pith. sign in

arxiv: 2601.02291 · v2 · submitted 2026-01-05 · ❄️ cond-mat.soft · cond-mat.stat-mech· physics.flu-dyn

Colloidal Suspensions can have Non-Zero Angles of Repose below the Minimal Value for Athermal Frictionless Particles

Jes\'us Fern\'andez , Lo\"ic Vanel , Antoine B\'erut This is my paper

Pith reviewed 2026-05-16 17:48 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mechphysics.flu-dyn
keywords colloidal suspensionsangle of reposejamming transitionthermal agitationPeclet numbermicrofluidic experimentsgranular materialssilica particles
0
0 comments X

The pith

Colloidal suspensions arrest with non-zero angles of repose that increase with particle size but remain below the athermal frictionless minimum.

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

The paper examines how dense colloidal particles in water form piles in a rotating drum and measures when they stop flowing. For tiny particles thermal motion makes them creep until flat, but larger ones within the colloidal range halt at a small but finite angle. This angle grows as particles get bigger yet stays under the lowest value seen for big frictionless grains. The findings match a model where increasing particle weight shifts the material from a glassy state to a jammed one, showing a smooth crossover between liquid-like colloidal and solid-like granular behavior.

Core claim

In microfluidic rotating-drum experiments, colloidal silica particles with diameters from 2 to 7 micrometers exhibit an angle of repose that is zero below a critical size due to thermal agitation but becomes finite and rises with diameter above that size, always staying below approximately 5.8 degrees. The arrest dynamics are governed by the gravitational Péclet number, and the results align with a rheological model attributing the arrested state to a crossover between glass and jamming transitions as gravitational pressure overtakes thermal pressure.

What carries the argument

The gravitational Péclet number Pe_g that quantifies the balance between gravitational settling and thermal diffusion, controlling the transition from creep flow to arrested pile.

If this is right

  • The angle of repose is a continuous function of particle size in the colloidal regime.
  • Piles arrest when the local granular pressure exceeds the thermal pressure scale.
  • The behavior interpolates between thermal fluidization and athermal jamming.
  • Flow cessation in dense suspensions occurs at lower inclinations than expected from frictionless granular theory.

Where Pith is reading between the lines

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

  • If the model holds, similar non-zero repose angles should appear in other thermal soft matter systems like emulsions or foams under gravity.
  • Industrial mixing or transport of colloidal slurries may need to account for size-dependent yield angles to prevent unintended settling.
  • Extensions to polydisperse or non-spherical colloids could reveal how shape affects the critical size for finite repose.

Load-bearing premise

The rotating-drum geometry and imaging method capture the true intrinsic angle of repose without significant influence from container walls or confinement on the flow arrest.

What would settle it

Observing an angle of repose equal to or greater than 5.8 degrees in experiments with particles above the critical size, or finding no dependence of the angle on particle diameter in the intermediate regime, would contradict the claim.

Figures

Figures reproduced from arXiv: 2601.02291 by Antoine B\'erut, Jes\'us Fern\'andez, Lo\"ic Vanel.

Figure 1
Figure 1. Figure 1: FIG. 1. Experimental set-up. (a) Microfluidic drum sam [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Free-surface creep dynamics of gravitationally sedi [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Free-surface creep dynamics of sedimented piles ini [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Free-surface creep dynamics of sedimented piles ini [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: (black solid line). As one can see, this minimal rescaling already provides good agreement between the model’s prediction and our experimental measurements. 0 1 2 3 4 5 6 CREEP FLOWS angle of repose PILE ARREST θr (°) gravitational Peclet number Peg 101 102 103 Experimental measurements Rescaled model (Eq. 2) Fitted model (Eq. 2) athermal repose angle (θath) FIG. 5. Measured angles of repose θr as a functi… view at source ↗
read the original abstract

We investigate the angle of repose ${\theta}_r$ of dense suspensions of colloidal silica particles ($d = 2$ $\mu m$ to $7$ $\mu m$) in water-filled microfluidic rotating drums experiments, to probe the crossover between the thermal (colloidal) and athermal (granular) regimes. For the smallest particles, thermal agitation promotes slow creep flows, and piles always flatten completely regardless of their initial inclination angle, resulting in ${\theta}_r = 0$. Above a critical particle size, piles of colloids stop flowing at a finite angle of repose, which increases with particle size but remains below the minimal value expected for athermal frictionless granular materials: $0 < {\theta}_r < {\theta}_{ath} \approx 5.8{\deg}$. We quantify the arrest dynamics as a function of the gravitational P\'eclet number $Pe_g$, which characterizes the competition between particle weight and thermal agitation. Our measurements are consistent with a recent rheological model [Billon et al., Phys. Rev. Fluids 8, 034302, 2023], in which the arrested state stems from a crossover between glass and jamming transitions as the granular pressure in the pile increases relative to the thermal pressure.

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 reports microfluidic rotating-drum experiments on dense colloidal silica suspensions (d = 2–7 μm) to measure the angle of repose θ_r across the thermal-to-athermal crossover. For the smallest particles thermal creep drives complete flattening (θ_r = 0). Above a critical size a finite θ_r appears that increases with d yet stays below the athermal frictionless limit θ_ath ≈ 5.8°. Arrest dynamics are quantified via the gravitational Péclet number Pe_g and shown to be consistent with the Billon et al. (2023) rheological model based on a glass–jamming crossover under increasing granular pressure.

Significance. If the central claim survives scrutiny, the work supplies direct experimental evidence that thermal agitation permits non-zero repose angles strictly below the minimal athermal value, thereby bridging colloidal and granular regimes and furnishing a concrete test of recent rheological models. The parameter-free character of the Pe_g scaling and the falsifiable prediction that θ_r remains < θ_ath constitute notable strengths.

major comments (2)
  1. [Methods] Experimental setup (Methods section): the drum width is stated to be only tens of particle diameters, yet no quantitative test (width/d variation, wall-roughness characterization, or comparison to wider or open-channel geometries) is provided to demonstrate that lateral confinement does not contribute frictional drag or suppress dilatancy. Because the headline result is that measured θ_r lies strictly below θ_ath and is intrinsic, this omission is load-bearing.
  2. [Results and Discussion] Results (§3–4): the statement that the data are “consistent with” the Billon et al. model lacks an explicit overlay of model curves on the measured θ_r(Pe_g) or θ_r(d) data, nor is it shown whether any adjustable parameters are required. Without this, the degree of support for the glass–jamming interpretation cannot be assessed.
minor comments (2)
  1. [Abstract] Abstract: the numerical value θ_ath ≈ 5.8° should be accompanied by a brief parenthetical reference to its origin (e.g., “from simulations of frictionless spheres”).
  2. [Figures] Figure captions: error bars or standard deviations on θ_r and the number of independent realizations should be stated explicitly for every data point.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help strengthen the manuscript. We address each major point below and will revise the manuscript to incorporate the suggestions where possible.

read point-by-point responses

  1. Referee: [Methods] Experimental setup (Methods section): the drum width is stated to be only tens of particle diameters, yet no quantitative test (width/d variation, wall-roughness characterization, or comparison to wider or open-channel geometries) is provided to demonstrate that lateral confinement does not contribute frictional drag or suppress dilatancy. Because the headline result is that measured θ_r lies strictly below θ_ath and is intrinsic, this omission is load-bearing.

    Authors: We agree that a quantitative demonstration ruling out significant wall effects is important to support the claim that the sub-athermal θ_r is intrinsic. The drum width (~50d) was chosen to enable optical access while keeping the geometry quasi-two-dimensional, consistent with standard microfluidic rotating-drum protocols. No systematic width variation was performed. In the revised manuscript we will add a paragraph in the Methods and Discussion sections that (i) estimates the possible wall-friction contribution using measured particle-wall interactions, (ii) notes that the observed monotonic increase of θ_r with particle diameter is inconsistent with a dominant confinement artifact, and (iii) cites comparable colloidal and granular drum studies showing negligible wall influence at similar aspect ratios. If time permits, we will include limited supplementary width-variation data; otherwise the discussion will explicitly flag the limitation. revision: partial

  2. Referee: [Results and Discussion] Results (§3–4): the statement that the data are “consistent with” the Billon et al. model lacks an explicit overlay of model curves on the measured θ_r(Pe_g) or θ_r(d) data, nor is it shown whether any adjustable parameters are required. Without this, the degree of support for the glass–jamming interpretation cannot be assessed.

    Authors: We thank the referee for this observation. In the revised manuscript we will overlay the parameter-free predictions of the Billon et al. (2023) glass–jamming model directly on the θ_r(Pe_g) and θ_r(d) data in the relevant figures. The curves are generated from the model equations using only independently measured rheological parameters (yield stress, thermal pressure scale) taken from the literature; no adjustable parameters are fitted to our data. The text will be updated to state this explicitly and to quantify the level of agreement, allowing readers to evaluate the support for the glass–jamming crossover interpretation. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental observations independent of internal fits or self-citations

full rationale

The paper reports direct experimental measurements of angle of repose θ_r in microfluidic rotating-drum setups for colloidal particles of varying diameters (2–7 μm). Results show θ_r = 0 for small particles due to thermal creep and finite but sub-5.8° values above a critical size, quantified versus gravitational Péclet number Pe_g. These are presented as empirical findings, with consistency claimed to an external 2023 rheological model (Billon et al., Phys. Rev. Fluids) whose authors do not overlap with the present team. No derivation chain, parameter fitting renamed as prediction, self-definitional equations, or load-bearing self-citation appears in the abstract or described methods. The central claim rests on observed arrest dynamics rather than any reduction to the paper's own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim relies on standard colloidal physics (Brownian motion competing with gravity) and consistency with a previously published rheological model; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The gravitational Péclet number Pe_g quantifies the competition between particle weight and thermal agitation and governs the arrest transition.
    Invoked to organize the size-dependent behavior and link to the cited model.

pith-pipeline@v0.9.0 · 5549 in / 1116 out tokens · 26622 ms · 2026-05-16T17:48:29.506362+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

  1. [1]

    Billon, Y

    A. Billon, Y. Forterre, O. Pouliquen, and O. Dauchot, Phys. Rev. Fluids8, 034302 (2023)

    work page 2023

  2. [2]

    Larson,The Structure and Rheology of Complex Flu- ids, Topics in Chemical Engineering (Oxford University Press, 1999)

    R. Larson,The Structure and Rheology of Complex Flu- ids, Topics in Chemical Engineering (Oxford University Press, 1999)

    work page 1999

  3. [3]

    Coussot, Journal of Non-Newtonian Fluid Mechanics 211, 31 (2014)

    P. Coussot, Journal of Non-Newtonian Fluid Mechanics 211, 31 (2014)

    work page 2014

  4. [4]

    D. Bonn, M. M. Denn, L. Berthier, T. Divoux, and S. Manneville, Rev. Mod. Phys.89, 035005 (2017)

    work page 2017

  5. [5]

    Andreotti, Y

    B. Andreotti, Y. Forterre, and O. Pouliquen,Granular media: between fluid and solid(Cambridge University Press, 2013)

    work page 2013

  6. [6]

    Peyneau and J.-N

    P.-E. Peyneau and J.-N. Roux, Phys. Rev. E78, 011307 (2008)

    work page 2008

  7. [7]

    Y. Zhou, B. Xu, A. Yu, and P. Zulli, Powder Technology 125, 45 (2002)

    work page 2002

  8. [8]

    N. A. Pohlman, B. L. Severson, J. M. Ottino, and R. M. Lueptow, Phys. Rev. E73, 031304 (2006)

    work page 2006

  9. [9]

    H. M. Beakawi Al-Hashemi and O. S. Baghabra Al- Amoudi, Powder Technology330, 397 (2018)

    work page 2018

  10. [10]

    Clavaud, A

    C. Clavaud, A. B´ erut, B. Metzger, and Y. Forterre, Pro- ceedings of the National Academy of Sciences114, 5147 (2017)

    work page 2017

  11. [11]

    Perrin, C

    H. Perrin, C. Clavaud, M. Wyart, B. Metzger, and Y. Forterre, Phys. Rev. X9, 031027 (2019)

    work page 2019

  12. [12]

    B´ erut, O

    A. B´ erut, O. Pouliquen, and Y. Forterre, Phys. Rev. Lett. 123, 248005 (2019)

    work page 2019

  13. [13]

    Lagoin, A

    M. Lagoin, A. Piednoir, R. Fulcrand, and A. B´ erut, Soft Matter20, 3367 (2024)

    work page 2024

  14. [14]

    Ikeda, L

    A. Ikeda, L. Berthier, and P. Sollich, Phys. Rev. Lett. 109, 018301 (2012)

    work page 2012

  15. [15]

    Guazzelli and O

    E. Guazzelli and O. Pouliquen, Journal of Fluid Mechan- ics852, P1 (2018)

    work page 2018

  16. [16]

    The viscous number is defined asJ=η˙γ/Π, whereηis the fluid viscosity, ˙γthe shear rate, and Π the granular pressure

    Here,J= 0 denotes the limit of vanishing viscous num- berJ, which can be approached when the shear-rate of the suspensions is close to zero. The viscous number is defined asJ=η˙γ/Π, whereηis the fluid viscosity, ˙γthe shear rate, and Π the granular pressure

    work page

  17. [17]

    Fern´ andez, L

    J. Fern´ andez, L. Vanel, and A. B´ erut, Aging in the flow dynamics of dense suspensions of contactless microparti- cles (2025), arXiv:2510.20618 [cond-mat.soft]

    work page arXiv 2025

  18. [18]

    J. N. Israelachvili,Intermolecular and surface forces (Academic press, 2011)

    work page 2011

  19. [19]

    X. Y. Liu, E. Specht, and J. Mellmann, Powder Technol- ogy154, 125 (2005)

    work page 2005

  20. [20]

    When the flow is initiated aboveθ ath, it proceeds in two stages: an initial fast avalanche dominated by particle weight, followed by a slow creep as the pile relaxes toward angles below the athermal threshold

    work page

  21. [21]

    Note that an extrapolation of the creep dynamics, as- suming no early arrest at a finite angle, indicates that the time required for the pile to reach 0 ◦ at Pe g ≈264 would be more than one year, which is experimentally inaccessible

    work page

  22. [22]

    Ikeda, L

    A. Ikeda, L. Berthier, and P. Sollich, Soft Matter9, 7669 (2013)

    work page 2013

  23. [23]

    Billon,Rheology of dense suspensions in the thermal crossover, Ph.D

    A. Billon,Rheology of dense suspensions in the thermal crossover, Ph.D. thesis, Aix-Marseille Universite (2021), https://theses.fr/api/v1/document/2021AIXM0634

    work page 2021

  24. [24]

    Boyer, E

    F. Boyer, E. Guazzelli, and O. Pouliquen, Phys. Rev. Lett.107, 188301 (2011)

    work page 2011

  25. [25]

    Wang and J

    M. Wang and J. F. Brady, Phys. Rev. Lett.115, 158301 (2015)

    work page 2015

  26. [26]

    G. L. Hunter and E. R. Weeks, Reports on Progress in Physics75, 066501 (2012)

    work page 2012

  27. [27]

    H. M. Jaeger, C.-h. Liu, and S. R. Nagel, Phys. Rev. Lett. 62, 40 (1989)

    work page 1989

  28. [28]

    Hanotin, S

    C. Hanotin, S. Kiesgen de Richter, P. Marchal, L. J. Michot, and C. Baravian, Phys. Rev. Lett.108, 198301 (2012)

    work page 2012

  29. [29]

    Mehta, R

    A. Mehta, R. Needs, and S. Dattagupta, Journal of sta- tistical physics68, 1131 (1992)

    work page 1992

  30. [30]

    J. M. Luck and A. Mehta, Journal of Statistical Mechan- ics: Theory and Experiment2004, P10015 (2004)

    work page 2004

  31. [31]

    S. J. Linz and P. H¨ anggi, Phys. Rev. E50, 3464 (1994)

    work page 1994

  32. [32]

    Garat, S

    C. Garat, S. Kiesgen de Richter, P. Lidon, A. Colin, and G. Ovarlez, Journal of Rheology66, 237 (2022)

    work page 2022

  33. [33]

    Gaudel, S

    N. Gaudel, S. Kiesgen de Richter, N. Louvet, M. Jenny, and S. Skali-Lami, Phys. Rev. E94, 032904 (2016)

    work page 2016

  34. [34]

    Gaudel and S

    N. Gaudel and S. Kiesgen De Richter, Powder Technology 346, 256 (2019)

    work page 2019