Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.01142 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911413984821248 |
|---|---|
| author | Cach, Jakub Farrell, Patrick E. Málek, Josef Tůma, Karel |
| author_facet | Cach, Jakub Farrell, Patrick E. Málek, Josef Tůma, Karel |
| contents | Viscoelastic rate-type fluids represent a popular class of non-Newtonian fluid models due to their ability to describe phenomena such as stress relaxation, non-linear creep, and normal stress differences. The presence of normal stress differences in a simple shear flow gives rise to forces acting in directions orthogonal to the primary flow direction. The rod climbing effect, i.e. the rise of a fluid along a rod rotating about its axis, is associated with this phenomenon. Within the class of viscoelastic rate-type fluids that includes the Oldroyd-B and Giesekus models with Gordon--Schowalter convected derivatives, we show -- by means of thermodynamical analysis and numerical simulations -- that a thermodynamically consistent variant of the Johnson--Segalman model captures experimental data exceedingly well and is therefore superior to other models in this class, including the standard Johnson--Segalman model, which is widely used in engineering applications but is shown here to be incompatible with the second law of thermodynamics. We release a robust and computationally efficient higher-order finite-element implementation as open-source software on GitHub. The implementation is based on an arbitrary Lagrangian--Eulerian (ALE) formulation of the governing equations and is developed using the Firedrake library. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01142 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A thermodynamically consistent Johnson-Segalman-Giesekus model: numerical simulation of the rod climbing effect Cach, Jakub Farrell, Patrick E. Málek, Josef Tůma, Karel Fluid Dynamics Viscoelastic rate-type fluids represent a popular class of non-Newtonian fluid models due to their ability to describe phenomena such as stress relaxation, non-linear creep, and normal stress differences. The presence of normal stress differences in a simple shear flow gives rise to forces acting in directions orthogonal to the primary flow direction. The rod climbing effect, i.e. the rise of a fluid along a rod rotating about its axis, is associated with this phenomenon. Within the class of viscoelastic rate-type fluids that includes the Oldroyd-B and Giesekus models with Gordon--Schowalter convected derivatives, we show -- by means of thermodynamical analysis and numerical simulations -- that a thermodynamically consistent variant of the Johnson--Segalman model captures experimental data exceedingly well and is therefore superior to other models in this class, including the standard Johnson--Segalman model, which is widely used in engineering applications but is shown here to be incompatible with the second law of thermodynamics. We release a robust and computationally efficient higher-order finite-element implementation as open-source software on GitHub. The implementation is based on an arbitrary Lagrangian--Eulerian (ALE) formulation of the governing equations and is developed using the Firedrake library. |
| title | A thermodynamically consistent Johnson-Segalman-Giesekus model: numerical simulation of the rod climbing effect |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2602.01142 |