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Dense Suspensions in Rotary Shear

T0 review · 2 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Rotary shear makes dense suspensions always diffusive, and viscosity minima no longer signal a reversible–irreversible transition.

desk verdict A genuinely new shear protocol with a clean decoupling result; the 'always diffusive' claim is somewhat stronger than the evidence. read the letter →

arxiv 2411.13463 v1 pith:RCVRK3ZO submitted 2024-11-20 cond-mat.soft physics.flu-dyn

Naveen Kumar Agrawal , Zhouyang Ge , Martin Trulsson , Outi Tammisola , Luca Brandt This is my paper · ORCID
classification cond-mat.softphysics.flu-dyn MSC 76T20 PACS 47.57.Qk83.80.Hj
keywords densesuspensionsrotaryshearoscillatoryreversible-irreversibletransitionnon-Brownianmicrostructurenormalstressdifferencesreversal
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

This paper introduces rotary shear (RS), a periodic flow in which two orthogonal oscillatory shears are applied out of phase so that the shear direction rotates continuously about the velocity-gradient axis while the shear-rate magnitude stays constant. Using simulations of dense non-Brownian suspensions, the authors try to establish that RS separates rheology from dynamics: although the suspension viscosity shows the same non-monotonic strain-amplitude dependence and the same onset of second normal stress differences as in oscillatory shear (OS), the particles never organize into a reversible absorbing state. At every strain amplitude tested, stroboscopic particle motion is diffusive, because the absence of sudden shear reversal keeps the microstructure in contact and anisotropic at all times. A reversible variant (RRS) that reverses the rotation each half-cycle behaves like OS and recovers the reversible–irreversible transition. The upshot is that viscosity minima and normal-stress onsets are not sufficient evidence for reversible–irreversible transitions; the time-reversibility of the driving protocol is the controlling factor.

What carries the argument

The carrying object is the rotary-shear rate-of-strain tensor $$$E^{{\infty}}$_{\text{RS}} = \begin{pmatrix} 0 & 0 & \dot{\gamma}_{xz}/2 \\ 0 & 0 & \dot{\gamma}_{yz}/2 \\ \dot{\gamma}_{zx}/2 & \dot{\gamma}_{zy}/2 & 0 \end{pmatrix}$$ with $\dot{\gamma}_{xz} = \gamma_0\omega \sin(\omega t)$ and $\dot{\gamma}_{yz} = \gamma_0\omega \cos(\omega t)$. This imposes shear of constant magnitude whose flow–vorticity plane rotates around the gradient direction without any sudden reversal, so the protocol is not time-reversible. The control protocol RRS reverses both shears and the rotation direction every half-cycle. The argument is carried by the microstructure diagnostics: coordination number $Z$ and pair distribution $g(h,\theta)$ show that OS/RRS absorbing states are contact-free and isotropic at low amplitude, while RS is in contact and anisotropic at all amplitudes; persistent contacts produce collisions and hence diffusion.

What would settle it

Extend the RS simulation at $\phi=0.55$, $\mu_c=0.5$, and $\gamma_0=0.05$ to at least $10^4$ strain units from both presheared and random isotropic initial conditions, and track the stroboscopic MSD and coordination number; the claim that RS is always diffusive collapses if the MSD slope drops below 1 or $Z$ falls to zero at late times.

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Extended reading notes

Core claim

The paper establishes that rotary shear, a periodic drive with constant shear-rate magnitude but continuously rotating direction, produces diffusive particle dynamics at every strain amplitude tested, for volume fractions 0.40 to 0.55 and friction coefficients 0, 0.2, and 0.5. Unlike oscillatory shear, no reversible absorbing state forms under RS: the stroboscopic mean squared displacement grows linearly with strain, the effective diffusivity remains finite even at the smallest amplitude, and the coordination number stays positive. The microstructure is always in contact and anisotropic, whereas OS and RRS show a contact-free, isotropic microstructure at low amplitudes and a transition to an in-contact, anisotropic state above the critical amplitude. From this, the paper concludes that rheological markers such as a minimum viscosity and the onset of the second normal stress difference are not sufficient conditions for a reversible–irreversible transition; the absence of shear reversal is what keeps RS dynamics permanently diffusive.

Load-bearing premise

The load-bearing premise is that 300 strain units of simulation are enough to reveal the long-time dynamical state, so no reversible absorbing state appears later under RS, and that the presheared starting configuration used for the dynamics is representative.

Editorial extensions

If this is right

  • Rheological signals alone cannot certify reversible dynamics: a suspension can show a viscosity minimum and the onset of $N_2$ without undergoing a reversible–irreversible transition.
  • Shear reversal is the controlling ingredient for absorbing states; a periodic drive that merely rotates the shear direction keeps particles diffusive at every amplitude.
  • The RRS protocol restores OS-like dynamics, showing that the suppression of RIT comes from the absence of sudden reversal, not from rotation itself.
  • For processing applications, RS provides continuous diffusive transport even at tiny strain amplitudes, which could be used for mixing without large deformations.
  • The microstructure criterion—contact-free and isotropic for reversible states versus in-contact and anisotropic for diffusive states—holds across all three protocols.

Reading between the lines

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

  • Editorial inference: because RS keeps particles diffusive at arbitrarily small strain amplitudes, it offers a clean protocol for measuring shear-induced diffusion in dense suspensions without an absorbing state masking the signal.
  • Editorial inference: the empirical $\gamma_{0,c} \sim \phi^{-2}$ scaling reported for OS is tied to reversal-based protocols; under RS the transition disappears, so the scaling is not a universal property of periodic shear.
  • Editorial inference: varying the reversal angle in RRS between 0 and $\pi$ should interpolate continuously between RS-like and OS-like dynamics, giving a quantitative measure of how much shear reversal is needed to nucleate an absorbing state.
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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 / 6 minor

Summary. This paper introduces a rotary shear (RS) protocol for dense non-Brownian suspensions, in which two orthogonal oscillatory shears are imposed out of phase so that the shear direction rotates continuously, and compares it with classical oscillatory shear (OS) and a reversible variant (RRS). Using hybrid lubrication/granular dynamics simulations at volume fractions 0.40–0.55 and friction coefficients 0.0–0.5, the authors report that the complex viscosity and normal stress differences are qualitatively similar across protocols, with a non-monotonic viscosity and a minimum at an intermediate strain amplitude, but that the particle dynamics differ fundamentally: OS and RRS exhibit a reversible–irreversible transition, whereas RS is claimed to be stroboscopically diffusive at all strain amplitudes, with no absorbing state. The paper attributes this to the absence of shear reversal in RS, which leaves a persistent, contact-bearing anisotropic microstructure, and validates the OS rheology and diffusion data against Bricker & Butler (2006) and Pine et al. (2005).

Significance. If the central claim holds, the paper is significant because it demonstrates that rheological signatures previously associated with the reversible–irreversible transition—minimum complex viscosity and onset of second normal stress differences—are not sufficient conditions for the transition, thereby decoupling bulk rheology from dynamical phase behavior. The study also introduces a practically realizable protocol and an internal control (RRS) that helps isolate the role of sudden shear reversal. Strengths include validation against two independent datasets, the absence of fitted target quantities, and consistency between the stress decomposition, coordination number, and observed dynamics. The main uncertainties concern the support for the strong 'always diffusive at any γ0' claim.

major comments (2)
  1. [§3.2 and Appendix D (Fig. 15)] The claim that suspensions under RS 'do not show self-adsorbing states at any γ0' is established only for the presheared, contact-rich initial condition described in §2.2. Appendix D verifies initial-condition independence only for the relative complex viscosity; the dynamical observables that define the RIT—MSD, Deff, and Z—are never tested from a different initial state. This is load-bearing because the affine RS deformation over a full cycle is the identity: the velocity-gradient tensor L(t) is nilpotent with L(t)L(s)=0, so a collision-free trajectory would close stroboscopically every period. The authors' own mechanism attributes RS irreversibility to persistent contacts, and the simulations begin every run with contacts present; a dynamics-specific test from an initially isotropic, contact-free configuration at small γ0 is therefore required to rule out a reversible branch. Without such a test, the 'at any γ0' assertion is not established, and the conclusion that rheological signatures are not sufficient for RIT may need qualification.
  2. [§3.2, Figs. 7–8] The 'always diffusive' conclusion rests on single 500-particle runs of 300 strain units, with Deff obtained from a linear fit over an unspecified window. At γ0=0.05, 300 strain units corresponds to roughly 955 cycles, but the per-cycle displacement is small and the MSD data are shown over only about 1.5 decades in strain; a slow crossover to subdiffusive or absorbing behavior beyond the simulated window cannot be excluded from the reported data. The authors should provide error bars or a second independent run for representative cases, specify the fitting window used for Deff, and perform a longer-time check (or a finite-time scaling analysis) for at least one small and one intermediate γ0 under RS.
minor comments (6)
  1. [Abstract and §3.2] The term 'self-adsorbing states' is nonstandard and likely intended to mean 'absorbing states' or 'self-organized reversible states'; the wording should be corrected for clarity.
  2. [Eq. (2.15)] The mean squared displacement formula is typeset as '[Δr(γt)/d]^2 = 6Deffγt'; it should use an ensemble average notation such as ⟨|Δr(γt)|^2⟩/d^2.
  3. [§2.1 and Appendix C] The sign convention for the rotation angle θ is inconsistent: §2.1 states θ=ωt, while Appendix C states that θ is negative for the clockwise RS rotation. This could affect the sign of the elastic component η′′ and should be clarified.
  4. [Fig. 10] The caption states that the figure is shown for φ=0.40 and μc=0.0, but the figure contains multiple panels for OS and RS at different strain amplitudes; each panel's parameters should be identified.
  5. [§2.2] The phrase 'a total strain of ˙γt = 40' uses an odd notation; the accumulated strain should be written as γt=40 to distinguish it from the shear rate.
  6. [§4 (Conclusion)] The sentence 'Our RS and RSS protocols...' contains a typo: 'RSS' should be 'RRS'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the RS/RRS dynamics are measured outputs, the HLGD model is externally benchmarked, and the central comparison does not reduce to a fit or to a self-citation.

full rationale

The paper's central claims are empirical outputs of particle simulations, not quantities fitted to the conclusions. Deff is obtained from a linear fit to MSD trajectories (Eq. 2.15), and Z, g(h,theta), and the viscosities are directly measured; none of these is a parameter adjusted to force the absence of RIT in RS. The only externally imported curve, the Pine et al. scaling gamma0,c = C phi^-alpha, is used as a reference band (Fig. 8), not as an input to the model or as a fitted prediction. The self-citations to Ge & Brandt (2020) supply the HLGD force model, but the model is independently validated in Appendix D against the experiments of Bricker & Butler (2006) and Pine et al. (2005), so the self-citation is not the load-bearing evidence. The RRS protocol is constructed to be time-reversible, but the paper does not equate protocol reversibility with stroboscopic particle reversibility: it measures MSD and Deff and finds that RRS, like OS, develops an absorbing state only below a threshold, which is a nontrivial dynamical result. The only substantive concern is that initial-condition independence is checked for rheology (Appendix D, Fig. 15) but not for the dynamical observables that define the RIT, and all runs are stopped at gamma t = 300; this is a robustness limitation, not a circular reduction of the kind where the prediction equals the input by construction.

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

The simulations use an established lubrication/granular model. No free parameters are fitted to the target phenomena; φ, μc, and γ0 are control variables, and St and stiffness are set to physical limits. No new physical entities are introduced; RS and RRS are flow protocols.

assumptions (4)
  • domain assumption Long-range hydrodynamic interactions are neglected; particle forces are Stokes drag, pairwise short-range lubrication, and contact/friction (Eq. 2.4)
    Section 2. Standard for dense suspensions; cited to Cheal & Ness (2018) and Seto et al. (2013).
  • domain assumption The rigid, inertialess limit is reached with St ≈ 1e-2 and stiffness-scaled shear rate ≈ 1e-4
    Section 2; values are stated without sensitivity analysis.
  • domain assumption A cubic box of 500 bidisperse particles (size ratio 1.4) with Lees-Edwards boundary conditions is a representative bulk sample
    Section 2.2; finite-size effects are not quantified.
  • standard math Stress in the rotating frame follows tensor rotation, σ' = R σ R^T (Eqs. 2.9-2.10)
    Linear algebra transform; no approximation.

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Cite this review

Pith. "Pith review of Dense Suspensions in Rotary Shear." pith.science (2026). https://pith.science/paper/RCVRK3ZO

@misc{pith2026241113463,
  author       = {Pith},
  title        = {Pith review of: Dense Suspensions in Rotary Shear},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RCVRK3ZO}},
  note         = {Machine review of arXiv:2411.13463}
}
abstract

We introduce a novel unsteady shear protocol, which we name Rotary Shear (RS), where the flow and vorticity directions are continuously rotated around the velocity gradient direction by imposing two out-of-phase oscillatory shear (OS) in orthogonal directions. We perform numerical simulations of dense suspensions of rigid non-Brownian spherical particles at volume fractions ($\phi$) between 0.40 and 0.55 subject to this new RS protocol and compare to the classical OS protocol. We find that the suspension viscosity displays a similar non-monotonic response as the strain amplitude ($\gamma_0$) is increased: a minimum viscosity is found at an intermediate, volume-fraction dependent strain amplitude. However, the suspension dynamics is different in the new protocol. Unlike the OS protocol, suspensions under RS do not show self-adsorbing states at any $\gamma_0$ and do not undergo the reversible-irreversible transition: the stroboscropic particle dynamics are always diffusive, which we attribute to the fact that the RS protocol is irreversible. To validate this hypothesis, we introduce a reversible-RS (RRS) protocol, a combination of RS and OS, where we rotate the shear direction (as in RS) until it is instantaneously reversed (as in OS), and find the resulting rheology and dynamics to be closer to OS. Detailed microstructure analysis shows that both the OS and RRS protocols result in a contact-free, isotropic to an in-contact, anisotropic microstructure at the dynamically reversible-to-irreversible transition. The RS protocol does not render such a transition, and the dynamics remain diffusive with an in-contact, anisotropic microstructure for all strain amplitudes.

Figures

Figures reproduced from arXiv: 2411.13463 by the authors.

Figure 1
Figure 1. (a) Schematic view of the dense suspension. Top view showing the directions of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Stress-strain evolution for OS (a) γ0 = 0.05, (b) γ0 = 10.0. The signals are normalized for comparison. Here, T represents the period of a shear cycle. direction. Therefore we need to use tensor rotation to calculate the stress tensor in the frame of reference rotating with the imposed shear, σ ′ = RσRT , (2.9) where R is the rotation matrix (c.f. Eq. C 2), and σ and σ ′ are the stress tensor in the laboratory and r… view at source ↗
Figure 3
Figure 3. (a) Complex viscosity for OS (circles), RS (stars), SS (dotted lines). Black lines [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Viscosity budget, total stress (solid lines), contribution from contact (circles), [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: The first (a) and second (b) normal stress differences under RS at three volume [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: The first (a) and second (b) normal stress differences under OS at three volume [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Mean square displacements (MSD) for OS (a) and RS (b) at different [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Effective diffusivity (Deff) vs γ0 for OS and RS. The shaded region shows the region of prediction of the critical amplitude from the empirical scaling, γ0,c = Cϕ−α, where C = 0.14 ± 0.03, and α = 1.93 ± 0.14 (Pine et al. 2005). a minimal viscosity at an intermediate γ…
Figure 9
Figure 9. Figure 9: Coordination number (Z). Left: OS, right: RS. The coordination number is [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Pairwise particle distribution g(h, θ). θ = 0◦ and 90◦ represent the flow and velocity gradient directions respectively. θ ∈ [0, π/2] or [π, 3π/2] represents extensional quadrants and θ ∈ [π/2, π] or [3π/2, 2π] represents the compressional qudrants. The contact point …
Figure 11
Figure 11. Figure 11: (a) Viscosity budget: total stresses (solid lines), contact stresses (circles), [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: (a) Particle mean-square displacement versus strain for suspensions undergoing [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 13
Figure 13. Figure 13: Coordination number (Z) in OS, RS and RRS for [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]
Figure 14
Figure 14. Figure 14: Validation at 40% volume fraction in OS. (a) Complex viscosity ratio against [PITH_FULL_IMAGE:figures/full_fig_p022_14.png]
Figure 15
Figure 15. Figure 15: Effect of initial condition on suspension rheology. Two initial conditions are [PITH_FULL_IMAGE:figures/full_fig_p023_15.png]

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Reviewed August 12, 2026 · model on record in the stance chip above.