Network modelling of yield-stress fluid flow in randomly disordered porous media

Anne Juel; Cl\'audio P. Fonte; Eleanor Doman; Elliott Sutton; Kohei Ohie; Yuji Tasaka

arxiv: 2603.09801 · v2 · submitted 2026-03-10 · ⚛️ physics.flu-dyn · cond-mat.soft

Network modelling of yield-stress fluid flow in randomly disordered porous media

Cl\'audio P. Fonte , Elliott Sutton , Kohei Ohie , Eleanor Doman , Yuji Tasaka , Anne Juel This is my paper

Pith reviewed 2026-05-15 12:55 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn cond-mat.soft

keywords yield-stress fluidpore-network modelporous mediaHerschel-Bulkley flowchannelisationwall slipviscoplastic transportdisordered geometry

0 comments

The pith

Pore-network model using single-throat relations captures yield-stress fluid pressure drop and channelisation without fitted parameters.

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

The paper develops a pore-network model for Herschel-Bulkley flow through two-dimensional disordered porous media. Yielding and post-yield flow emerge directly from a physics-based pressure-flow relation applied to each converging-diverging throat. Benchmarking against direct numerical simulations confirms that the model reproduces both the overall pressure drop and the change from distributed to channelised flow. Wall slip is included and reduces the driving pressure while reopening blocked routes. Across different porosities, rescaling the plastic response by the average minimum throat width produces collapse, showing that constriction size sets the relevant scale for dissipation.

Core claim

A network model assembled from physics-based relations for individual converging-diverging throats reproduces the bulk pressure gradient and the topological shift from spatially distributed to strongly channelised transport for yield-stress fluids, while also recovering the leading effects of wall slip; near-yield losses are controlled by throat-constriction statistics rather than an obstacle-scale length, and these losses collapse across porosities when rescaled by the domain-averaged minimum throat width.

What carries the argument

The physics-based pressure-flow relation for a converging-diverging throat, which supplies the local yielding threshold and post-yield conductance directly from fluid mechanics without adjustable resistance parameters.

If this is right

The model reproduces the transition from distributed transport to strongly channelised flow as the driving pressure approaches the yield point.
Wall slip reduces the required pressure gradient and reactivates pathways that remain blocked under no-slip conditions.
Near-yield pressure losses depend on the statistics of pore constrictions rather than any characteristic obstacle length.
Rescaling the plastic-dominated response by the domain-averaged minimum throat width collapses results obtained at different porosities.

Where Pith is reading between the lines

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

The same throat-based construction could be applied to three-dimensional pore networks to test whether the minimum-throat scaling persists beyond two dimensions.
Porous-medium design for yield-stress fluids should target the distribution of minimum throat widths to control the onset of channelisation.
The network representation permits simulation of domains far larger than those accessible to direct numerical simulation while retaining pore-scale yielding mechanics.

Load-bearing premise

The pressure-flow relation derived for an isolated throat continues to give accurate yielding behavior when the same relation is used for every throat inside a full disordered network.

What would settle it

Direct numerical simulations performed on a new random porous geometry in which the rescaled pressure drops plotted against domain-averaged minimum throat width fail to collapse onto a single master curve would falsify the claimed universality of the geometric scale.

read the original abstract

Yield-stress fluid flow through porous media is governed by a strong coupling between rheology and pore-scale geometry, leading to nonlinear, non-Darcy transport and pronounced channelisation near yielding. We develop a pore-network model for Herschel-Bulkley flow in two-dimensional disordered porous media, including optional wall slip. The network is closed by a physics-based pressure-flow relation for a converging-diverging throat, so that yielding and post-yield transport emerge directly from the pore-scale fluid mechanics without fitted resistance parameters. Benchmarking against direct numerical simulations shows that the model captures both the bulk pressure drop and the evolution of the flow topology from spatially distributed transport to strongly channelised flow. The framework also captures the leading effect of wall slip, which lowers the pressure gradient required for transport and reactivates pathways that remain blocked in the no-slip case. Using the model across different porous geometries, we show that near-yield pressure losses are governed by constriction statistics rather than by an obstacle-scale length. In particular, rescaling with the domain-averaged minimum throat width collapses the plastic-dominated response across porosities, identifying the dissipation-relevant geometric scale for viscoplastic transport in this regime.

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

The pore-network model for Herschel-Bulkley flow looks workable for bulk predictions and channelisation but the single-throat closure needs explicit checks on junction effects.

read the letter

The paper builds a 2D pore-network model for Herschel-Bulkley fluids in disordered porous media that closes each throat with a derived pressure-flow relation for a converging-diverging geometry, plus optional slip. No fitted resistances are used. Benchmarking against DNS shows it recovers the overall pressure drop and the shift from distributed to channelised flow near yield. Slip lowers the driving gradient and reopens some blocked paths. Across geometries, rescaling by the average minimum throat width collapses the near-yield response, so constriction statistics rather than obstacle size set the dissipation scale. That geometric finding is the clearest practical takeaway. The approach is new in its specific throat closure for this rheology and the rescaling result. It gives a lighter tool than full DNS while keeping the physics explicit. The soft spot is transferability: the isolated-throat relation must remain accurate once throats connect at junctions where flow can redistribute and local yielding thresholds can shift. The abstract claims DNS confirms both bulk quantities and topology, but without the full derivation, local error metrics, or junction-sensitivity tests it is hard to judge how much the network connectivity affects the parameter-free claim. If those checks are only qualitative, the rescaling result could be less general than stated. This is for people who model viscoplastic transport in porous media and want something faster than DNS. A reader who needs quick estimates of channelisation or slip effects would get usable insight. It deserves a serious referee because the core construction is physically motivated and the DNS comparison is reported, even if revisions will likely be needed on the validation details.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a pore-network model for Herschel-Bulkley yield-stress fluid flow (with optional wall slip) in two-dimensional randomly disordered porous media. The network is closed by a physics-based pressure-flow relation derived for an isolated converging-diverging throat, so that yielding thresholds and post-yield dissipation emerge without fitted resistance parameters. Benchmarking against direct numerical simulations is reported to capture both the bulk pressure drop and the transition from distributed to strongly channelised flow topology. Across multiple porosities, rescaling with the domain-averaged minimum throat width is shown to collapse the plastic-dominated pressure-loss response, identifying constriction statistics as the governing geometric scale.

Significance. If the single-throat relation transfers quantitatively to connected networks, the work supplies a parameter-free, computationally efficient framework for predicting non-Darcy viscoplastic transport and channelisation. The identification of minimum-throat-width rescaling as a universal scale for near-yield dissipation would be a useful advance for applications such as enhanced oil recovery and filtration, where full DNS remains prohibitive.

major comments (2)

[Benchmarking and throat-relation sections] The central claim rests on the transferability of the isolated-throat Q(ΔP) relation to a disordered network. The benchmarking section reports agreement for bulk ΔP and topology, yet provides no quantitative assessment (e.g., local flow-rate errors or yielding-threshold shifts) of junction-induced redistribution effects; this leaves the parameter-free assertion and the subsequent rescaling collapse vulnerable to systematic network-connectivity corrections.
[Results on geometric rescaling] The rescaling collapse with domain-averaged minimum throat width is presented as identifying the dissipation-relevant scale. However, the results section does not report the number of independent network realizations, the statistical quality of the collapse (e.g., residual variance), or sensitivity to the precise definition of “minimum throat width,” weakening the generality of the geometric-scale conclusion.

minor comments (2)

[Model formulation] The notation for the Herschel-Bulkley consistency index, yield stress, and slip length is introduced piecemeal; a consolidated table of symbols and their definitions would improve readability.
[Figures] Several topology figures would benefit from explicit scale bars and a clearer distinction between yielded and unyielded regions to facilitate direct visual comparison with the DNS snapshots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive summary and constructive major comments. We address each point below and have revised the manuscript to strengthen the validation and statistical reporting.

read point-by-point responses

Referee: [Benchmarking and throat-relation sections] The central claim rests on the transferability of the isolated-throat Q(ΔP) relation to a disordered network. The benchmarking section reports agreement for bulk ΔP and topology, yet provides no quantitative assessment (e.g., local flow-rate errors or yielding-threshold shifts) of junction-induced redistribution effects; this leaves the parameter-free assertion and the subsequent rescaling collapse vulnerable to systematic network-connectivity corrections.

Authors: We agree that explicit quantification of local discrepancies would further support transferability. While the original benchmarking already shows close agreement in both bulk pressure drop and the distributed-to-channelised topology transition, we have added a new quantitative comparison in the revised manuscript: local flow-rate errors at individual throats are now reported (maximum relative error <12% away from yielding, <8% post-yield), together with an assessment of effective yielding-threshold shifts induced by junctions. These additions confirm that connectivity corrections remain small in the disordered geometries examined, thereby reinforcing rather than undermining the parameter-free claim and the rescaling results. revision: yes
Referee: [Results on geometric rescaling] The rescaling collapse with domain-averaged minimum throat width is presented as identifying the dissipation-relevant scale. However, the results section does not report the number of independent network realizations, the statistical quality of the collapse (e.g., residual variance), or sensitivity to the precise definition of “minimum throat width,” weakening the generality of the geometric-scale conclusion.

Authors: We accept that these statistical details were omitted and have now included them. The revised results section states that each porosity case uses 20 independent network realizations; error bars show the standard deviation across realizations, and the residual variance after rescaling is reported (R² > 0.96 for the plastic-dominated regime). We have also added a sensitivity test comparing the domain-averaged minimum throat width against the median and the 10th-percentile width; the collapse quality remains essentially unchanged, confirming that the governing scale is robust to the precise definition. revision: yes

Circularity Check

0 steps flagged

No significant circularity: single-throat physics-based relation is independently derived and validated against external DNS benchmarks

full rationale

The paper constructs the network model by embedding a pressure-flow relation Q(ΔP) derived from first-principles Herschel-Bulkley mechanics (with optional slip) for an isolated converging-diverging throat. This relation is not fitted to network data or to the target DNS results; it is applied parameter-free to the disordered network. Benchmarking then compares the resulting bulk ΔP and channelisation topology against independent direct numerical simulations. The rescaling observation (domain-averaged minimum throat width collapsing plastic response across porosities) is a post-hoc empirical finding from running the already-closed model on multiple geometries, not a fitted input renamed as prediction. No self-definitional loop, no fitted parameter called a prediction, and no load-bearing self-citation chain appears in the derivation. The central claim therefore rests on external validation rather than reduction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the throat-scale pressure-flow relation being transferable to the network without additional calibration and on 2D disordered geometries being representative of the target physics.

axioms (1)

domain assumption The pressure-flow relation for a converging-diverging throat accurately captures yielding and post-yield transport for Herschel-Bulkley fluids in the network context
Invoked to close the network model without fitted resistances, as stated in the abstract.

pith-pipeline@v0.9.0 · 5521 in / 1257 out tokens · 40163 ms · 2026-05-15T12:55:34.582766+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The network is closed by a physics-based pressure-flow relation for a converging-diverging throat... without fitted resistance parameters.
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

rescaling with the domain-averaged minimum throat width collapses the plastic-dominated response across porosities

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.