mixed solvent-temperature gradients, as well as important operational parameters, on peak shape and separation efficiency are quantified through numerical simulations. The findings show that, in comparison to single-gradient or isothermal operations, combined gradients achieve faster elution, better peak symmetry, and better separation performance. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:In liquid chromatography simultaneous gradients of solute and temperature can be applied to control adsorption of solute on the stationary phase by simultaneously changing the composition of the mobile phase and the temperature. These parallel variations alter adsorption equilibria and solute migration rates. The work extends a general rate model to incorporate such parallel gradients, enabling the simulation of two-mode gradient elution. The model consists of coupled nonlinear convection-diffusion equations which describe the simultaneous transport of mass, energy, and solvent composition within a chromatographic column. By introducing time-dependent gradients of temperature and solvent composition, it accurately represents advanced elution protocols. The integrated retention model combines the theory of linear solvent strengths with modified van't Hoff behavior, defining Henry's constants and the non-linearity coefficients as functions of solvent composition and temperature. The governing equations are solved with a high-resolution finite-volume scheme, effectively capturing temperature-dependent retention, nonlinear adsorption, and sharp concentration fronts. The effects of positive, negative, and mixed solvent-temperature gradients, as well as important operational parameters, on peak shape and separation efficiency are quantified through numerical simulations. The findings show that, in comparison to single-gradient or isothermal operations, combined gradients achieve faster elution, better peak symmetry, and better separation performance. [ABSTRACT FROM AUTHOR]
ISSN:10826076
DOI:10.1080/10826076.2026.2648995