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arxiv: 2604.05073 · v1 · submitted 2026-04-06 · ❄️ cond-mat.mtrl-sci · physics.flu-dyn

Experimental measurements and modeling of characteristic time scales in single iron particle ignition

Liulin Cen , Yong Qian , XiaoCheng Mi , Xingcai Lu This is my paper

Pith reviewed 2026-05-10 19:00 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.flu-dyn
keywords iron particle ignitionsolid-phase oxidationparabolic rate lawtemperature plateausmetal fuelsexternal oxygen transportphase transitionsdiameter-resolved data
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The pith

Single iron particle experiments and modeling show pre-melting oxidation time stays nearly constant while melting stages depend on oxygen concentration.

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

The paper measures oxidation and phase-change times for micron-sized iron particles intended as recyclable, carbon-free fuels. High-speed holography and pyrometry capture three distinct temperature plateaus during ignition that correspond to FeO melting, the gamma-to-delta iron transition, and iron melting. A model that applies a parabolic rate law to solid-phase oxidation and treats later melting stages as limited by external oxygen transport matches the data for the pre-melting stage, which shows little dependence on oxygen level, and correctly predicts the oxygen-sensitive melting durations. These results matter because ignition timing controls how efficiently and stably iron particles burn in practical combustors. The work supplies the first dataset of these times resolved by particle diameter.

Core claim

Using digital in-line holography and ultra-high-speed single-color pyrometry, the authors resolve three temperature plateaus in burning spherical iron particles that mark FeO melting, the gamma-Fe to delta-Fe transition, and Fe melting. They construct an ignition model that combines solid-phase oxidation kinetics following a parabolic rate law with an external-oxygen-transport-limited description of the melting stages. The model reproduces the observed pre-melting oxidation time, which remains nearly independent of oxygen concentration, while the FeO, gamma-to-delta, and Fe melting stages exhibit strong oxygen-concentration dependence consistent with external-transport control. The combined

What carries the argument

Ignition model that applies a parabolic rate law to solid-phase iron oxidation and limits melting-stage rates by external oxygen transport.

Load-bearing premise

Solid-phase oxidation obeys a parabolic rate law whose parameters remain valid across the observed temperature plateaus, and external oxygen diffusion alone controls the melting-stage rates without major internal diffusion or heat-transfer effects.

What would settle it

A set of measurements in which pre-melting oxidation time varied strongly with oxygen concentration or in which melting durations failed to follow the predicted external-transport dependence would falsify the model's accuracy.

Figures

Figures reproduced from arXiv: 2604.05073 by Liulin Cen, XiaoCheng Mi, Xingcai Lu, Yong Qian.

Figure 1
Figure 1. Figure 1: (a): Schematic of the experimental setup; the yellow dot in the enlarged front view marks a single iron particle. (b–d): [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic illustration of the digital in-line holography principle, where [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reconstructed holograms of the USAF 1951 resolution target at different distances from the focal plane and the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Reconstructed holograms of the thermocouple wire. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Reconstructed holograms of two circular targets at [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Spectral transmittance of the long-pass filter and [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Calibrated relation between relative single-color [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Mean FeO melting temperatures of the particles with [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Schematic of the simulation model and calculated [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: (a) Reconstructed holographic image and temporal evolution of raw luminosity, smoothed luminosity, and its second [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: 𝑡଴ଵ for particles with different diameters and roundness (R). Here 𝑡଴ଵ is the time from burner entry to the onset of FeO￾scale melting, i.e., SOT୊ୣ୓. in surface area and volume and thus in comparison with the models. The binned SOT୊ୣ୓ values clearly show the weak dependence on oxygen concentration. The simulations agree with the measurements, except for a slight overprediction for particles larger than 30… view at source ↗
Figure 12
Figure 12. Figure 12: Fig.12. Diameter-binned mean [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Kinetics-controlled oxidation time (𝑡୩), 𝑡଴ଵ, and their ratio for particles of different diameters at 1200 K and 11% O2, calculated using the Stefan-flow model. the transition point in [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: 𝑡୩ and 𝑡଴ଵ of 30 μm iron particles at various O2 concentrations and temperatures from Stefan-flow model [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FeO melting time 𝑡ଵଶ for particles with different diameters. Hollow symbols denote diameter-binned means for particles with R > 0.9 and lines denote simulations results [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: (a) Diameter-binned mean 𝑇ଷସ for particles with R > 0.9; (b) Fe–C phase diagram, adapted from Ref. [42] [PITH_FULL_IMAGE:figures/full_fig_p012_17.png] view at source ↗
Figure 19
Figure 19. Figure 19: Diameter-binned mean 𝑡ହ଺ for particles with roundness (R > 0.9), and corresponding simulated durations of the third luminosity (temperature) plateau [PITH_FULL_IMAGE:figures/full_fig_p012_19.png] view at source ↗
read the original abstract

Recyclable metal fuels such as iron are promising carbon-free energy carriers for heat and power. In such systems, particle ignition characteristics strongly affect combustion efficiency and combustor stability, making them critical for burner and reactor design. However, predictive ignition modelling remains limited by the lack of time-resolved data for single-particle solid-phase oxidation and phase transitions. In this work, digital in-line holography combined with ultra-high-speed single-color pyrometry is used to resolve characteristic solid-phase oxidation times of spherical micron-sized iron particles burning in well-defined hot oxidizing environments. Three temperature plateaus are identified, corresponding to FeO melting, the {\gamma}-Fe to {\delta}-Fe transition, and Fe melting, from which pre-melting oxidation times and melting durations are extracted. An ignition model based on solid-phase iron oxidation kinetics following a parabolic rate law, coupled with external-oxygen-transport-limited description, is used to simulate these characteristic times. The model accurately captures the FeO-scale pre-melting oxidation time, which is nearly independent of oxygen concentration, while the FeO, {\gamma}-Fe to {\delta}-Fe, and Fe melting stages show strong oxygen-concentration dependence consistent with external-oxygen-transport-limited reaction rates. These measurements and simulations provide the first diameter-resolved dataset for FeO and Fe melting processes and show that this modelling framework can quantitatively predict characteristic times for single iron particles in metal-fuel applications.

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 reports experimental measurements of characteristic time scales during ignition of single micron-sized spherical iron particles using digital in-line holography combined with ultra-high-speed single-color pyrometry in well-defined hot oxidizing environments. Three temperature plateaus are identified (FeO melting, γ-Fe to δ-Fe transition, and Fe melting), from which pre-melting oxidation times and melting durations are extracted as functions of particle diameter and oxygen concentration. An ignition model employing a parabolic rate law for solid-phase oxidation coupled to an external-oxygen-transport-limited description is shown to reproduce the observed near-independence of pre-melting time on oxygen concentration and the strong oxygen dependence of the melting stages, providing what is claimed to be the first diameter-resolved dataset for these processes.

Significance. If the central claims hold, the work supplies the first diameter-resolved experimental dataset on FeO-scale pre-melting oxidation and subsequent melting stages for iron particles, directly addressing a key gap in predictive modeling for recyclable metal fuels. The combination of time-resolved optical diagnostics with a transport-limited model offers quantitative guidance for burner and reactor design in carbon-free combustion systems. Explicit credit is due for the reproducible experimental protocol and the falsifiable, parameter-light modeling framework that separates internal kinetics from external diffusion limits.

major comments (2)
  1. [§4] §4 (model formulation): The central claim that the model 'accurately captures' the oxygen-concentration independence of the FeO-scale pre-melting time rests on the assumption that a single parabolic rate law with fixed parameters remains valid across the three temperature plateaus. No sensitivity study or literature comparison is provided to show that the chosen k_p(T) form does not shift when the particle crosses the FeO melting point or the γ-to-δ transition, which is load-bearing for the reported agreement.
  2. [Results section] Results section and abstract: The quantitative validation that melting-stage durations are controlled exclusively by external O2 diffusion (with negligible internal diffusion or heat-transfer resistance) is stated but not supported by explicit comparison plots, residual statistics, or error propagation from the pyrometry data. Without these, the claim that the external-transport idealization holds for the observed micron-particle thermal histories cannot be assessed.
minor comments (2)
  1. [Figures] Figure captions and axis labels should explicitly state the number of particles per condition and the criterion used to identify the onset and end of each temperature plateau.
  2. [§4] The manuscript would benefit from a short table listing the literature sources or fitted values for the parabolic prefactor and activation energy together with the temperature range over which they were originally determined.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive evaluation of the significance of our work. We address each major comment below, indicating the revisions planned for the manuscript.

read point-by-point responses

  1. Referee: [§4] §4 (model formulation): The central claim that the model 'accurately captures' the oxygen-concentration independence of the FeO-scale pre-melting time rests on the assumption that a single parabolic rate law with fixed parameters remains valid across the three temperature plateaus. No sensitivity study or literature comparison is provided to show that the chosen k_p(T) form does not shift when the particle crosses the FeO melting point or the γ-to-δ transition, which is load-bearing for the reported agreement.

    Authors: We acknowledge that the assumption of a single parabolic rate law across the temperature plateaus is central to the model and that the manuscript would benefit from explicit justification. The parameters were drawn from established literature on iron oxidation, but we agree that a dedicated sensitivity analysis and additional literature comparisons are warranted to confirm applicability across the FeO melting point and γ-to-δ transition. In the revised manuscript we will add a sensitivity study varying k_p(T) around these transitions together with direct comparisons to relevant literature data on phase-specific oxidation kinetics. revision: yes

  2. Referee: [Results section] Results section and abstract: The quantitative validation that melting-stage durations are controlled exclusively by external O2 diffusion (with negligible internal diffusion or heat-transfer resistance) is stated but not supported by explicit comparison plots, residual statistics, or error propagation from the pyrometry data. Without these, the claim that the external-transport idealization holds for the observed micron-particle thermal histories cannot be assessed.

    Authors: We agree that stronger quantitative support is needed to substantiate the external-transport-limited description. The current manuscript shows model-experiment agreement for the melting durations, but additional diagnostics will improve transparency. In the revision we will add direct comparison plots of measured versus modeled melting times across oxygen concentrations, include residual statistics, and propagate uncertainties from the single-color pyrometry measurements into the extracted time scales. These elements will allow a clearer assessment of the idealization for the micron-sized particles. revision: yes

Circularity Check

0 steps flagged

No significant circularity; established parabolic kinetics applied to new data as validation

full rationale

The paper applies a standard parabolic rate law for solid-phase oxidation together with an external-oxygen-transport limit to simulate observed temperature-plateau durations. These inputs are drawn from prior literature rather than fitted to the present diameter-resolved dataset; the reported agreement is framed as model validation against fresh experimental measurements. No self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the derivation chain. The central result therefore remains independent of the new observations.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the parabolic oxidation kinetics and external-transport limitation; these are standard domain assumptions rather than new postulates, with possible free parameters in the rate constants.

free parameters (1)
  • parabolic rate constant prefactor
    Required to set the absolute oxidation time scale; value is not stated in the abstract and may be taken from prior literature or adjusted to match data.
axioms (2)
  • domain assumption Solid-phase iron oxidation obeys a parabolic rate law
    Invoked to describe pre-melting oxidation time in the ignition model.
  • domain assumption Melting-stage rates are limited by external oxygen transport
    Used to explain the observed strong oxygen-concentration dependence of melting durations.

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