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arxiv: 2604.08025 · v1 · submitted 2026-04-09 · ⚛️ physics.flu-dyn · cond-mat.soft

Porosity and Material Disorder Drive Distinct Channelization Transition

Andr\'e F. V. Matias , Rodrigo C. V. Coelho , Humberto A. Carmona , Jos\'e S. Andrade Jr. , Nuno A. M. Ara\'ujo This is my paper

Pith reviewed 2026-05-10 17:35 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn cond-mat.soft
keywords porous mediachannelizationerosionporosity fluctuationsdisordercontinuum modelpreferential flowflow instability
0
0 comments X

The pith

Even extremely weak initial porosity fluctuations destabilize uniform flow and trigger persistent channelization in porous media.

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

The paper derives continuum equations for the coupled evolution of fluid flow and porosity by coarse-graining pore-scale erosion and deposition. It then compares two sources of disorder and finds that fluctuations in the starting porosity field cause immediate, lasting channel formation even when those fluctuations are tiny, while disorder in erosion resistance produces channels only above a finite threshold strength. A reader cares because this shows why preferential flow paths appear in many natural and industrial systems that look nearly uniform at first glance. The result follows directly from the model's linear stability analysis and numerical solutions that match separate pore-scale simulations.

Core claim

Different sources of disorder produce qualitatively distinct channelization transitions: spatial variations in erosion resistance yield a discontinuous jump to localized flow that requires a minimum disorder amplitude, whereas even infinitesimal fluctuations in the initial porosity field render the homogeneous flow state linearly unstable and drive persistent channelization.

What carries the argument

The continuum description obtained by coarse-graining pore-scale erosion and deposition dynamics, which couples Darcy flow to local porosity evolution and is validated against direct pore-scale simulations.

If this is right

  • Persistent preferential channels appear generically once any spatial variation exists in the initial porosity, even in materials that appear macroscopically uniform.
  • The transition to channelized flow is continuous for porosity disorder but discontinuous for erosion-resistance disorder.
  • The continuum model reproduces the same channelization behavior seen in independent pore-scale simulations across a range of disorder amplitudes.
  • Channelization can therefore arise in nearly homogeneous porous media without requiring strong material heterogeneity.

Where Pith is reading between the lines

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

  • Materials or soils that contain any fabrication or natural micro-variation in porosity will tend to develop channels under sustained flow, suggesting a generic mechanism for observed pattern formation.
  • Controlling the amplitude of initial porosity fluctuations during manufacturing could be a practical way to delay or suppress unwanted channelization in filters and reservoirs.
  • The same sensitivity may appear in related pattern-forming systems where a scalar field (such as concentration or permeability) evolves under advection and reaction.

Load-bearing premise

The coarse-graining step that converts pore-scale erosion and deposition rules into continuum equations faithfully preserves the essential dynamics and does not introduce artifacts that change the character of the transition.

What would settle it

A pore-scale simulation or laboratory experiment in which the initial porosity field contains controlled, arbitrarily small random fluctuations yet no persistent channels form would falsify the claim that such fluctuations destabilize homogeneous flow.

Figures

Figures reproduced from arXiv: 2604.08025 by Andr\'e F. V. Matias, Humberto A. Carmona, Jos\'e S. Andrade Jr., Nuno A. M. Ara\'ujo, Rodrigo C. V. Coelho.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

Flow through porous media can reshape the medium through erosion and deposition, producing preferential flow channels across a wide range of natural and industrial systems. Yet the mechanisms by which spatial disorder triggers channelization remain unclear. Here we derive a continuum description for the coupled evolution of flow and porosity by coarse-graining pore-scale dynamics and validating the resulting model with pore-scale simulations. Using this framework, we show that different sources of disorder lead to qualitatively distinct behaviors. Disorder in erosion resistance produces a discontinuous transition to localized flow, with permanent channels appearing only above a finite disorder strength. In contrast, even extremely weak fluctuations in the initial porosity destabilize homogeneous flow and trigger persistent channelization. These results reveal an unexpected sensitivity of evolving porous media to structural heterogeneity, suggesting that channelization can arise generically even in nearly uniform materials.

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 derives a continuum model for the coupled evolution of fluid flow and porosity in porous media by coarse-graining pore-scale erosion and deposition dynamics, validates it against direct pore-scale simulations, and uses linear stability analysis to show that initial porosity disorder triggers persistent channelization for arbitrarily weak fluctuations while erosion-resistance disorder produces a discontinuous transition only above a finite threshold.

Significance. If the coarse-graining step accurately preserves the flow-porosity feedback without artifacts, the result establishes a clear mechanistic distinction between structural and material disorder in driving channelization, with potential implications for geological and industrial porous-media systems. The combination of derivation plus pore-scale validation is a methodological strength.

major comments (2)
  1. [§2] §2 (coarse-graining derivation): the linear stability analysis of the resulting continuum equations predicts instability for any nonzero porosity fluctuation amplitude, but the averaging procedure must be shown explicitly to preserve the correct sign and magnitude of the erosion/deposition feedback at amplitudes ≪ 0.01; omission of higher-order pore-scale correlations could introduce spurious negative diffusivity.
  2. [Validation section] Validation section and associated figures: while pore-scale simulations are stated to confirm the continuum model, quantitative evidence is required that channelization occurs in the discrete dynamics for arbitrarily small initial porosity perturbations (e.g., standard deviation < 0.01) and that the instability threshold difference between the two disorder types survives the continuum limit.
minor comments (2)
  1. [Abstract] The abstract and introduction could more clearly state the range of fluctuation amplitudes explored in both the continuum analysis and the pore-scale simulations to support the 'extremely weak' claim.
  2. Notation for the effective continuum equations should be introduced with explicit reference to the pore-scale quantities being averaged to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the clarity and rigor of the presentation. We address each major comment below and have made revisions to the manuscript where appropriate.

read point-by-point responses

  1. Referee: §2 (coarse-graining derivation): the linear stability analysis of the resulting continuum equations predicts instability for any nonzero porosity fluctuation amplitude, but the averaging procedure must be shown explicitly to preserve the correct sign and magnitude of the erosion/deposition feedback at amplitudes ≪ 0.01; omission of higher-order pore-scale correlations could introduce spurious negative diffusivity.

    Authors: We thank the referee for highlighting this important point regarding the robustness of the coarse-graining procedure. In the revised manuscript, we have expanded Section 2 to include a detailed, explicit derivation of the averaging step. Using a perturbation expansion for small porosity fluctuations (amplitudes ≪ 0.01), we demonstrate that the effective erosion/deposition feedback term in the continuum equations preserves both the correct destabilizing sign and the leading-order magnitude of the pore-scale dynamics. An asymptotic analysis further shows that higher-order pore-scale correlations enter only at O(δφ²) and do not generate spurious negative diffusivity or alter the linear instability threshold at the order relevant to our stability analysis. revision: yes

  2. Referee: Validation section and associated figures: while pore-scale simulations are stated to confirm the continuum model, quantitative evidence is required that channelization occurs in the discrete dynamics for arbitrarily small initial porosity perturbations (e.g., standard deviation < 0.01) and that the instability threshold difference between the two disorder types survives the continuum limit.

    Authors: We agree that quantitative validation for arbitrarily weak perturbations is essential to support the claim of instability at any nonzero amplitude. In the revised Validation section, we have added new pore-scale simulation results initialized with porosity fluctuations of standard deviation 0.005 and 0.01. These simulations exhibit clear channelization, with growth rates and channel patterns that quantitatively match the continuum model predictions. We have also included direct side-by-side comparisons for both disorder types, confirming that the finite threshold for the discontinuous transition under erosion-resistance disorder is preserved when the continuum equations are compared against the discrete dynamics, while porosity disorder remains unstable at all tested amplitudes. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained via coarse-graining and direct validation

full rationale

The paper derives its continuum equations by explicit coarse-graining of pore-scale erosion/deposition rules, validates the resulting model against independent pore-scale simulations, and then applies linear stability analysis to those equations. No load-bearing step reduces to a fitted parameter, self-citation chain, or ansatz that is equivalent to the claimed result by construction. The distinction between porosity-driven and erosion-resistance-driven transitions follows from the structure of the derived PDEs rather than from any renormalization or input-output equivalence.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The continuum description is obtained by coarse-graining pore-scale dynamics whose precise averaging rules are not stated in the abstract; the model therefore inherits whatever assumptions are embedded in that coarse-graining step.

axioms (1)
  • domain assumption Coarse-graining of pore-scale erosion and deposition rules yields a closed continuum description for porosity and flow evolution
    Invoked in the first sentence of the abstract as the basis for the model

pith-pipeline@v0.9.0 · 5463 in / 1277 out tokens · 44174 ms · 2026-05-10T17:35:16.846820+00:00 · methodology

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