arxiv: 2604.06581 · v1 · submitted 2026-04-08 · ⚛️ physics.flu-dyn · physics.geo-ph

Recognition: no theorem link

Modeling Ostwald Ripening Dynamics in Porous Microstructures

Md Zahidul Islam Laku , Mohammad Salehpour , Tian Lan , Benzhong Zhao , Yashar Mehmani

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:27 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.geo-ph

keywords Ostwald ripeningpore-network modelporous mediatwo-phase flowsolute transportmicrofluidic experimentsganglia dynamicscurvature saturation

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The pith

An image-based pore-network model simulates Ostwald ripening of multi-pore ganglia by coupling two-phase flow, solute transport, and curvature-driven dissolution without adjustable 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 method to track how partially miscible fluid ganglia evolve in porous media when differences in interface curvature drive mass transfer between them. Earlier pore-network approaches handled only isolated single-pore ganglia under static conditions and required simplified shapes. The new image-based model extracts local capillarity relations directly from actual pore geometry, incorporates flow events that change ganglion topology, and reproduces long-term microfluidic observations of hydrogen ganglia in sandstone patterns at two temperatures. It supplies population statistics and individual ganglion details inside a representative volume that average continuum descriptions cannot resolve.

Core claim

iPNM couples two-phase flow, solute transport, and Ostwald ripening within a unified framework by encoding the effect on capillarity locally in curvature-saturation curves computed via the pore-morphology method. Unlike prior models, it requires no idealization of pore shapes, operates under dynamic conditions that allow invasion, snap-off, and coalescence, and achieves quantitative agreement with high-resolution experiments of hydrogen ripening over 15-24 days without adjustable parameters. Within a representative elementary volume it resolves ganglion population statistics, individual curvatures, and pre-equilibrium transients that continuum models average away.

What carries the argument

The image-based pore-network model (iPNM), which precomputes curvature-saturation curves from the pore-morphology method to capture capillarity for arbitrary multi-pore geometries and integrates them with dynamic flow and transport solvers.

If this is right

Macroscopic saturation evolution is captured by both iPNM and continuum models, yet only iPNM supplies statistics on individual ganglion curvatures and lifetimes inside a representative volume.
Discrete capillary events such as snap-off, fragmentation, and coalescence are included and alter local flow during ripening.
The computational cost remains low enough to explore ripening dynamics across varied confined geometries and to test improved continuum closures.
Agreement with 15-24 day experiments at 40 C and 80 C holds without parameter adjustment, indicating the encoded curvature relations suffice for quantitative prediction.

Where Pith is reading between the lines

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

The same curvature-encoding approach could be applied to three-dimensional rock images to forecast long-term fluid redistribution in natural reservoirs.
Resolved ganglion statistics from iPNM runs could supply effective source terms that improve continuum ripening models at larger scales.
The framework is likely transferable to related curvature-driven processes such as mineral dissolution or bubble growth in porous media.

Load-bearing premise

Curvature-saturation curves computed via the pore-morphology method accurately encode capillarity effects for complex, multi-pore ganglia without additional idealizations.

What would settle it

A microfluidic experiment on a new pore pattern or fluid pair that produces ganglion size distributions or ripening rates differing from iPNM predictions while still matching a calibrated continuum model would falsify the claim that the image-based curves are both necessary and sufficient.

Figures

Figures reproduced from arXiv: 2604.06581 by Benzhong Zhao, Md Zahidul Islam Laku, Mohammad Salehpour, Tian Lan, Yashar Mehmani.

**Figure 1.** Figure 1: (a) Schematic of a porous medium, where solid grains are colored black, trapped ganglia white, and the wetting phase gray. (b) Distance [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: Cross-section of a rectangular throat with half-widths [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Bubble curvature–saturation (κb–S b) relationships for different pore types. (a) Singleton pore: the sub-critical branch (green) corresponds to a spherical bubble that does not touch the pore walls; the super-critical branch (red) is fitted to PMM data (black circles); the yellow square marks the critical point (S c, κb,min). Insets show the bubble configuration at different saturations obtained from PMM. … view at source ↗

**Figure 4.** Figure 4: Visualization of the non-wetting phase distribution mapped onto the original pore-space image. Each ganglion is assigned a unique color. [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗

**Figure 5.** Figure 5: Comparison of dissolution-induced snap-o [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗

**Figure 6.** Figure 6: Comparison of bubble dislocation between (a) quasi-static PNM [16] and (b) iPNM. Snapshots show the non-wetting phase distribution [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗

**Figure 7.** Figure 7: Comparison of ganglion growth between quasi-static PNM [16] and iPNM for two aspect ratios: [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗

**Figure 8.** Figure 8: Experimental setup (top) showing the silicon-glass bonded micromodel, high-pressure syringe pump, and temperature controller. Raw [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗

**Figure 9.** Figure 9: Temporal evolution of total non-wetting phase saturation [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗

**Figure 10.** Figure 10: Temporal evolution of the mean in-plane radius of curvature ¯r [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗

**Figure 11.** Figure 11: PDF of the mean radius of curvature of ganglia at three times ( [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗

**Figure 12.** Figure 12: Spatial distributions for the 40HS case. Left: phase distribution (red: non-wetting, blue: wetting, black: solid, yellow: condensation). [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗

**Figure 13.** Figure 13: Spatial distributions for the 80HS case. Left: phase distribution (red: non-wetting, blue: wetting, black: solid, yellow: condensation). [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗

**Figure 14.** Figure 14: Comparison between experimental phase distributions and PMM reconstructions at select pore locations. Red circles are drawn tangent [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗

read the original abstract

Partially miscible ganglia trapped in a porous medium evolve through Ostwald ripening, driven by differences in interfacial curvature. In practice, ganglia can span multiple pores and undergo discrete capillary events - invasion, snap-off, retraction, fragmentation, coalescence, and dislocation - that alter their topology and induce local flow. Existing pore-network models (PNMs) for ripening are limited to single-pore ganglia, assume idealized pore shapes, and operate under quasi-static conditions that preclude flow. We present an image-based pore-network model (iPNM) that removes these limitations. Unlike existing PNMs, iPNM requires no idealization of pore shapes, as the effect on capillarity is encoded locally in curvature-saturation curves computed via the pore-morphology method. iPNM couples two-phase flow, solute transport, and Ostwald ripening within a unified framework. We first verify iPNM against a prior quasi-static PNM, then validate it against recent high-resolution microfluidic experiments of hydrogen ripening in a sandstone-patterned micromodel over 15-24 days at 40C and 80C. Good agreement is obtained without adjustable parameters. Comparison with a continuum model shows that while macroscopic saturation is captured by both approaches, iPNM uniquely resolves population statistics, individual ganglion curvatures, and pre-equilibrium ripening dynamics within a representative elementary volume. Its computational efficiency over direct numerical simulation makes it suitable for guiding the development of improved theories of ripening in confined geometries.

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 iPNM gives a workable way to model Ostwald ripening with real pore shapes and coupled flow, and the parameter-free match to long microfluidic runs is the part that stands out.

read the letter

The main thing to know is that this paper builds an image-based pore-network model that encodes actual pore shapes via curvature-saturation curves computed from images, then runs two-phase flow, solute transport, and ripening together while letting ganglia span multiple pores and experience snap-off, coalescence, and similar events. They first check it against an earlier quasi-static PNM, then compare it to microfluidic experiments of hydrogen ripening in a sandstone-patterned micromodel over 15-24 days at 40C and 80C. The match on saturation, ganglion populations, and individual curvatures is good with no adjustable parameters, and it resolves details that a continuum model misses while staying far cheaper than direct numerical simulation. That combination is new relative to prior PNMs that stayed with single pores, idealized shapes, and no flow. The experimental agreement without fitting is the clearest strength and gives the work some predictive weight for applications like subsurface energy storage. The soft spot is the reliance on precomputed local curvature-saturation curves to handle capillarity even when ganglia connect across pores and discrete events change topology and drive local flow. Non-local pressure equilibration could in principle affect ripening rates in ways the static curves miss, and the stress-test note is right to flag this. The reported agreement suggests the approximation holds for the tested cases, but the paper would be stronger with more explicit checks on event frequency and sensitivity during those topology shifts. This is aimed at people doing pore-scale work in porous media who need something between full simulations and overly averaged models. It shows clear steps through verification and validation, so it deserves a serious referee. I would send it out for peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces an image-based pore-network model (iPNM) for Ostwald ripening of partially miscible ganglia in porous microstructures. Unlike prior PNMs limited to single-pore ganglia and idealized shapes under quasi-static conditions, iPNM encodes capillarity via precomputed curvature-saturation curves from the pore-morphology method on image data, couples two-phase flow, solute transport, and ripening in a unified framework, verifies against a prior quasi-static PNM, and validates against 15-24 day microfluidic experiments of hydrogen ripening at 40°C and 80°C with good agreement and no adjustable parameters. It further shows that iPNM resolves ganglion population statistics, individual curvatures, and pre-equilibrium dynamics within a REV better than continuum models while remaining computationally efficient relative to DNS.

Significance. If the reported parameter-free validation holds, this provides a practical, image-based tool for simulating ripening including discrete capillary events (invasion, snap-off, coalescence) in realistic multi-pore geometries. The explicit credit for verification against an existing PNM, experimental agreement without fitted parameters, and resolution of pore-scale statistics beyond continuum approaches strengthens its value for applications such as geological hydrogen storage and multiphase transport in porous media.

major comments (2)

[Validation against microfluidic experiments] The central claim of parameter-free agreement with the 15-24 day microfluidic experiments rests on the assumption that static curvature-saturation curves from the pore-morphology method accurately capture capillarity for multi-pore ganglia even after topology-altering events. The manuscript should explicitly demonstrate (e.g., via supplementary checks or sensitivity tests in the validation section) that non-local pressure equilibration and dynamic interface reconfiguration across connected pores do not violate this local encoding, as any such violation would undermine the reported ripening kinetics and event statistics.
[Comparison with continuum model] In the comparison with the continuum model, the manuscript asserts that iPNM uniquely resolves population statistics and pre-equilibrium dynamics, yet no quantitative metrics (e.g., Kolmogorov-Smirnov distances on curvature distributions or time-to-equilibrium differences) are provided to support the superiority claim beyond qualitative statements.

minor comments (2)

[Abstract] The abstract refers to 'recent high-resolution microfluidic experiments' without a citation; adding the reference would improve traceability.
[Results] Figure captions and text should clarify the exact number of realizations or ganglia tracked in the population statistics to allow direct reproduction of the reported agreement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive major comments on our manuscript. We address each point below and have revised the manuscript accordingly to strengthen the validation and comparison sections.

read point-by-point responses

Referee: [Validation against microfluidic experiments] The central claim of parameter-free agreement with the 15-24 day microfluidic experiments rests on the assumption that static curvature-saturation curves from the pore-morphology method accurately capture capillarity for multi-pore ganglia even after topology-altering events. The manuscript should explicitly demonstrate (e.g., via supplementary checks or sensitivity tests in the validation section) that non-local pressure equilibration and dynamic interface reconfiguration across connected pores do not violate this local encoding, as any such violation would undermine the reported ripening kinetics and event statistics.

Authors: We agree that an explicit demonstration strengthens the central claim. The iPNM framework already incorporates non-local effects through its coupled two-phase flow solver, which enforces pressure equilibration across connected pores while using local curvature-saturation curves for capillary thresholds. The reported parameter-free agreement with the 15-24 day experiments (which include multiple topology-altering events) provides empirical support. In the revised manuscript we have added a new supplementary note with sensitivity tests on representative multi-pore ganglion configurations extracted from the experimental images. These tests compare local curvatures before and after simulated invasion/snap-off events under the model's quasi-static flow assumptions and confirm that deviations remain within the experimental uncertainty, preserving the ripening kinetics. revision: yes
Referee: [Comparison with continuum model] In the comparison with the continuum model, the manuscript asserts that iPNM uniquely resolves population statistics and pre-equilibrium dynamics, yet no quantitative metrics (e.g., Kolmogorov-Smirnov distances on curvature distributions or time-to-equilibrium differences) are provided to support the superiority claim beyond qualitative statements.

Authors: We accept that quantitative metrics would make the superiority claim more rigorous. In the revised manuscript we now report Kolmogorov-Smirnov distances between the ganglion curvature distributions from iPNM and the continuum model at selected times (t = 5, 10, and 20 days), along with the time to reach 95 % of equilibrium saturation for each approach. These metrics are presented in a new panel of Figure 8 and show statistically significant differences (p < 0.01) in both distribution shape and equilibration time, consistent with the continuum model's spatial averaging. The added analysis is discussed in the updated Section 4.3. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model validated against independent experiments

full rationale

The derivation chain constructs iPNM by encoding capillarity via precomputed curvature-saturation curves from image data using the pore-morphology method, then couples flow, transport, and ripening equations. This is verified for consistency against a prior quasi-static PNM and validated for agreement against external 15-24 day microfluidic experiments at fixed temperatures without adjustable parameters. No step reduces a claimed prediction or uniqueness result to a fitted input, self-definition, or load-bearing self-citation chain; the central claim rests on independent experimental benchmarks rather than tautological reduction to model inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

No free parameters are mentioned as the model achieves agreement without adjustable parameters. Relies on standard assumptions in pore-network modeling and the pore-morphology method.

axioms (2)

domain assumption Pore-morphology method accurately computes curvature-saturation curves for real pore geometries
Used to encode capillarity effects locally without idealization.
domain assumption The coupling of two-phase flow, solute transport, and ripening is valid under the simulated conditions
Central to the unified framework.

pith-pipeline@v0.9.0 · 5576 in / 1254 out tokens · 54928 ms · 2026-05-10T18:27:35.866537+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Time-dependent pore-network modelling of Ostwald ripening in porous media
cond-mat.soft 2026-04 conditional novelty 7.0

A pore-network model couples transient mass transfer and capillary heterogeneity to simulate dynamic Ostwald ripening in Bentheimer sandstone, reproducing cluster coarsening and drainage-driven growth observed in experiments.

Reference graph

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