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REVIEW 2 major objections 5 minor 42 references

A thermodynamically consistent Johnson-Segalman-Giesekus model: numerical simulation of the rod climbing effect

T0 review · 2 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read A thermodynamically consistent Johnson–Segalman–Giesekus model reproduces rod-climbing experiments better than the engineering version, which the paper argues is incompatible with the second law of thermodynamics.

desk verdict Solid thermodynamic core and usable open-source solver; empirical 'superiority' is a per-point fit, and the abstract overstates the Model II inconsistency. read the letter →

arxiv 2602.01142 v2 pith:T6ABH7M3 submitted 2026-02-01 physics.flu-dyn

Jakub Cach , Patrick E. Farrell , Josef Málek , Karel Tůma This is my paper · ORCID
classification physics.flu-dyn MSC 76A1076M10
keywords viscoelasticrate-typefluidsJohnson–SegalmanmodelGiesekusthermodynamicconsistencyrodclimbingeffectWeissenbergconformationtensorfiniteelementmethod
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper aims to show that the standard engineering Johnson–Segalman viscoelastic model, even when augmented with Giesekus relaxation, is not thermodynamically defensible outside the upper-convected limit, and that a variant derived from a prescribed free energy and dissipation function is both consistent with the second law and better at reproducing a classic non-Newtonian phenomenon: the rise of a fluid along a rotating rod (the Weissenberg effect), caused by normal stress differences. For a neo-Hookean free energy depending on the conformation tensor, the new model (Model I) always has non-negative rate of dissipation for all slip parameters, while the engineering model (Model II) acquires an indefinite term that can make dissipation negative. In numerical simulations of a rotating-rod viscometer, Model I matches the measured climbing heights and their trend across rotation speeds substantially better than Model II or earlier Oldroyd-B and Johnson–Segalman fits. If the paper is right, engineers should prefer thermodynamically derived conformation-tensor models over stress-based engineering forms for free-surface viscoelastic flows.

What carries the argument

The machinery centres on the conformation tensor B (a symmetric positive-definite tensor tracking elastic polymer deformation) and the reduced dissipation identity ξ=T:D−ρψ̇. The paper pairs a neo-Hookean free energy ψ(B)=G/(2ρ)(tr B−ln det B−d) with a Gordon–Schowalter objective time derivative (frame-indifferent, slip parameter a; a=1 gives the Oldroyd upper-convected derivative) and a Giesekus-type relaxation. The central algebraic identity (I−B⁻¹):(B−I)=Σ_i(λ_i^{1/2}−λ_i^{−1/2})²≥0 makes Model I's dissipation manifestly non-negative. This machinery converts two scalar constitutive choices—energy storage and dissipation—into one tensorial law, and it exposes Model II's flaw: its extra str

What would settle it

Attempt to find a Helmholtz free energy for Model II that makes its dissipation non-negative for all admissible B and D with a≠1; success would directly refute the paper's claim that the engineering Johnson–Segalman model is incompatible with the second law.

Watch

Extended reading notes

Core claim

The paper claims a structural distinction between two similar-looking constitutive equations. Model I writes the Cauchy stress with a factor a multiplying the elastic term and evolves a symmetric positive-definite conformation tensor B through a Gordon–Schowalter derivative with Giesekus-type relaxation; its dissipation is non-negative for all a∈[−1,1], α∈[0,1]. Model II has the same evolution but no factor a in the stress, producing an indefinite cross term G(1−a)(B+B⁻¹):D; for a≠1 its dissipation can go negative. In rotating-rod simulations, Model I matches experimental climbing heights and trends across rotation speeds; Model II predicts exaggerated rod descent and fits poorly. The author

Load-bearing premise

The charge that the engineering Johnson–Segalman model violates the second law presupposes that it must be judged by the same neo-Hookean free energy as the new model; if a different free energy is allowed, the indefinite term only shows incompatibility with one chosen thermodynamic structure, not with thermodynamics as such.

Editorial extensions

If this is right

  • Outside the upper-convected limit (a=1), the engineering Johnson–Segalman model should not be trusted for free-surface flows; the thermodynamically consistent variant gives physically plausible surfaces across a∈[0,1].
  • Model I has a clean Newtonian limit as a→0, with elastic stresses and stored energy vanishing continuously; Model II lacks this limit, which explains its anomalous rod-descent predictions.
  • The non-negative dissipation result holds for all a∈[−1,1] and α∈[0,1], so the thermodynamically consistent construction covers the whole Gordon–Schowalter family, not just the Oldroyd-B case.
  • Higher-order finite-element ALE simulations of the rotating-rod viscometer reach mesh- and p-converged free-surface shapes at a fraction of the cost of low-order simulations, making quantitative rod-climbing comparisons routine.
  • The numerical results for the Giesekus case show the analytical climb/descent criterion is conservative and systematically offset from the actual transition, so asymptotic criteria should be used with caution beyond their formal limits.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The second-law critique of Model II is conditional: the indefinite cross term appears when the engineering model is tested against the same neo-Hookean free energy used for Model I. A different free energy could in principle restore non-negative dissipation, so the paper's 'incompatible with the second law' wording is stronger than the calculation alone supports.
  • The slip parameter a is fitted separately at each rotation speed, drifting from about 0.83 at lower speeds to about 0.805 at higher speeds. A sharper test of the model would fix a single value across all speeds and check whether the experimental trend still matches, since a should be a material parameter.
  • The same construction likely transfers to other rate-type models: putting the free energy and dissipation on the same footing and scaling the elastic stress by the objective-derivative parameter eliminates the indefinite cross term, which suggests a general recipe for thermodynamically admissible viscoelasticity.
  • The systematic offset between the asymptotic Giesekus transition criterion and the numerical transition suggests comparable asymptotic criteria for other free-surface effects may inherit a conservative bias.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper introduces a thermodynamically consistent Johnson–Segalman–Giesekus model (Model I, Eq. 3) in which the slip parameter multiplies the elastic stress contribution, and contrasts it with the classical engineering JSG model (Model II, Eqs. 4/6) in which it does not. The authors prove non-negativity of the rate of dissipation for Model I under a neo-Hookean free energy (Eqs. 16–21), show that Model II has an indefinite cross term under the same free energy (Eq. 30), and derive Model I in the a=1 case from the Rajagopal–Srinivasa framework. They then develop a high-order finite-element ALE scheme, validate it against mesh and p-refinement studies and against earlier Oldroyd-B results, and compare rod climbing predictions with the Beavers–Joseph experiments and prior numerical studies. The central empirical claim is that Model I captures the experimental climbing heights 'exceedingly well' and is therefore superior to Model II and other models in the class.

Significance. If the empirical claim were fully supported, the paper would deliver a thermodynamically admissible JSG-type model with a clear advantage over the widely used engineering version, plus an open-source, reusable computational tool for free-surface viscoelastic flows. The thermodynamic part is genuinely strong: the positivity proof in Section 2.1 is transparent, parameter-free, and correct for Model I, and the derivation in Section 3 connects the model to evolving natural configurations. The numerical sections show careful convergence studies and release code on GitHub. However, the headline claim of empirical superiority is currently under-supported because the slip parameter is fitted separately at each rotation speed, and the abstract overstates the Model II thermodynamic result. These issues are fixable but they are load-bearing for the paper's main selling points.

major comments (2)
  1. [§7.3, Figure 8] The abstract states that the engineering Johnson–Segalman model is 'incompatible with the second law of thermodynamics,' but the analysis in Section 2.2 only shows that, for the neo-Hookean free energy (7), the rate of dissipation in Eq. (30) contains an indefinite term G(1−a)(B+B^{−1}):D that can become negative. This does not prove incompatibility with the second law in general, because another choice of free energy and dissipation structure might generate the same stress/evolution equations with non-negative dissipation. The paper's own Section 2.2 wording ('does not guarantee non-negative rate of dissipation') is appropriately conditional; the abstract and conclusion should be aligned with that weaker, defensible statement.
  2. [§7.4, Figure 9] The text claims that the Giesekus implementation 'reproduce[s] the analytical condition for the presence of fluid climbing ... achieving good agreement,' but the following discussion reports a systematic quantitative offset that persists even in the asymptotic regime We≪1, Re≪1, G≫1, and larger deviations as the assumptions are relaxed. This internal tension should be resolved: either state explicitly that the comparison is qualitative, quantify the offset, or discuss whether the offset reflects the finite domain, the contact line treatment, or limitations of the asymptotic criterion. Since this comparison is used as a validation of the numerical method, the discrepancy merits a clearer presentation.
minor comments (5)
  1. [§3] The derivation in Section 3 is restricted to the case a=1, while Model I in Eq. (3) is defined for general a. The positivity proof in Section 2.1 covers general a, but the derivation of the general-a structure is attributed to [9]. Please clarify this division explicitly in the text.
  2. [Eq. (5) and Eq. (6)] The derivation of Eq. (6) from Eq. (4) via S=G(B−I), μ_p=τG is terse. It is correct, but a reader may be confused by the fact that the Gordon–Schowalter derivative of the identity tensor contributes −2aD. A one-line remark would help.
  3. [§7.2, Figure 4] The comparison with the reference results is clear, but the captions do not state the extraction procedure for the literature data except a general reference to automeris.io. Please state this in the main text once and note the uncertainty associated with digitized data.
  4. [§7.1] The statement 'The fluid parameters specified in the simulations ... are the slip parameter a, the mobility parameter α, and the dimensionless numbers' is slightly misleading, because a and α are material parameters while Re, We, St, Ca are flow/dimensionless parameters. Reword to avoid confusion.
  5. [General] There are occasional language issues (e.g., 'does not guarantee non-negative rate of dissipation fora,1' should be 'for a≠1') and inconsistent use of 'a' as both the slip parameter and the rod radius in the definition H:=h(r=a,t→∞) in Section 7.2. Please check notation consistency.

Circularity Check

1 steps flagged · score 6.0 of 10

Empirical superiority claim reduces to per-rotation-speed fit of slip parameter a; thermodynamic proof itself is self-contained.

  1. fitted input called prediction [Section 7.3, Figure 8 (a)–(d) and accompanying text; model equations (3)]
    "More importantly, the thermodynamically consistent Model I (cyan color in the plot) provides significantly better agreement with the experimental measurements of rod climbing reported in [15, 16]. ... Present work, Model I, with a = 0.830 (a) ω=1.7 rev/s ... Present work, Model I, with a = 0.815 (b) ω=2.1 rev/s ... Present work, Model I, with a = 0.805 (c) ω=2.6 rev/s ... Present work, Model I, with a = 0.805 (d) ω=2.9 rev/s"

    Model I's stress is T=-pI+2μ_s D+aG(B-I) (Eq. 3), so a is a material parameter scaling the elastic stress and directly controlling the climbing height. The figure labeled 'Predictions' uses a different a for each rotation speed (0.830, 0.815, 0.805, 0.805), with no fixed-a set reported. With one free parameter per experimental curve, the 'exceedingly well' agreement is an interpolation exercise; the claimed superiority over the fixed-a Model II curves is not a parameter-free prediction. The text's admission that τ and γ could be further adjusted to improve agreement confirms the comparison is not a fixed-material-parameter test.

full rationale

The thermodynamic-consistency analysis is not circular: given ψ(B)=G/(2ρ)(trB−ln detB−d) and Model I's evolution, Eqs. (16)–(21) prove ξ≥0 algebraically for all a and α∈[0,1]; no fitted or external input enters. The Section 3 construction from prescribed ψ and dissipation is a constitutive derivation, not a prediction, and the non-negativity of ξ follows from the chosen dissipation, which is standard in this framework. The Giesekus comparison (§7.4) is checked against an external analytical condition (Ruangkriengsin et al.), so it is independently falsifiable. The only load-bearing reduction I find is the empirical 'superiority' claim: Model I's agreement in Figure 8 is achieved with a different slip parameter a at each rotation speed, and the paper even notes further improvement could be obtained by varying τ and γ. Since a is a material parameter in Eq. (3), per-ω selection makes the 'captures experimental data exceedingly well' statement equivalent to fitting one parameter per data set rather than a fixed-parameter prediction. Separately, the abstract's 'incompatible with the second law' for Model II is stronger than the paper's own §2.2 conclusion ('does not guarantee non-negative rate of dissipation'); that is an overstatement, not a circular step. Self-citations ([8], [10]) are used as background/derivation references, not as the sole justification for the central empirical claim. Score 6 reflects partial circularity: the thermodynamic derivation stands, but the headline empirical comparison reduces, at least in part, to a per-datum fit.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The thermodynamic-consistency result depends on the chosen free energy and dissipation; the empirical result depends on a slip parameter fitted per rotation speed. No new physical entities are introduced.

free parameters (4)
  • Gordon–Schowalter slip parameter a (Model I experimental fit) = 0.830 (ω=1.7 rev/s), 0.815 (ω=2.1 rev/s), 0.805 (ω=2.6, 2.9 rev/s)
    Chosen separately to match Beavers–Joseph/Debbaut–Hocq rod-climbing data in Figure 8; no single fixed a is tested across all rotation speeds.
  • Slip parameter a (Model II comparison) = 0.716 and 0.682
    Taken from prior numerical studies [17,18]; the comparison inherits those fits.
  • Giesekus mobility parameter α = scanned (α∈[0,1]; chosen to set Λ in [0.53, 2.14])
    Used to define the Giesekus relaxation term and to set the elasticity number Λ in the Ruangkriengsin et al. validation; not determined by independent measurement.
  • Relaxation time τ and surface tension γ = τ=0.0162/(1−μ_s/μ_p), γ=0.0308 N m−1
    Section 7.3 says further agreement could be obtained by adjusting these parameters, so they are not fixed by independent measurement in the comparison.
assumptions (4)
  • domain assumption Model II is judged using the neo-Hookean free energy ψ(B)=G/(2ρ)(trB−ln detB−d) of Eq. (7), i.e. the same thermodynamic variable structure as Model I.
    Without this, the indefinite cross term in Eq. (30) only shows inconsistency of a particular energy choice, not a general violation of the second law.
  • ad hoc to paper The rate of dissipation for Model I is prescribed as ξ=2μs|D|^2+2μp D_{κp(t)} M(C_{κp(t)}):D_{κp(t)} with M(C)=((1−α)C^{-1}+αI)^{-1} (Eq. 44).
    This mobility choice is what generates the Giesekus α(B^2−B) term; it is postulated, not derived from first principles.
  • domain assumption The principle of maximal rate of entropy production selects the unique relation (48) between D_{κp(t)} and C_{κp(t)}.
    Core of the Rajagopal–Srinivasa framework; used in §3.3 to identify the constitutive equations uniquely.
  • domain assumption Standard incompressible balance laws (1), smooth single-valued free surfaces, and no-slip/free-slip boundary choices hold.
    The ALE method and boundary treatment rely on these; the paper explicitly notes limitations for steep or folding free surfaces and topological changes.

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Cite this review

Pith. "Pith review of A thermodynamically consistent Johnson-Segalman-Giesekus model: numerical simulation of the rod climbing effect." pith.science (2026). https://pith.science/paper/T6ABH7M3

@misc{pith2026260201142,
  author       = {Pith},
  title        = {Pith review of: A thermodynamically consistent Johnson-Segalman-Giesekus model: numerical simulation of the rod climbing effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T6ABH7M3}},
  note         = {Machine review of arXiv:2602.01142}
}
read the original 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.

Figures

Figures reproduced from arXiv: 2602.01142 by the authors.

Figure 1
Figure 1. Sketch of the reference configuration κR(B), the current configuration κt(B) and the natural configuration κp(t)(B). The deformation gradient FκR is multiplicatively decomposed. The natural configuration is defined as the configuration that the body in the current configuration would take if the external stimuli were removed. Hence the natural configuration κp(t)(B) is associated with the current configuration κt(B)… view at source ↗
Figure 2
Figure 2. Sketch of the axi-symmetric rod climbing configuration used in all simulations. The problem is formulated in the meridional plane of [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Spatial discretization convergence is examined for [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Comparison of the Oldroyd-B results obtained in the present work with the reference results [ [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]
Figure 5
Figure 5. Figure 5: Visualization of the resulting steady state for [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]
Figure 6
Figure 6. Figure 6: Comparison of results obtained in the present work for JS Models I and II at [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]
Figure 7
Figure 7. Figure 7: Comparison of the results obtained in the present work for JS Models I and II at [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: Comparison of rod climbing predictions for the commonly used Johnson–Segalman model in the engineering community (Model II) [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 9
Figure 9. Figure 9: Rod climbing heat maps for Giesekus model with di [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.