arxiv: 2605.06531 · v1 · submitted 2026-05-07 · ❄️ cond-mat.soft

Recognition: unknown

Non-Local Particle Flows Become Local When Considering Dissipative Stress

Martin Trulsson

Authors on Pith no claims yet

Pith reviewed 2026-05-08 04:11 UTC · model grok-4.3

classification ❄️ cond-mat.soft

keywords dense suspensionsgranular rheologynon-local effectsdissipative stressKolmogorov flowμ(J) lawyield stressinhomogeneous shear

0 comments

The pith

A shear-rate-weighted dissipative stress restores the local μ(J) rheology throughout the bulk of inhomogeneous dense suspension flows

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

The paper shows that persistent particle motion in sub-yield regions of inhomogeneous dense suspension flows does not require non-local models. Defining shear stress as the shear-rate-weighted average τ_W = ⟨τ γ̇⟩ / ⟨γ̇⟩ isolates irreversible work and recovers the standard homogeneous μ(J) relation everywhere except a thin reversal layer. A separate geometric mixing-length construction then accounts for that residual sub-yielding without fluctuation data. If valid, the result implies that conventional stress averaging has created an apparent breakdown of locality rather than any intrinsic non-local mechanism in the material.

Core claim

In particle-resolved simulations of frictionless dense suspensions under two-dimensional Kolmogorov flow, the shear-rate-weighted dissipative stress τ_W = ⟨τ γ̇⟩ / ⟨γ̇⟩ restores the homogeneous μ(J) law throughout the bulk while the inferred friction remains strictly above yield; a simple geometric mixing-length model with conventional stresses then explains the remaining sub-yield motion inside a sub-diameter layer at flow reversals.

What carries the argument

The shear-rate-weighted dissipative stress τ_W = ⟨τ γ̇⟩ / ⟨γ̇⟩, which isolates the irreversible-work component of stress and allows the local μ(J) relation to hold in the bulk.

If this is right

The bulk of the flow obeys the homogeneous local μ(J) law with friction strictly above yield when the dissipative stress is used.
Only a narrow sub-diameter layer at flow reversals requires an additional geometric mixing-length argument.
Much of the observed non-locality is an artifact of conventional stress averaging rather than an intrinsic material property.
Non-local rheological models are not required for this class of frictionless inhomogeneous flows once stress is redefined.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same weighting could be applied to experimental data or three-dimensional simulations to check whether locality is recovered in more realistic geometries.
If the approach holds, continuum models of industrial or geological flows could drop non-local terms in favor of this redefined local stress.
Analogous weighting might resolve apparent non-locality in other driven soft-matter systems where irreversible work is the relevant quantity.

Load-bearing premise

The shear-rate-weighted average correctly isolates only the irreversible dissipative component of stress and the 2D frictionless simulations generalize to other inhomogeneous granular and suspension flows.

What would settle it

A direct test in which the μ(J) curve measured in homogeneous simple shear (using the same weighted stress) fails to collapse onto the curve extracted from the inhomogeneous Kolmogorov flow would falsify the claim that the weighted stress restores locality.

Figures

Figures reproduced from arXiv: 2605.06531 by Martin Trulsson.

**Figure 1.** Figure 1: FIG. 1. Sketch of the processes leading to non-local stresses. view at source ↗

**Figure 2.** Figure 2: FIG. 2. Snapshot of the simulation cell showing the system view at source ↗

**Figure 3.** Figure 3: FIG. 3. Local fields versus position in the Kolmogorov flow: (a) viscous number view at source ↗

**Figure 4.** Figure 4: FIG. 4. Comparison of effective friction coefficients versus vis view at source ↗

**Figure 5.** Figure 5: FIG. 5. Local rheology using a mixing-length of size view at source ↗

**Figure 6.** Figure 6: FIG. 6. As in Fig. 4(c,d) but where the data points in the view at source ↗

**Figure 7.** Figure 7: FIG. 7. As in Fig. 4(d), but with (a) a view at source ↗

**Figure 8.** Figure 8: FIG. 8. As in Fig. 3 for a distorted Kolmogrov view at source ↗

**Figure 9.** Figure 9: FIG. 9. (a) view at source ↗

**Figure 11.** Figure 11: FIG. 11. Collapse of the rheology data using view at source ↗

**Figure 12.** Figure 12: FIG. 12. (a) Direct test of the relationship view at source ↗

**Figure 13.** Figure 13: FIG. 13. Direct test of Eq. 5: the rescaled correction view at source ↗

**Figure 14.** Figure 14: FIG. 14. Extracting view at source ↗

**Figure 15.** Figure 15: FIG. 15. Typical accumulated strain in the collected data for view at source ↗

read the original abstract

Dense granular and suspension flows under inhomogeneous shear exhibit persistent particle motion in regions where the local yield criterion is subcritical, an apparent breakdown of locality that has motivated the development of a generation of nonlocal rheological models. Using particle-resolved simulations of frictionless dense suspensions in two-dimensional Kolmogorov flow, we show that two independent considerations together account for this signature. First, replacing the conventional shear stress by a shear-rate-weighted dissipative stress $\tau_W=\langle \tau \dot \gamma \rangle/\langle \dot \gamma \rangle$, which isolates the component of stress that performs irreversible work, restores the homogeneous $\mu(J)$ law throughout the bulk of the flow, with the inferred friction remaining strictly above yield. Second, a simple geometric mixing-length construction, applied with conventional stresses and requiring no fluctuation input, accounts for the residual sub-yielding within a sub-diameter layer at flow reversals. Each approach is based on a different philosophy and mechanism, and together they suggest that much of the apparent non-locality in this geometry and frictionless case is an artefact of how stress is measured and averaged rather than an intrinsic breakdown of local rheology.

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 paper claims that apparent non-local particle flows in inhomogeneous shear of dense granular and suspension systems are largely an artifact of conventional stress averaging. Using particle-resolved simulations of frictionless dense suspensions in 2D Kolmogorov flow, it shows that a shear-rate-weighted dissipative stress τ_W = ⟨τ γ̇⟩/⟨γ̇⟩ restores the homogeneous μ(J) law throughout the bulk (with inferred friction strictly above yield), while a parameter-free geometric mixing-length construction using conventional stresses accounts for residual sub-yielding within a sub-diameter layer at flow reversals.

Significance. If the result holds, the work indicates that much of the non-locality observed in such flows arises from how irreversible work is isolated in stress measurement rather than requiring intrinsic non-local constitutive models. It is strengthened by its reliance on particle-resolved simulations and a parameter-free geometric construction, offering a concrete, falsifiable alternative for this geometry and the frictionless case.

major comments (2)

[Definition of dissipative stress τ_W] Definition of dissipative stress τ_W (abstract and the section introducing the weighted average): The steady-state momentum balance in Kolmogorov flow requires ∇·⟨τ⟩ to balance the body force, so the time-averaged stress ⟨τ(y)⟩ is fixed by the driving. The paper does not show that τ_W equals ⟨τ⟩ when fluctuations are uncorrelated or how a local μ(J) relation written with τ_W remains consistent with the integrated force balance; this is load-bearing for the claim that conventional local rheology is restored rather than redefined.
[Results on μ(J) restoration] Restoration of μ(J) law in the bulk (results section reporting the collapse): The claim that friction remains strictly above yield relies on τ_W; the manuscript should quantify the difference between τ_W and ⟨τ⟩ in low-⟨γ̇⟩ regions and demonstrate that the collapse survives when the weighting is replaced by a simple time average over the same windows, to rule out that the apparent restoration is an artifact of the weighting procedure.

minor comments (2)

[Abstract] The abstract states that the two approaches are 'based on a different philosophy and mechanism' but does not briefly indicate how the geometric mixing length is constructed (e.g., the precise length scale choice); adding one sentence would improve readability.
[Figures] Figure captions comparing stress profiles should explicitly label curves as ⟨τ⟩ versus τ_W to prevent reader confusion between the two measures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address the major comments point by point below, and will revise the manuscript accordingly where appropriate.

read point-by-point responses

Referee: [Definition of dissipative stress τ_W] Definition of dissipative stress τ_W (abstract and the section introducing the weighted average): The steady-state momentum balance in Kolmogorov flow requires ∇·⟨τ⟩ to balance the body force, so the time-averaged stress ⟨τ(y)⟩ is fixed by the driving. The paper does not show that τ_W equals ⟨τ⟩ when fluctuations are uncorrelated or how a local μ(J) relation written with τ_W remains consistent with the integrated force balance; this is load-bearing for the claim that conventional local rheology is restored rather than redefined.

Authors: We appreciate the referee pointing out this crucial aspect of consistency. Upon reflection, we acknowledge that the manuscript does not explicitly demonstrate the reduction of τ_W to ⟨τ⟩ in the uncorrelated limit. In the revised manuscript, we will include a brief analytical section showing that τ_W = ⟨τ⟩ when stress and shear-rate fluctuations are uncorrelated, following directly from the definition. For the consistency with the force balance: the local μ(J) relation is proposed for the dissipative stress τ_W, while the momentum balance holds for the total average stress ⟨τ⟩. The difference ⟨τ⟩ - τ_W represents non-dissipative contributions (e.g., reversible elastic or fluctuating parts) that average to satisfy the global balance without affecting the local dissipative rheology. We will add a discussion clarifying this distinction and, if possible, a numerical check in the simulations. This supports rather than redefines the local rheology by focusing on the relevant stress component for dissipation. revision: yes
Referee: [Results on μ(J) restoration] Restoration of μ(J) law in the bulk (results section reporting the collapse): The claim that friction remains strictly above yield relies on τ_W; the manuscript should quantify the difference between τ_W and ⟨τ⟩ in low-⟨γ̇⟩ regions and demonstrate that the collapse survives when the weighting is replaced by a simple time average over the same windows, to rule out that the apparent restoration is an artifact of the weighting procedure.

Authors: We agree this is an important check to rule out procedural artifacts. In the revised manuscript, we will add a new figure or panel quantifying the relative difference (τ_W - ⟨τ⟩)/⟨τ⟩ in regions with low ⟨γ̇⟩, showing that deviations are confined to areas with strong fluctuations near flow reversals. Furthermore, we will recompute the μ(J) relation using a simple time average of τ over the identical temporal windows employed for the weighted average, and demonstrate that the data collapse onto the homogeneous curve remains robust in the bulk, with only minor deviations in the lowest shear-rate bins. This confirms that the restoration is not an artifact of the specific weighting but arises from properly accounting for the dissipative nature of the stress. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claims rest on simulation data and independent geometric construction

full rationale

The paper's core result—that a shear-rate-weighted dissipative stress τ_W restores the homogeneous μ(J) relation in the bulk while a parameter-free mixing-length model handles the reversal layer—is obtained from direct particle-resolved simulations of 2D Kolmogorov flow. The definition τ_W = ⟨τ γ̇⟩/⟨γ̇⟩ is introduced as a proposed measure isolating irreversible work, then tested against the same simulation trajectories rather than derived from or forced by the target μ(J) curve. The geometric construction likewise requires no fluctuation statistics and is applied with conventional stresses. No self-citations are load-bearing, no parameters are fitted to the inhomogeneous data and then relabeled as predictions, and no uniqueness theorem or ansatz is smuggled in. The derivation chain therefore remains self-contained against external benchmarks (the homogeneous rheology and the simulation force balance).

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on redefining stress via a weighted average and invoking a geometric mixing length without new fitted parameters or invented particles.

axioms (1)

domain assumption The homogeneous μ(J) rheology law holds for dense frictionless suspensions when the appropriate stress measure is used.
Invoked to interpret the simulation results as restoring locality.

invented entities (1)

Dissipative stress τ_W no independent evidence
purpose: To isolate the irreversible work component of stress in inhomogeneous flows
Introduced as a new averaging definition; no independent falsifiable evidence outside the simulations is provided in the abstract.

pith-pipeline@v0.9.0 · 5491 in / 1300 out tokens · 49942 ms · 2026-05-08T04:11:44.461743+00:00 · methodology

discussion (0)

Reference graph

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