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REVIEW 3 major objections 4 minor 38 references

Internal motion of soft granular particles under circular shearing: Rate-dependent quaking and its spatial structure

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper claims that rate-dependent quaking in soft granular matter is a generic friction effect, captured by a single dimensionless shear rate that collapses data from two different shear geometries onto one curve.

desk verdict Genuinely new 3D cluster picture of rate-dependent quaking, but the S_l collapse is not quantitatively secured because V* drifted by an order of magnitude and was measured post-hoc. read the letter →

arxiv 2411.16293 v3 pith:TTTUD3QI submitted 2024-11-25 cond-mat.soft

Jr-Jun Lin , Cheng-En Tsai , Jung-Ren Huang , Jih-Chiang Tsai This is my paper · ORCID
classification cond-mat.soft
keywords granularmatterstick-slipquakingsoftparticlestribologydimensionlessshearrate3Dparticletrackingcircularcell
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

Tightly packed soft particles under slow shear do not flow smoothly; instead they intermittently release stress in sudden drops that the authors call quaking. The paper reports that this rate-dependent quaking, previously seen in a double-cone shear experiment, appears in a completely different circular shear cell, and that the two datasets line up when the shear rate is divided by a material-specific friction threshold speed to form the dimensionless number $S_\ell$. The new experiment also tracks particles in three dimensions through the bulk, showing that quakes are clusters of unusually large displacements: sparse patches at intermediate rates, system-spanning clusters at lower rates, and rare events at very low rates. The authors conclude that quaking is a generic, tribology-driven transition rather than a quirk of one geometry.

What carries the argument

The load-bearing object is the dimensionless shear rate $S_\ell \equiv \ell \dot{\gamma}/V_*$, which compares the typical sliding speed between neighboring particles, of order $\ell \dot{\gamma}$, to $V_*$, the material-specific speed at which the friction between PDMS particles drops dramatically — the Stribeck transition from solid-solid contact to mixed lubrication. Equally important are the experimental components: a circular shear cell that imposes a uniform, cyclically rotating shear with strain $\gamma_0 \approx 2.8$ per cycle so particles never return to their old positions; refractive-index-matched 3D imaging with particle tracking that gives bulk grain trajectories; and a cluster analysis that keeps the top 5% of fluctuating displacements, connects nearest neighbors through Laguerre tessellation, and counts connected clusters. Together these make quaking visible as a spatial, collective event and tie its rate dependence to the friction threshold.

What would settle it

Measure the large-drop count curves with $V_*$ determined in situ during the same runs, or with a fresh batch of particles whose threshold is stable; if the double-cone and circular-cell curves stop collapsing once the threshold is measured concurrently, the $S_\ell$ unification rests on a post-hoc choice. A sharper check: repeat the circular-cell experiment with newly molded PDMS particles ($V_* \approx 5$ mm/s) and verify that the quaking peak in the LD count shifts to an $S_\ell$ value matching the old particles' peak.

Watch

Extended reading notes

Core claim

The central claim is that intermittent stress drops — quaking — in tightly packed soft granular solids are a rate-dependent, tribology-controlled phenomenon whose onset and decline are organized by one dimensionless number, $S_\ell \equiv \ell \dot{\gamma}/V_*$, where $\ell$ is particle size, $\dot{\gamma}$ the shear rate, and $V_*$ the sliding speed at which interparticle friction drops sharply. In the new circular cell, quaking appears only at intermediate $S_\ell$: high rates give smooth flow, intermediate rates give clusters of large fluctuating displacements, low rates give rare system-spanning events, and the large-drop (LD) count per strain from this geometry collapses onto the earlier double-cone data once plotted against $S_\ell$ rather than $\dot{\gamma}$ alone. Within a system-spanning quake, particles do not all move together; patches move with and against the base flow, revealing substructure in the rearrangement.

Load-bearing premise

The collapse onto one curve assumes that the friction threshold speed used in the analysis, 0.2 mm/s, was valid during the shearing runs, even though it was measured only after data collection and had drifted from 5 mm/s to 1 mm/s over the preceding two years.

Editorial extensions

If this is right

  • The same dimensionless number $S_\ell$, not the raw shear rate, should organize quaking statistics in any quasi-static granular shear geometry once the material's $V_*$ is known.
  • Quaking is a bulk collective phenomenon: at intermediate rates the rearranging particles form connected clusters that can span the whole sample, so the transition cannot be reduced to isolated local shear transformation zones.
  • At very low $S_\ell$, quakes become rare and widely separated; below the lowest rate tested, quaking is undetectable within a strain window of about 0.7, so the material appears smooth again.
  • The stress-drop signature and the displacement-cluster signature mark the same transition: the peaks in higher moments of cluster size coincide with the peak in large-drop counts at intermediate rates.
  • Particle motion in a system-spanning quake is not coherent translation; the cluster contains patches moving along and against the local flow direction, implying internal rearrangement rather than rigid slip.

Reading between the lines

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

  • Beyond the paper: if $V_*$ changes with surface age, the practical implication is that $S_\ell$ should be treated as time-dependent; embedding a tribology reference measurement in every shearing run would turn the collapse into a continuously testable relation.
  • Beyond the paper: the substructure observed within large clusters suggests a quake is a percolating sequence of localized rearrangements rather than a single slip plane; one could test this by tracking the time ordering of activated patches within one event.
  • Beyond the paper: the cluster-size distributions reported here are the raw material for a soft-matter analogue of earthquake frequency-magnitude statistics; the analogue of the b-value should vary systematically with $S_\ell$, and that variation could be predicted from these data.
  • Beyond the paper: the same circular shear cell with variable packing fraction, which the authors say is under construction, would show whether $S_\ell$ remains the control parameter as the system moves away from volume fraction 0.59.
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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

3 major / 4 minor

Summary. The paper reports experiments in a circular shear cell on tightly packed PDMS spheres immersed in an index-matched fluid, with 3D particle tracking and simultaneous shear-stress measurement. It identifies a rate-dependent transition in internal motion: smooth, homogeneous flow at high shear rates; intermittent 'quaking' with localized clusters of large displacements at intermediate rates; system-spanning clusters at lower rates; and increasingly rare large events at the lowest rates. The authors then compare large stress-drop (LD) counts with their previous PRL 2021 experiment and claim that the dimensionless shear rate S_l = l*gamma_dot/V* collapses the LD-count curves from the two geometries into one master curve. The paper also documents cluster-size distributions, substructure within large clusters, and several appendices that address imaging, force-signal artifacts, and long-term drift of the tribological threshold V*.

Significance. If the central claims hold, the paper provides valuable three-dimensional, grain-scale evidence that the rate-dependent quaking transition is not specific to one shear geometry and that the previously proposed S_l parameter indeed organizes transitions across experiments. The paper has concrete strengths: the spatial cluster observations (cases I to IV) are directly illustrated and do not rely on S_l; the clustering results are checked against threshold choice in Appendix D; and the tribology input V* is obtained from an independent measurement reported in Appendix E rather than fitted to the LD-count curves. The paper is also candid about experimental limitations, including the drift of V* and the finite observation window. The main weaknesses are quantitative: the collapse in Fig. 10(b) depends on a single post-hoc V* value with no sensitivity analysis, the lowest-rate case rests on a single quaking event, and the variable strain-step convention across runs complicates the displacement-based comparisons.

major comments (3)
  1. [Section IV, Fig. 10(b), Appendix E] The central quantitative claim that S_l collapses the large-drop counts rests entirely on assigning V* = 0.2 mm/s, but Appendix E reports that V* for the same PDMS particles was 5 mm/s two years earlier and 1 mm/s after one year of submersion, and that 0.2 mm/s was determined only after all shearing data were collected. Because S_l is inversely proportional to V*, a factor-of-2.5 to 5 drift in the in-situ V* would shift the CSC curve horizontally on the log axis by that factor, and the 'reasonably good collapse' in Fig. 10(b) is judged only visually without error bars. Please provide a sensitivity analysis that recomputes the collapse using V* values covering the full documented drift range (e.g., 0.2, 1, and 5 mm/s), or concurrent V* measurements; without that, the claimed unification across geometries is not quantitatively secured.
  2. [Section III.A, Fig. 5(b); Section III.B, Fig. 7(b)] The non-monotonic decrease in Σ and in the higher moments <S^n>^{1/n} from case III to case IV is based on a single quaking event: the text states that case IV contains 'only a single quaking event' and that at the second-lowest shear rate a repeated run found one big event, but the plotted case is still n=1. This single-event statistics does not distinguish an intrinsic rareness from sampling noise. Please provide confidence intervals or replicate statistics, or at least report the repeated-run result quantitatively in the main figure, before treating the III-to-IV drop as part of the rate-dependent transition.
  3. [Section III.A and footnote 1] The fluctuating displacement δr⃗ is computed over a strain step Δγ that is not the same for all runs: case I is sampled at 16Δγ and the case at 2.8×10^{-2} s^{-1} at 4Δγ, while the rest use Δγ = γ0/800 ≈ 3.5×10^{-3}. Since |δr⃗|, the top-5% selection, and hence the cluster statistics all depend on the strain interval over which particle motion is accumulated, the comparison between case I and the other cases mixes the effect of shear rate with the effect of sampling interval. Please show the results for case I and the 2.8×10^{-2} s^{-1} run at the standard Δγ, or demonstrate explicitly that the conclusions are insensitive to the strain interval.
minor comments (4)
  1. [Abstract] The last paragraph begins 'system. and the cluster exhibits substructures'; this should be one sentence: 'system, and the cluster exhibits substructures...'.
  2. [Section II, paragraph after Fig. 2] The phrase 'the father half of the imaging area' should be 'the farther half of the imaging area'.
  3. [Section III.A] The phrase 'at slow driving ratess' contains a typo; it should be 'at slow driving rates'.
  4. [Fig. 3 caption] The caption says the shear-rate values are 'marked at the upper-right corner of every sub-plot', but those values are not legible in the printed figure; please add explicit numeric labels in the caption or in the panels.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction found: the S_l collapse is an out-of-sample test of the authors' own parameter using an independently measured V*, and the new spatial observations are independent of S_l; the documented V* drift is a robustness concern, not circularity.

full rationale

Walkthrough of the claimed derivation chain: the paper's central quantitative claim is that the LD-count (number of shear-stress drops exceeding the long-time RMS fluctuation, per unit strain) curves from the 2021 double-cone geometry (Ref 17) and the current CSC geometry collapse when plotted against S_l = l*gamma_dot/V* (Fig. 10b). This is a genuine out-of-sample test of a dimensionless parameter proposed in the same group's PRR 2024 numerical study (Ref 24): S_l is not defined in terms of the LD count, and the collapse is not a fit, because the only adjustable input, V*, is an independently measured tribological threshold (Ref 23 methodology; Appendix E reports V* = 0.2 mm/s measured immediately after data collection versus 5 mm/s in Ref 17). The LD-count curves are non-monotonic, so aligning them by a horizontal shift is non-trivial empirical content rather than a construction. The novel spatial observations — cluster-size distributions growing from sparse (case II) to system-spanning (case III) and rare (case IV), and substructures in delta-r_phi within large clusters (Figs. 6-9) — are plotted against the physical shear rate and do not depend on S_l at all. The self-citations (Refs 17, 23, 24) supply the interpretive framework (speed-dependent friction, Stribeck lubrication), but they are published prior measurements and simulations with external anchors in the tribology literature (Refs 22, 38), and the present experiment is a new geometry with new data. Flagged per the reviewing rule: Appendix E itself documents that V* has drifted (5 mm/s to 1 mm/s to 0.2 mm/s over two years) and that the value used was measured post-hoc; a factor-of-5 uncertainty in the in-situ V* would shift the CSC curve horizontally by the same factor on the log axis and could degrade the Fig. 10(b) collapse. This is a correctness and robustness limitation — no sensitivity analysis is provided — but it is not circularity, because V* is a measured input, not a parameter fitted to the LD-count curves. No equation in the paper reduces a target quantity to its own input by construction, and no fitted parameter is renamed as a prediction. Verdict: no significant circularity, with minor self-citation that is not load-bearing.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claims rest on a measured friction threshold (V*), several analysis choices (threshold, strain step, characteristic length), and standard tools (TRACKPY, Laguerre tessellation). There are no invented particles or forces, but the experiment assumes the imposed circular motion produces a clean linear shear base flow and that steady state is reached after preshear.

free parameters (4)
  • V* (threshold sliding speed) = 0.2 mm/s
    Measured by tribology after all shearing data were collected (Appendix E); used to define S_l. Its value has drifted over time (5 mm/s two years prior, 1 mm/s after one year), and no sensitivity analysis is reported.
  • Characteristic particle length ℓ = 10 mm
    Chosen as the representative size for the binary 9 mm/12 mm mixture when computing S_l (Section IV); a different average would shift the points.
  • Significant-displacement threshold ξ_p = 5%
    Particles with top 5% of |δr| are defined as significantly rearranged before clustering (Section III B); robustness checked with 2% and 10% in Appendix D.
  • Strain step Δγ = γ0/800 ≈ 3.5e-3
    Used to define fluctuating displacements; case I uses 16Δγ and another case 4Δγ due to camera limitations (footnote 1), so the compared snapshots are not all at identical strain steps.
assumptions (6)
  • domain assumption The imposed circular wall motion produces a clean linear shear base flow v0 = Ω (z - z0) tan α φ in the bulk, with no other velocity components.
    Section II defines the base flow and uses it to remove the mean displacement when computing fluctuating motion; boundary effects and wall slip are assumed negligible in the analyzed box.
  • domain assumption The system reaches a steady state after a preshear of about 0.7 strain units for each intended shear rate.
    Section II starts recordings at Ω t0 = 0.5π and assumes the steady state is established; no convergence test is reported.
  • domain assumption Speed-dependent interparticle friction, with a Stribeck-type transition at a material-specific speed V*, is the mechanism behind quaking.
    Section IV invokes Refs. [22,23] for the tribology and Ref. [24] for the numerical state diagram; the present paper does not directly measure friction during shearing.
  • domain assumption The inertial numbers are quasi-static, estimated at 7e-4 to 7e-9.
    Section II estimates P using an improved setup 'to be published in future work' and assumes a mild stress dependence on shear rate; the pressure was not measured in the current runs.
  • domain assumption TRACKPY reliably identifies and links particle positions from the processed 3D images.
    Appendix B describes the tracking flow chart but does not quantify tracking error or linking accuracy for the dense binary packing.
  • standard math Laguerre tessellation provides the correct neighbor connectivity for the binary mixture.
    Section III B uses Laguerre tessellation to define nearest neighbors and clusters; this is a standard geometric construction, though the physical meaning of bonds is assumed.

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Pith. "Pith review of Internal motion of soft granular particles under circular shearing: Rate-dependent quaking and its spatial structure." pith.science (2026). https://pith.science/paper/TTTUD3QI

@misc{pith2026241116293,
  author       = {Pith},
  title        = {Pith review of: Internal motion of soft granular particles under circular shearing: Rate-dependent quaking and its spatial structure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TTTUD3QI}},
  note         = {Machine review of arXiv:2411.16293}
}
read the original abstract

Tightly packed granular particles under shear often exhibit intriguing intermittencies, specifically, sudden stress drops that we refer to as quaking. To probe the nature of this phenomenon, we prototype a circular shear cell that is capable of imposing a uniform and unlimited shear strain under quasi-static cyclic driving. Spherical PDMS(polydimethylsiloxane) particles, immersed in fluid, are driven in a fixed total volume at a wide range of shear rates, with particle trajectories captured in 3D space via refraction-index-matched fluorescent tomography. Statistics on the magnitude of fluctuating displacements of individual particles shows distinct dependence on the shear rate. Particle motions are smooth at high shear rates. At intermediate shear rates, quaking emerges with clusters of particles exhibiting relatively large displacements. At low shear rates, a cluster can span the entire system. and the cluster exhibits substructures in view of localized particle movements. Overall, we have confirmed that the quaking phenomena in the current setup are consistent with our previous work [Phys. Rev. Lett.,126, 128001 (2021)], and that the dimensionless shear rate that we have proposed [Phys. Rev. Research 6, 023065 (2024)] is indeed a good parameter for unifying the transitions observed in different experimental geometries.

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