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This study presents a thermodynamically consistent variant of the Johnson-Segalman model for viscoelastic fluids and demonstrates its superiority in simulating the rod climbing effect, where fluid rises along a rotating rod. Through thermodynamic analysis and numerical simulations, the researchers show that their model matches experimental data better than existing models in its class, including the widely-used standard Johnson-Segalman model, which is revealed to violate the second law of thermodynamics. The team has released open-source software implementing their model using higher-order finite-element methods.
Why it matters
This work provides engineers and scientists with a more accurate and physically consistent tool for modeling non-Newtonian fluids, which are common in industrial processes involving polymers, food products, and biological materials. The discovery that the standard Johnson-Segalman model violates thermodynamic principles has significant implications for the reliability of existing engineering simulations using this model.
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arXiv:2602.01142v2 Announce Type: replace
Abstract: 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.