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Bibliographic Details
Main Authors: Cach, Jakub, Farrell, Patrick E., Málek, Josef, Tůma, Karel
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.01142
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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