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REVIEW 3 major objections 7 minor 45 references

Drop impact on a heated pre-wetted wall: deposition-on-crater splash regime

T0 review · 3 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Impact drop deposits on the crater while only the wall film splashes.

desk verdict A genuinely new IR observation with a plausible but under-supported compositional claim; deserves refereeing after the overclaims are trimmed. read the letter →

arxiv 2411.16524 v3 pith:CKKUQ2CU submitted 2024-11-25 physics.flu-dyn

Lukas Weimar , Bastian Stumpf , Jeanette Hussong , Ilia V. Roisman This is my paper · ORCID
classification physics.flu-dyn
keywords dropimpactwallfilmcoronasplashdeposition-on-craterregimespraycoolinginfraredthermographyboundarylayeranalysissiliconeoils
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to establish a new splash regime for a drop impacting a heated wall covered by a thin liquid film at high Reynolds and Weber numbers under the specific conditions studied here. In this regime, called deposition-on-crater, the cold impacting drop spreads and settles at the bottom of the crater it carves in the film, while the corona jet and any secondary droplets are produced entirely from the heated wall film. The evidence comes from simultaneous high-speed imaging and infrared thermography: the cold spot on the substrate is much smaller than the corona base, persists after the corona collapses, and its maximum diameter matches the theoretically predicted spreading diameter of the drop. If true, this finding matters for spray cooling because the entire cold drop mass deposits and contributes to wall cooling instead of being lost to splash.

What carries the argument

The argument rests on a boundary-layer description of the spreading drop on a thin wall film, combined with a thermal-boundary-layer model for the substrate cooling. The lamella flow is described by a similarity solution with radial velocity $u_r = r/(t+\tau)$ and thickness decaying as $t^{-2}$; the residual thickness of the combined layers is $h_{\mathrm{res}} = A(\delta) D \mathrm{Re}^{-2/5}$, with $A$ built from the film influence parameter $\chi = \delta^{1/5}\omega/[(1+3.86\omega)\kappa^{1/10}]$. From mass balance, the drop's maximum spreading diameter becomes $D_{\mathrm{spread}} \approx 1.1 D \mathrm{Re}^{1/5}$, which is identified with the maximum cold-spot diameter. The matching of $d_{\mathrm{cold,max}}$ to $D_{\mathrm{spread}}$ is the key comparison that assigns the cold spot to the deposited drop rather than to the corona region; because this diameter is much smaller than the corona base, the drop liquid is confined to the crater floor. The thermal delay before substrate cooling appears is modeled by equating the thermal boundary layer thickness $\sqrt{\alpha_{\mathrm{film}} t}/c$ to the evolving film thickness, yielding a validated formula for the delay time.

What would settle it

Repeat a deposition-on-crater impact with a small amount of dye or fluorescent tracer added to the cold drop and inspect the corona and secondary droplets; any tracer signal in either would show that drop material leaves the crater, contradicting the regime.

Watch

Extended reading notes

Core claim

The central discovery is that under the studied conditions (silicone oil drops and films, Reynolds numbers 130--350, Weber numbers 880--1030, film thickness below 30% of the drop diameter, heated film), the impacting drop never becomes part of the corona. The drop spreads along the floor of the crater it forms in the film, depositing there, while the kinematic-discontinuity corona is created only from the wall film. This is shown by infrared images in which the cold spot left by the drop has a diameter close to the predicted spreading diameter $D_{\mathrm{spread}} \approx 1.1 D \mathrm{Re}^{1/5}$, much smaller than the corona base, and by the delayed appearance of cooling that matches a thermal boundary layer crossing the residual film. The paper validates models for the cold-spot diameter, the delay time before the cooling signal reaches the substrate, and the contact temperature, and argues that this deposition-on-crater regime is the most favorable for spray cooling, since the cold drop avoids splashing and the secondary drops carry only already-hot film liquid.

Load-bearing premise

The regime classification assumes that the maximum diameter of the infrared cold spot equals the footprint of the drop liquid on the crater floor; if thermal smearing or lateral conduction shrinks or blurs the cold spot, the drop could spread wider than the cold spot indicates and even feed the corona without being detected.

Editorial extensions

If this is right

  • In the deposition-on-crater regime, the full mass of the cold drop lands on the wall, so spray cooling efficiency is higher than in a drop-dominant corona where cold drops are lost to splash.
  • The cold spot's maximum diameter is predictable from $D_{\mathrm{spread}} \approx 1.1 D \mathrm{Re}^{1/5}$, giving an estimate of the cooled surface area per individual drop.
  • The delay between impact and substrate cooling is set by the time a thermal boundary layer takes to cross the residual film, so the model can be used to estimate contact temperature and heat flux in spray-cooling simulations.
  • Because the corona and secondary drops in this regime contain only wall-film liquid, their material and temperature differ from the drop's, so models that mix drop and film contributions in the corona need revision.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The regime boundary is left open in the paper; a natural criterion is that deposition-on-crater holds whenever the predicted spreading diameter $D_{\mathrm{spread}}$ stays below the corona base diameter, which could be expressed as a condition on $\mathrm{Re}$, $\mathrm{We}$, and the dimensionless film thickness $\delta$ using existing corona-growth laws.
  • The cold-spot measurement could be validated as a non-invasive footprint diagnostic by repeating the experiments with a fluorescing species in the drop; if it holds, it would let researchers map drop deposition in sprays without adding tracers.
  • If the same regime occurs in water-based sprays at practical temperatures, spray-cooling models would need to count the deposited cold drop mass as wall heat extraction and treat corona splash as pure film loss, changing the predicted heat flux.
  • The persistence of the cold spot long after the corona collapses suggests a slow, post-corona cooling phase on the crater floor that the present models do not explicitly describe.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. The paper reports an experimental study of a silicone-oil drop impacting a heated, pre-wetted sapphire wall, using simultaneous high-speed shadowgraphy (side view) and high-speed infrared thermography (bottom view through the IR-transparent substrate). The authors observe that the infrared cold spot at the substrate is much smaller than the corona base, persists after corona collapse, and reaches a maximum diameter close to a model prediction for the drop spreading diameter. From this, they propose a new impact regime, 'deposition-on-crater', in which the impacting cold drop deposits at the crater floor while only the heated wall film feeds the corona and the secondary splash droplets. They further develop boundary-layer models for the contact temperature, the time delay of the cold-spot appearance, and the spreading diameter, and discuss implications for spray cooling.

Significance. If the central compositional claim is correct, the paper identifies a previously unreported impact regime that is directly relevant to spray-cooling efficiency, since it implies that the cold drop mass is fully deposited while only the heated film is lost to splash. The experimental setup is a strength: the simultaneous side-view and calibrated bottom-view IR measurements provide a direct, quantitative view of substrate cooling during impact, and the cold-spot persistence is an interesting observation. However, the paper's main claim rests on an indirect proxy (IR cold-spot diameter) rather than on direct measurement of liquid origin, and the quantitative 'validation' of the models involves fitted constants. The work is therefore a promising contribution that currently overstates the certainty of its central conclusion.

major comments (3)
  1. [Section IV, Figs. 10 and 11] The central claim that the drop deposits at the crater base and does not enter the corona or secondary drops rests entirely on identifying the maximum IR cold-spot diameter d_cold,max with the drop's deposited footprint. This proxy is asserted in Section IV ('This result confirms our assumption that the cold spot ... is associated with the deposited liquid drop') but is never checked against a direct tracer such as dye or fluorescence. Since the drop and film are the same silicone oil at different temperatures, side-view shadowgraphy cannot distinguish fluid origin. A cold drop that is entrained into the corona and ejected upward would not necessarily cool the substrate outside the crater, so the observed small cold spot is compatible with drop liquid participating in the corona. Consequently, the abstract's claims that 'only the wall film produces the corona and splashes' and that 'secondary drops consist only of the heated material of the wall film' go beyond what the measurements establish. This is load-bearing because the claimed novelty and the spray-cooling efficiency conclusion depend on it.
  2. [Section III C, Eq. (23), and Eq. (26)] The 'validated' prediction for the time delay t_delay contains an ad hoc fitting parameter c=0.36 (with standard error 0.0086), and the spreading diameter D_spread in Eq. (26) uses the empirical constant A0=0.55 fitted in the authors' own reference [9]. As a result, the agreement between d_cold,max and D_spread in Fig. 11 is partly by construction: both sides of the comparison incorporate fitted numbers. The authors should either determine these constants independently from first principles or explicitly frame the comparisons as consistency checks with fitted parameters rather than as parameter-free predictions. This also affects the abstract's phrase 'validated models'.
  3. [Section IV, Fig. 13] The supplementary evidence from the residual-film radius r_res being smaller than the maximum corona radius r_max is qualitative and comes from a single case (S10, H_film=52 µm) that appears to involve corona detachment rather than the deposition-on-crater regime studied in Figs. 4 and 10. It is not clear how this observation supports the claim that the drop does not enter the corona in the main experiments. A quantitative comparison between r_res and the expected drop-spreading diameter for that detachment case, or a dye-tracer experiment, would strengthen the argument.
minor comments (7)
  1. [Section II A] The calibration procedure uses a thermocouple placed 'close to the surface', but the exact position, the thermal contact with the graphite coating, and the uncertainty propagation into the temperature maps are not described. Please clarify how the ±1°C thermocouple accuracy and the NETD of 0.05°C translate into the reported temperature fields.
  2. [Fig. 4 caption] The caption states that side-view and bottom-view images are 'scaled identically', but the two cameras have different fields of view (23×23 mm versus 23×18 mm). Please specify the scaling procedure and confirm that the comparison of diameters is unaffected by optical distortion.
  3. [Section IV] The outer cold-spot diameter d_cold,2 is defined by a dimensionless temperature threshold of 0.08, but the choice of threshold and its sensitivity to the results are not discussed. Please state how the threshold was selected and whether the conclusions in Figs. 10 and 11 are robust to reasonable variations of this threshold.
  4. [Fig. 11] The range of the dimensionless parameter chi is narrow (0.1 to 0.25), and the claimed monotonic increase of d_cold,max/D_spread with chi could be within experimental scatter. Please include error bars and, if possible, a least-squares fit with confidence intervals to assess the trend.
  5. [Introduction and Section IV] The distinction between the proposed deposition-on-crater regime and the previously reported double-corona regime (Fig. 2a) should be clarified. If the double corona is a wall-film-dominant corona, how does it differ from the new regime in terms of the liquid-origin composition of the corona? The current text leaves this ambiguity.
  6. [Introduction, ref. [5]] The statement that 'conventional theories suggest that the corona-forming liquid jet comprises material from the impacting drop and wall film' is attributed to the Yarin-Weiss kinematic discontinuity model, which does not explicitly address the composition of the jet. A more specific reference to the origin-composition assumption would help the reader evaluate the novelty claim.
  7. [Section III C, Eq. (16)] There is a typographical issue in Eq. (16): the integral notation is unclear (the dummy variable is not distinguished), and the derivative with respect to r is missing a factor. Please revise the equation to the standard form u_z = -(1/r) ∂/∂r ∫_0^z r u_r(r,z') dz'.

Circularity Check

3 steps flagged · score 6.0 of 10

Central regime claim is partly self-confirming: the cold-spot proxy is assumed to mark deposited drop liquid, and that assumption is then used to infer that the corona and secondary drops contain no drop liquid; the validated time-delay model also contains an in-sample fitted constant c=0.36.

  1. fitted input called prediction [Section III C, Eq. (23) and Fig. 8]
    "The time evolution of the thickness of the thermal boundary layer can be estimated with hΘ=√(αfilm t/c), where αfilm is the thermal diffusivity of the liquid film, t is the time and c is a fitting parameter in the order of unity. ... For the fitting parameter c=0.36 (standard fitting error σ≈0.0086), good agreement between the experiments and the model, indicated by the straight dashed line, is observed."

    The 'theoretical prediction' of t_delay in Eq. (23) is obtained only after inserting c=0.36, which is fitted to the same time-delay measurements shown in Fig. 8. The agreement is therefore an in-sample measure of the fit quality, not an independent out-of-sample prediction. Because the abstract lists the characteristic time among the validated models, this part of the validation reduces to a fitted parameter renamed as a prediction.

  2. self citation load bearing [Sections III B and IV, Eq. (26) and Fig. 11]
    "The dimensionless constant A0=0.55 was obtained 9 by fitting experimental data for isothermal drop impact onto a liquid film of a different liquid. ... Since the residual thickness of the drop lamella is determined by Eq. (20), the drop spreading diameter can be estimated from the drop mass balance and the empirical coefficient A0=0.55, in the form Dspread=... This result confirms our assumption that the cold spot in our experiments is associated with the deposited liquid drop."

    The spreading diameter D_spread used to 'confirm' the cold-spot interpretation is not a parameter-free first-principles quantity; it inherits A0=0.55, an empirical coefficient fitted in the authors' own Ref. 9. The match d_cold,max/D_spread≈1 is therefore calibrated by a self-cited fitted constant rather than an independent geometric prediction. This is not fully circular because A0 was fit to different experimental data, but the load-bearing inference 'the drop liquid therefore does not enter the corona' depends on this self-citation.

1 more flagged steps
  1. self definitional [Section IV, paragraph following Fig. 11]
    "This result confirms our assumption that the cold spot in our experiments is associated with the deposited liquid drop. Its maximum diameter is much smaller than that of the crater, and the drop liquid therefore does not enter the corona. In the case of a splash, the secondary drops consist exclusively of the wall film liquid."

    The central compositional claim—secondary drops consist exclusively of wall-film liquid—is presented as the outcome of the assumption that the cold spot marks the deposited drop. No dye, tracer, or compositional measurement distinguishes drop liquid from film liquid (both are the same silicone oil at different temperatures). The conclusion that the corona contains no drop liquid is the assumed cold-spot-to-drop correspondence restated, so the defining claim of the new regime is confirmed by the same proxy used to define it.

full rationale

The paper contains an independent raw observation that is not circular: the IR cold spot is much smaller than the corona base, persists after corona collapse, and Fig. 13 shows a residual film smaller than the corona. Those facts are real and support the existence of an unexpected cooling pattern. However, the interpretive leap from 'small cold spot' to 'drop liquid never enters the corona and secondary drops are pure wall film' is not directly measured; it is inferred from the assumption that the cold spot corresponds to the deposited drop. The validation of the characteristic-time model uses an in-sample fitted constant c=0.36, and the spreading-diameter check inherits a fitted A0=0.55 from the authors' own earlier work. Thus parts of the claimed validation reduce to the fitted constants being tested, giving partial circularity rather than complete equivalence. The raw phenomenology and the dimensional scalings are independent, so the score is 6 rather than 8 or higher.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The paper's semi-empirical predictions contain two fitted constants: A0 from the authors' previous isothermal experiments and c fitted to the present delay data. No new entities or forces are introduced; the rest of the input is standard fluid mechanics and prior similarity solutions.

free parameters (2)
  • A0 = 0.55
    Empirical coefficient fitted to isothermal drop impact data in reference 9 by the same group. Appears in Eqs. (20), (21) and controls the predicted drop spreading diameter in Eq. (26); the agreement in Fig.11 depends on it.
  • c = 0.36
    Fitting parameter in the thermal boundary layer thickness h_Theta = sqrt(alpha_film t / c). Fitted to the paper's own time-delay data in Fig.8 and used in Eqs. (22) and (23).
assumptions (7)
  • standard math Navier-Stokes equations and the thin-lamella mass and momentum balances are valid for the impact flow.
    Used to derive the similarity solution (2)-(3) and throughout Section III.
  • standard math The similarity solution for the spreading lamella, Eq. (5), has a solution matching the inviscid outer solution Eq. (2), and the constants gamma=0.6 and eta=0.39 from reference 30 are accepted.
    Lifted from prior work, not re-derived in this paper.
  • domain assumption For t >> t_nu,film, the shear stress at the drop/film interface equals the dry-wall value Eq. (7).
    Section III B, Eq. (15), treats the wall film as a passive viscous layer driven by the drop lamella.
  • domain assumption For silicone oils, Pr >> 1, so the thermal boundary layer is much thinner than the viscous boundary layer and heat transfer is confined to thin boundary layers.
    Section III C; this assumption delays the appearance of the cold spot in the IR images.
  • domain assumption Thermal boundary layer thickness follows h_Theta = sqrt(alpha_film t / c) with c of order unity.
    Section III C, Eq. (22); the functional form is standard diffusion, but c is fitted to data.
  • domain assumption The empirical coefficient A0=0.55, fitted to isothermal impact data in the authors' own reference 9, remains valid for heated films of the same liquid.
    Used in Eq. (21) and Eq. (26) to predict the drop spreading diameter; Fig.11 depends on this transfer.
  • domain assumption No phase change or significant evaporation occurs in the heated silicone-oil film at temperatures up to 140 C.
    The modeling ignores phase change, and this is not explicitly stated but required for the thermal model.

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Cite this review

Pith. "Pith review of Drop impact on a heated pre-wetted wall: deposition-on-crater splash regime." pith.science (2026). https://pith.science/paper/CKKUQ2CU

@misc{pith2026241116524,
  author       = {Pith},
  title        = {Pith review of: Drop impact on a heated pre-wetted wall: deposition-on-crater splash regime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CKKUQ2CU}},
  note         = {Machine review of arXiv:2411.16524}
}
read the original abstract

The impact of a liquid drop with high Reynolds and Weber numbers on a wet solid surface typically results in the emergence, rising, and expansion of a corona-like thin jet. This phenomenon is explained by the propagation of a kinematic discontinuity within the wall film. Conventional theories suggest that the corona-forming liquid jet comprises material from the impacting drop and wall film. In this study, the impact of a drop on a wall film is observed using a high-speed video system. Simultaneously, the distribution of the contact temperature at the substrate surface is measured with a high-speed infrared system. The results reveal that heat transfer predominantly occurs within the thin thermal boundary layers in the drop and substrate. Moreover, our experiments show that under our specific conditions, the drop deposits at the base of the crater while only the wall film produces the corona and splashes. Correspondingly, the secondary drops consist only of the heated material of the wall film. This regime has not been previously reported in the literature. The validated models for the diameter of the cold spot, the characteristic time, and the contact temperature developed in this study can be potentially useful for reliable modeling of spray cooling.

Figures

Figures reproduced from arXiv: 2411.16524 by the authors.

Figure 2
Figure 2. FIG. 2: Regimes of drop corona splash [PITH_FULL_IMAGE:figures/full_fig_p001_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1: Sketch of the corona formation due to the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Schematic illustration of the experimental setup. [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Non-isothermal drop impact on a heated film; formation of the corona and a cold spot at the surface. Impact [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Sketches of the main assumed stages of drop impact, its initial penetration and spreading. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Dependence of the parameter [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Normalized temperature evolution in center area of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Definition of the characteristic diameters of the cold [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Different exemplary time evolutions of the crown base diameter compared with the characteristic diameters of the cold [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Sketches of various regimes of corona splash: (a) [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: Temporal evolution of corona with the maximum corona radius [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14: Impact of an EPDM sphere [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.