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arxiv: 2604.14109 · v1 · submitted 2026-04-14 · ❄️ cond-mat.soft · cond-mat.stat-mech

A Unified Glassy Rheology for Granular Matter

Zhikun Zeng , Jiazhao Xu , Hanyu Li , Shiang Zhang , Houfei Yuan , Chijin Zhou , Xueliang Dai , Haiyang Lu
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Xin Wang Jun Zhao Yonglun Jiang Zhuan Ge Gang Huang Chengjie Xia Jianqi Sun Yan Xi Yujie Wang
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Pith reviewed 2026-05-10 14:06 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech
keywords granular rheologystructural relaxationCarnahan-Starling equationglassy dynamicsμ(I) rheologyCouette flowX-ray tomography
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The pith

Granular flows follow a single constitutive law based on structural relaxation across quasi-static to inertial regimes.

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

The paper uses high-speed X-ray tomography to track particle motions in dense granular flows inside a Couette cell. It extracts a structural relaxation time that directly supplies a constitutive relation for stress and strain rate. This relation remains single-valued and continuous from very slow shearing to fast inertial motion, unlike the standard μ(I) model. The authors add a non-equilibrium statistical description showing that the particles obey the same Carnahan-Starling equation of state as equilibrium hard-sphere fluids, which accounts for the observed glassy slowing.

Core claim

A constitutive law derived from measured structural relaxation times spans quasi-static to inertial regimes and removes the multivalued character of the original μ(I) rheology; a non-equilibrium statistical framework further shows that driven granular matter shares the Carnahan-Starling equation of state with hard-sphere liquids, thereby explaining the rheology and the appearance of glassy dynamics.

What carries the argument

Structural relaxation time extracted from high-speed X-ray tomography data, which supplies both the universal constitutive relation and the non-equilibrium statistical framework.

Load-bearing premise

The structural relaxation time measured in tomography experiments directly produces a constitutive law that works without any separate adjustments for different flow speeds, and the Carnahan-Starling equation of state holds for these driven granular systems exactly as it does for equilibrium hard-sphere liquids.

What would settle it

A set of stress and strain-rate measurements in granular flows, obtained either experimentally or in simulation, that lie outside the curve predicted by inserting the independently measured structural relaxation times into the proposed constitutive law across a wide range of shear rates.

read the original abstract

Granular flows are ubiquitous in nature and industrial applications, yet a complete continuum theory remains a long-standing challenge. The leading empirical approach, {\mu}(I) rheology, lacks microscopic foundations and becomes multivalued in dense, slowly sheared flows where nonlocal corrections are required. Exploiting state-of-the-art high-speed X-ray tomography to investigate microscopic dynamics of dense granular flows in a Couette geometry, we establish a new, universal constitutive law spanning quasi-static to inertial regimes based on structural relaxation, resolving the fundamental difficulty in the original {\mu}(I) framework. By further establishing a non-equilibrium statistical framework for granular flows, we demonstrate an intrinsic analogy between driven granular matter and hard-sphere liquids owing to their identical Carnahan-Starling equation of state, naturally explaining our rheological approach and the emergence of glassy behaviors. Our framework unifies granular rheology with the broader physics of disordered systems and provides a complete, microscopically-based theoretical framework for dense granular flow.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims to derive a universal constitutive relation for dense granular flows from the structural relaxation time τ measured via high-speed X-ray tomography in Couette geometry. This relation is asserted to span quasi-static to inertial regimes, eliminate the multivaluedness of the empirical μ(I) law, and rest on a non-equilibrium statistical mechanics framework whose pressure-density relation is identical to the Carnahan-Starling equation of state for equilibrium hard-sphere liquids, thereby unifying granular rheology with glassy dynamics.

Significance. If the central mapping from tomography-derived τ to a parameter-free constitutive law is shown to be independent of regime-specific assumptions, the work would supply a microscopically grounded alternative to μ(I) rheology and a concrete link between driven granular matter and equilibrium hard-sphere liquids. The explicit use of tomography data and the Carnahan-Starling analogy constitute falsifiable, data-driven elements that strengthen the claim relative to purely phenomenological models.

major comments (2)
  1. [constitutive-law derivation] Section deriving the constitutive law from structural relaxation: the manuscript must demonstrate explicitly that the extraction of τ from the tomography correlation functions does not embed an implicit averaging over local shear rates or contact networks that already assumes a μ(I)-type dependence; otherwise the claimed universality and resolution of multivaluedness reduce to a reparametrization rather than an independent derivation.
  2. [statistical-framework section] Non-equilibrium statistical framework section: the assertion that the granular pressure-density relation is identical to the Carnahan-Starling equation of state requires a quantitative comparison (including any necessary rescaling for dissipative friction or driving) showing that the analogy survives without regime-dependent adjustments; the current presentation leaves open whether the EOS identity is derived from first principles or fitted to the same data used for the rheology.
minor comments (2)
  1. [figures] Figure captions should explicitly define the operational window used to compute the structural relaxation time τ and state whether any smoothing or averaging over the Couette gap is applied.
  2. [abstract/introduction] The abstract and introduction would benefit from a one-sentence statement of the precise functional form of the new constitutive law (e.g., μ(τ) or η(τ)) before the analogy is invoked.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The two major comments identify key areas where additional explicit demonstrations are needed to support the independence of the derivation and the robustness of the statistical analogy. We respond to each point below and will incorporate revisions to address them.

read point-by-point responses

  1. Referee: Section deriving the constitutive law from structural relaxation: the manuscript must demonstrate explicitly that the extraction of τ from the tomography correlation functions does not embed an implicit averaging over local shear rates or contact networks that already assumes a μ(I)-type dependence; otherwise the claimed universality and resolution of multivaluedness reduce to a reparametrization rather than an independent derivation.

    Authors: We agree that an explicit demonstration is required. The relaxation time τ is extracted by fitting the decay of the self-intermediate scattering function computed directly from tracked particle positions in the tomography data. These correlation functions are evaluated in local spatial bins using only particle coordinates; no rheological model or μ(I)-dependent averaging over shear rates or contact networks enters the calculation. Local shear rates are obtained independently from the measured velocity profiles. In the revised manuscript we will add a dedicated subsection in the methods that details the correlation-function definition, binning procedure, and fitting protocol, thereby confirming that the constitutive law follows from the microscopic data without presupposing the form of μ(I). revision: yes

  2. Referee: Non-equilibrium statistical framework section: the assertion that the granular pressure-density relation is identical to the Carnahan-Starling equation of state requires a quantitative comparison (including any necessary rescaling for dissipative friction or driving) showing that the analogy survives without regime-dependent adjustments; the current presentation leaves open whether the EOS identity is derived from first principles or fitted to the same data used for the rheology.

    Authors: The non-equilibrium framework is constructed from first principles by mapping the configurational statistics of the driven granular assembly onto an effective hard-sphere system whose excluded-volume entropy yields the Carnahan-Starling equation of state without adjustable parameters. To supply the requested quantitative test we will add a new figure that directly compares the measured pressure versus packing fraction (from both experiment and simulation) against the Carnahan-Starling prediction, after a single rescaling of the effective packing fraction that accounts for frictional dissipation. The comparison will be shown for data spanning quasi-static and inertial regimes to verify that no regime-specific adjustments are required. The EOS relation is therefore derived from the statistical mapping rather than fitted to the rheological data. revision: yes

Circularity Check

1 steps flagged

Structural relaxation time from tomography data used to define constitutive law; Carnahan-Starling analogy presented as independent but may require verification of independence from fitted parameters

specific steps
  1. fitted input called prediction [Abstract / constitutive law derivation]
    "Exploiting state-of-the-art high-speed X-ray tomography to investigate microscopic dynamics of dense granular flows in a Couette geometry, we establish a new, universal constitutive law spanning quasi-static to inertial regimes based on structural relaxation"

    The structural relaxation time is extracted from the identical tomography dataset in the same Couette flows; using this τ to define the constitutive relation μ(τ) or η(τ) that is then claimed to hold universally makes the 'prediction' or unification statistically forced by the input data rather than independently derived.

full rationale

The paper extracts structural relaxation time τ via high-speed X-ray tomography in Couette geometry and directly bases the universal constitutive law on it, spanning regimes. This risks the fitted_input_called_prediction pattern if τ extraction incorporates averaging or network properties that implicitly encode shear-rate dependence from the same flows used to validate μ(τ) or η(τ). The non-equilibrium framework then invokes identical Carnahan-Starling EOS for granular and hard-sphere systems to explain glassy behaviors; if this identity is demonstrated via direct measurement of pressure-density in the driven system without rescaling assumptions, it remains independent. No explicit self-citation chain or self-definitional loop is evident from abstract and framework description, but the central unification step hinges on τ-to-rheology mapping being parameter-free and regime-agnostic. Overall partial circularity risk at the data-to-law step, but derivation retains independent content from tomography observations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of a structural-relaxation constitutive law and the direct applicability of the Carnahan-Starling equation of state to driven granular matter; both are stated without derivation details in the abstract.

axioms (1)
  • domain assumption The Carnahan-Starling equation of state applies identically to driven granular matter and hard-sphere liquids.
    Invoked to explain the rheological law and the emergence of glassy behaviors.

pith-pipeline@v0.9.0 · 5522 in / 1426 out tokens · 69262 ms · 2026-05-10T14:06:54.909059+00:00 · methodology

discussion (0)

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Reference graph

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