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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]
Copyright of Journal of Liquid Chromatography & Related Technologies is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 193623142
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Label: Title
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  Data: Numerical approximation of a general rate model of liquid chromatography considering solvent and thermal gradients.
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  Data: <searchLink fieldCode="AR" term="%22Shehzad%2C+Amir%22">Shehzad, Amir</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Perveen%2C+Sadia%22">Perveen, Sadia</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sadia.ahsan@au.edu.pk</i><br /><searchLink fieldCode="AR" term="%22Fatima%2C+Andleeb%22">Fatima, Andleeb</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Qamar%2C+Shamsul%22">Qamar, Shamsul</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Liquid+Chromatography+%26+Related+Technologies%22">Journal of Liquid Chromatography & Related Technologies</searchLink>. Mar-May2026, Vol. 49 Issue 5-8, p208-228. 21p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Gradient+elution+%28Chromatography%29%22">Gradient elution (Chromatography)</searchLink><br /><searchLink fieldCode="DE" term="%22Rate+equation+model%22">Rate equation model</searchLink><br /><searchLink fieldCode="DE" term="%22Adsorption+isotherms%22">Adsorption isotherms</searchLink><br /><searchLink fieldCode="DE" term="%22Thermal+gradient+measurment%22">Thermal gradient measurment</searchLink><br /><searchLink fieldCode="DE" term="%22Transport+equation%22">Transport equation</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Liquid+chromatography%22">Liquid chromatography</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Liquid Chromatography & Related Technologies is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/10826076.2026.2648995
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 21
        StartPage: 208
    Subjects:
      – SubjectFull: Gradient elution (Chromatography)
        Type: general
      – SubjectFull: Rate equation model
        Type: general
      – SubjectFull: Adsorption isotherms
        Type: general
      – SubjectFull: Thermal gradient measurment
        Type: general
      – SubjectFull: Transport equation
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Liquid chromatography
        Type: general
    Titles:
      – TitleFull: Numerical approximation of a general rate model of liquid chromatography considering solvent and thermal gradients.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Shehzad, Amir
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          Name:
            NameFull: Perveen, Sadia
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            NameFull: Fatima, Andleeb
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            NameFull: Qamar, Shamsul
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          Dates:
            – D: 01
              M: 03
              Text: Mar-May2026
              Type: published
              Y: 2026
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              Value: 49
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              Value: 5-8
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            – TitleFull: Journal of Liquid Chromatography & Related Technologies
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