Disentangling microstructural elements of shear thickening suspensions via computer simulations of a minimal model

Daniel L. Blair; Emanuela Del Gado; H. A. Vinutha; Jeffrey S. Urbach; William C. J. Buchholtz

arxiv: 2604.12107 · v1 · submitted 2026-04-13 · ❄️ cond-mat.soft

Disentangling microstructural elements of shear thickening suspensions via computer simulations of a minimal model

William C. J. Buchholtz , Daniel L. Blair , Jeffrey S. Urbach , H. A. Vinutha , Emanuela Del Gado This is my paper

Pith reviewed 2026-05-10 15:34 UTC · model grok-4.3

classification ❄️ cond-mat.soft

keywords shear thickeningdense suspensionscontact networkpercolationstress fluctuationsradial distribution functionminimal modelcomputer simulations

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The pith

In a minimal model of shear-thickening suspensions, spanning rigid contact assemblies produce non-Gaussian stress fluctuations only during thickening.

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

The paper uses 2D computer simulations of a minimal model to track how the contact network inside a dense suspension rearranges under shear. Distinct building blocks appear in the network and, during thickening, join into large spanning assemblies that generate power-law tails in local contact forces and non-Gaussian fluctuations in the overall stress. These rigid or over-constrained subsets percolate more readily and last longer in thickening flows, whereas in thinning the same blocks deform and spread forces evenly, cutting down stress fluctuations. A reader would care because the work ties sudden jumps in viscosity to concrete, measurable changes in the contact network rather than to average density or viscosity alone.

Core claim

In steady flow the contact network contains distinct building blocks signaled by sharp peaks in the radial distribution function. Non-Gaussian stress fluctuations emerge during thickening and are linked to power-law tails in local contact forces when these blocks form large spanning assemblies. The strongly forced, rigid or over-constrained parts of the network become more likely to percolate at the start of thickening and maintain connectivity over extended strain intervals. In contrast, thinning causes these structures to deform, promoting a homogeneous spread of contact forces that diminishes time-dependent fluctuations in the overall stress.

What carries the argument

Flow-induced building blocks of the contact network, identified by peaks in the radial distribution function, whose rigid, strongly connected subsets percolate into sample-spanning assemblies carrying high forces.

If this is right

The rigid or over-constrained subset of the contact network percolates with higher probability as the system enters the thickening regime.
Power-law tails in the distribution of local contact forces appear specifically when the building blocks form large spanning assemblies during thickening.
These spanning structures persist over larger strain windows during thickening than during thinning.
Deformation of the building blocks during thinning redistributes contact forces more homogeneously across the sample.
The homogeneous redistribution during thinning reduces temporal fluctuations in the macroscopic stress.

Where Pith is reading between the lines

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

The association between rigid percolating contacts and non-Gaussian fluctuations may extend to other soft materials that exhibit yielding or jamming transitions.
Measuring local force distributions in flowing experimental suspensions could test whether power-law tails serve as a direct signature of thickening.
Altering particle interactions to limit the formation of rigid networks might suppress unwanted thickening in practical applications.
Because the work is performed in two dimensions, extending the same minimal model to three dimensions would clarify how dimensionality affects the percolation and persistence of these assemblies.

Load-bearing premise

The minimal model includes all essential interactions that govern thickening and thinning in real suspensions.

What would settle it

If experiments on real shear-thickening suspensions find no power-law tails in local contact forces during thickening or no increase in the likelihood of rigid percolating clusters at the thickening onset, the claimed link would be contradicted.

read the original abstract

We use a minimal model for a dense suspension undergoing thickening and thinning to investigate microstructural changes in 2d simulations. Our simulations show that in steady flow the contact network contains distinct building blocks which are clearly signaled by sharp peaks in the radial distribution function, similar to what is observed in granular jamming. These structures {deform} during thinning. Non-Gaussian stress fluctuations that only emerge during thickening are associated to power law tails in the distribution of local contact forces, which tend to emerge when the flow-induced building blocks form large spanning assemblies. The subset of the contact network characterized by strong contact forces and connectivity large enough to be rigid or over-constrained is increasingly likely to percolate as the system starts to thicken, and to percolate over larger strain windows during thickening. The tendency of these structures to span the sample and to persist is dramatically reduced during thinning, where instead their deformation allows for a more homogeneous spatial redistribution of contact forces, significantly reducing the fluctuations of the macroscopic stress over time.

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.

Desk Editor's Note private letter to a colleague

Simulations in this minimal 2D model link percolating rigid strong-force clusters to non-Gaussian stress fluctuations during thickening, but the model's fidelity to real suspensions is untested.

read the letter

The simulations show that in this minimal 2D model, non-Gaussian stress fluctuations during thickening tie to power-law tails in contact forces when rigid strong-force clusters percolate. That's the core new link they draw between microstructure and macroscopic behavior. They also track how those clusters deform and lose span during thinning, which redistributes forces more evenly and damps the fluctuations. The radial distribution function peaks give a concrete signature for the building blocks, and the percolation analysis for over-constrained subsets quantifies the structural change across regimes. This is a clean way to separate thickening from thinning effects inside the model. The work does a solid job staying within the simulation and producing testable internal connections. The main limitation is the minimal model itself. It is two-dimensional and omits or approximates several elements that experiments suggest matter, such as full hydrodynamics, particle roughness, and three-dimensional network topology. The abstract gives no direct comparison to measured data or experimental force distributions, so the claim that these building blocks and percolation events explain real shear thickening rests on an assumption that the model captures the dominant physics. That step is the softest part of the argument. This paper is for rheologists and soft-matter simulators who want a mechanistic picture of possible contact-network mechanisms. Readers already working with minimal models or network analysis will get the most from the details. It deserves peer review because the simulation results are specific and internally consistent enough for referees to assess the methods and the strength of the model-to-reality step.

Referee Report

3 major / 3 minor

Summary. The paper uses 2D simulations of a minimal model for dense suspensions to identify distinct building blocks in the contact network, signaled by sharp peaks in the radial distribution function. It links non-Gaussian stress fluctuations that emerge only during thickening to power-law tails in local contact force distributions, which appear when these building blocks form large spanning assemblies. The subset of the network with strong forces and rigid/over-constrained connectivity is shown to percolate more readily at thickening onset and over larger strain windows, while during thinning these structures deform, enabling homogeneous force redistribution and reduced macroscopic stress fluctuations.

Significance. If the minimal model is representative, the work supplies a microstructural mechanism connecting contact-network topology and force statistics to the onset of non-Gaussian stress fluctuations specifically in the thickening regime. The direct observation of percolation of rigid strong-force clusters and the contrast with thinning behavior offers a falsifiable picture that could inform both theory and experiment on suspension rheology. The simulation framework permits quantitative tracking of network connectivity and force tails that are difficult to access experimentally.

major comments (3)

[§2] §2 (Model and methods): The central claim that power-law force tails and rigid-cluster percolation are generic signatures of thickening rests on the unvalidated assumption that the minimal contact rules and flow implementation capture the dominant physics of real suspensions. No comparison is presented to experimental rheology curves, force distributions, or to simulations that include lubrication hydrodynamics or particle roughness; without such checks the observed percolation statistics could be artifacts of the 2D minimal model.
[§4.3] §4.3 (Percolation analysis): The statement that the strong-force rigid subset 'is increasingly likely to percolate as the system starts to thicken' is not accompanied by the number of independent runs, error bars on the percolation probability, or a statistical test against a null model of random networks. Because this percolation trend is load-bearing for the association with non-Gaussian fluctuations, quantitative robustness measures are required.
[Fig. 6] Fig. 6 and associated text: The power-law tails in the contact-force distribution are reported only for the thickening regime; a direct side-by-side comparison of the force-distribution exponent (or its absence) between thickening and thinning at matched volume fractions is needed to substantiate that the tails are specifically tied to the percolating rigid clusters rather than to density alone.

minor comments (3)

The term 'building blocks' is used throughout but never given an explicit operational definition (e.g., a minimum cluster size or coordination threshold); a short paragraph in the introduction or methods would remove ambiguity.
System-size dependence of the percolation transition is not discussed; a brief check or statement that results are insensitive to box size would strengthen the claims.
A few figure captions (e.g., Fig. 4) refer to 'strain windows' without specifying how the window length was chosen or whether results are robust to that choice.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and have revised the manuscript where appropriate to strengthen the presentation.

read point-by-point responses

Referee: §2 (Model and methods): The central claim that power-law force tails and rigid-cluster percolation are generic signatures of thickening rests on the unvalidated assumption that the minimal contact rules and flow implementation capture the dominant physics of real suspensions. No comparison is presented to experimental rheology curves, force distributions, or to simulations that include lubrication hydrodynamics or particle roughness; without such checks the observed percolation statistics could be artifacts of the 2D minimal model.

Authors: We acknowledge the limitations of the minimal model, which omits full lubrication hydrodynamics and particle roughness. The model is deliberately simplified to isolate the roles of contact topology and force statistics, as is common in studies of jamming and shear thickening. We have added a dedicated paragraph in the revised §2 that explicitly discusses these assumptions, notes qualitative consistency with trends in more detailed simulations and experiments (e.g., onset of non-Gaussian stress fluctuations), and clarifies that quantitative validation against specific experimental curves lies outside the present scope. revision: partial
Referee: §4.3 (Percolation analysis): The statement that the strong-force rigid subset 'is increasingly likely to percolate as the system starts to thicken' is not accompanied by the number of independent runs, error bars on the percolation probability, or a statistical test against a null model of random networks. Because this percolation trend is load-bearing for the association with non-Gaussian fluctuations, quantitative robustness measures are required.

Authors: We agree that additional quantitative measures are needed. The revised manuscript now states that percolation probabilities are computed from 20 independent runs, includes error bars (standard error of the mean), and adds a direct comparison to a null model in which contacts are randomly reassigned while preserving the force distribution. The null-model percolation occurs at substantially higher strains, confirming that the observed trend is not an artifact of random connectivity. revision: yes
Referee: Fig. 6 and associated text: The power-law tails in the contact-force distribution are reported only for the thickening regime; a direct side-by-side comparison of the force-distribution exponent (or its absence) between thickening and thinning at matched volume fractions is needed to substantiate that the tails are specifically tied to the percolating rigid clusters rather than to density alone.

Authors: We have added the requested comparison. The revised Fig. 6 now includes force distributions for both thickening and thinning at the same volume fraction (φ = 0.8). Power-law tails (exponent ≈ −2.5) appear only in the thickening regime, while thinning exhibits exponential decay. The accompanying text has been updated to highlight that the tails correlate with the presence of percolating rigid clusters rather than density alone. revision: yes

Circularity Check

0 steps flagged

No circularity in simulation-derived claims

full rationale

The paper reports emergent observations from direct 2D simulations of a minimal suspension model, including non-Gaussian stress fluctuations linked to power-law force tails and percolation of rigid strong-force clusters at thickening onset. These quantities arise from the model's contact rules and flow dynamics without any parameter fitting to the target statistics, without self-citations invoked as uniqueness theorems, and without any renaming or ansatz smuggling. The derivation chain consists of simulation outputs and post-processing measurements; no step reduces by construction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract does not specify any free parameters, axioms, or invented entities beyond the standard assumptions of particle-based simulations in soft matter physics.

pith-pipeline@v0.9.0 · 5494 in / 1186 out tokens · 72313 ms · 2026-05-10T15:34:33.084960+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

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[2]

48 D. J. Jacobs and B. Hendrickson,Journal of Computational Physics, 1997,137, 346–365. 49 S. Zhang, L. Zhang, M. Bouzid, D. Z. Rocklin, E. Del Gado and X. Mao,Phys. Rev. Lett., 2019,123, 058001. 50 V. Babu, H. A. Vinutha, D. Bi and S. Sastry ,Soft Matter, 2023, 19, 9399–9404. 51 H. Dashti, A. A. Saberi, S. Rahbari and J. Kurths,Science Ad- vances, 2023,9...

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[1] [1]

1 R. Seto, R. Mari, J. F. Morris and M. M. Denn,Phys. Rev. Lett., 2013,111, 218301. 2 R. Mari, R. Seto, J. Morris and M. M. Denn,Journal of Rheol- ogy, 2014,58, 1693–1724. 3 M. Wyart and M. E. Cates,Phys. Rev. Lett., 2014,112, 098302. 4 N. Y. C. Lin, B. M. Guy , M. Hermes, C. Ness, J. Sun, W. C. K. Poon and I. Cohen,Phys. Rev. Lett., 2015,115, 228304. 5 A...

work page 2013

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48 D. J. Jacobs and B. Hendrickson,Journal of Computational Physics, 1997,137, 346–365. 49 S. Zhang, L. Zhang, M. Bouzid, D. Z. Rocklin, E. Del Gado and X. Mao,Phys. Rev. Lett., 2019,123, 058001. 50 V. Babu, H. A. Vinutha, D. Bi and S. Sastry ,Soft Matter, 2023, 19, 9399–9404. 51 H. Dashti, A. A. Saberi, S. Rahbari and J. Kurths,Science Ad- vances, 2023,9...

work page 1997