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A thermodynamically consistent variational framework for non-Newtonian fluids with evolving internal variables.

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Title: A thermodynamically consistent variational framework for non-Newtonian fluids with evolving internal variables.
Authors: Choi, Yongbin1 (AUTHOR) choi@ikm.uni-hannover.de, Soleimani, Meisam2 (AUTHOR), Wick, Thomas3 (AUTHOR) thomas.wick@ifam.uni-hannover.de, Junker, Philipp2 (AUTHOR) junker@ikm.uni-hannover.de
Source: International Journal of Numerical Methods for Heat & Fluid Flow. 2026, Vol. 36 Issue 7, p2568-2599. 32p.
Subjects: Non-Newtonian fluids, Hamilton's principle function, Variational principles, Latent variables, Thermodynamics, Dynamic viscosity, Pseudoplastic fluids
Abstract: Purpose: This study presents a new variational model for non-Newtonian fluids based on Hamilton's principle with an internal variable describing spatial and temporal variations of the viscosity. Design/methodology/approach: The internal variable evolves in response to local flow conditions, enabling more refined and dynamic representation of complex non-Newtonian behaviors. The Type 1 model, originally introduced by Junker and Wick (2025) [P. Junker and T. Wick, " Space-Time Modeling and Numerical Simulations of Non-Newtonian Fluids Using Internal Variables," International Journal for Numerical Methods in Fluids 97, no. 12 (2025)] is revisited in the present work within an unified variational framework, and extended by introducing a new Type 2 model. Both models are derived from distinct free energy potentials: the Type 1 model describes viscosity evolution through the interaction between velocity and displacement gradients, while the Type 2 model captures viscosity variations driven by the magnitude of the strain. Findings: Both formulations are capable of reproducing shear-thinning and shear-thickening behaviors within a unified and thermodynamically consistent setting. Unlike conventional constitutive laws expressed as nonlinear algebraic relations between stress and the rate of strain, the proposed framework naturally incorporates the evolution of the viscosity both in space and time. Simulations in two and three spatial dimensions demonstrate that the proposed models effectively capture a wide range of non-Newtonian flow characteristics. Originality/value: The variational approach based on Hamilton's principle, incorporating an internal variable, is novel. This allows for a wider range of non-Newtonian fluid flows models, which can be further studied in engineering and applied mathematics. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Numerical Methods for Heat & Fluid Flow is the property of Emerald Publishing Limited 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.)
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DbLabel: Engineering Source
An: 194733978
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  Data: A thermodynamically consistent variational framework for non-Newtonian fluids with evolving internal variables.
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  Data: <searchLink fieldCode="AR" term="%22Choi%2C+Yongbin%22">Choi, Yongbin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> choi@ikm.uni-hannover.de</i><br /><searchLink fieldCode="AR" term="%22Soleimani%2C+Meisam%22">Soleimani, Meisam</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wick%2C+Thomas%22">Wick, Thomas</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> thomas.wick@ifam.uni-hannover.de</i><br /><searchLink fieldCode="AR" term="%22Junker%2C+Philipp%22">Junker, Philipp</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> junker@ikm.uni-hannover.de</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Numerical+Methods+for+Heat+%26+Fluid+Flow%22">International Journal of Numerical Methods for Heat & Fluid Flow</searchLink>. 2026, Vol. 36 Issue 7, p2568-2599. 32p.
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  Data: <searchLink fieldCode="DE" term="%22Non-Newtonian+fluids%22">Non-Newtonian fluids</searchLink><br /><searchLink fieldCode="DE" term="%22Hamilton's+principle+function%22">Hamilton's principle function</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+principles%22">Variational principles</searchLink><br /><searchLink fieldCode="DE" term="%22Latent+variables%22">Latent variables</searchLink><br /><searchLink fieldCode="DE" term="%22Thermodynamics%22">Thermodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+viscosity%22">Dynamic viscosity</searchLink><br /><searchLink fieldCode="DE" term="%22Pseudoplastic+fluids%22">Pseudoplastic fluids</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Purpose: This study presents a new variational model for non-Newtonian fluids based on Hamilton's principle with an internal variable describing spatial and temporal variations of the viscosity. Design/methodology/approach: The internal variable evolves in response to local flow conditions, enabling more refined and dynamic representation of complex non-Newtonian behaviors. The Type 1 model, originally introduced by Junker and Wick (2025) [P. Junker and T. Wick, " Space-Time Modeling and Numerical Simulations of Non-Newtonian Fluids Using Internal Variables," International Journal for Numerical Methods in Fluids 97, no. 12 (2025)] is revisited in the present work within an unified variational framework, and extended by introducing a new Type 2 model. Both models are derived from distinct free energy potentials: the Type 1 model describes viscosity evolution through the interaction between velocity and displacement gradients, while the Type 2 model captures viscosity variations driven by the magnitude of the strain. Findings: Both formulations are capable of reproducing shear-thinning and shear-thickening behaviors within a unified and thermodynamically consistent setting. Unlike conventional constitutive laws expressed as nonlinear algebraic relations between stress and the rate of strain, the proposed framework naturally incorporates the evolution of the viscosity both in space and time. Simulations in two and three spatial dimensions demonstrate that the proposed models effectively capture a wide range of non-Newtonian flow characteristics. Originality/value: The variational approach based on Hamilton's principle, incorporating an internal variable, is novel. This allows for a wider range of non-Newtonian fluid flows models, which can be further studied in engineering and applied mathematics. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Numerical Methods for Heat & Fluid Flow is the property of Emerald Publishing Limited 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:
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 32
        StartPage: 2568
    Subjects:
      – SubjectFull: Non-Newtonian fluids
        Type: general
      – SubjectFull: Hamilton's principle function
        Type: general
      – SubjectFull: Variational principles
        Type: general
      – SubjectFull: Latent variables
        Type: general
      – SubjectFull: Thermodynamics
        Type: general
      – SubjectFull: Dynamic viscosity
        Type: general
      – SubjectFull: Pseudoplastic fluids
        Type: general
    Titles:
      – TitleFull: A thermodynamically consistent variational framework for non-Newtonian fluids with evolving internal variables.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Choi, Yongbin
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            NameFull: Soleimani, Meisam
      – PersonEntity:
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            NameFull: Wick, Thomas
      – PersonEntity:
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            NameFull: Junker, Philipp
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          Dates:
            – D: 01
              M: 07
              Text: 2026
              Type: published
              Y: 2026
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              Value: 36
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              Value: 7
          Titles:
            – TitleFull: International Journal of Numerical Methods for Heat & Fluid Flow
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