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REVIEW 4 major objections 3 minor 1 cited by

Fast droplet impact onto slowly moving deep pools

T0 review · 4 major / 3 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Slowly moving pool water flips droplet impact from a separate ejecta sheet to a lamella upstream, driven by the pool-to-drop speed ratio and viscosity.

desk verdict Solid, honestly-reported experimental mapping of the upstream SES-to-lamella transition on slowly moving pools; the sqrt(ut/un) parameterization is new and useful, but the quantitative boundary needs better validation of the inferred pool speed. read the letter →

arxiv 2511.03682 v1 pith:76OI2CS2 submitted 2025-11-05 physics.flu-dyn

Thomas C. Sykes , Luke F.L. Alventosa , J. Rafael Castrejon-Pita , Radu Cimpeanu , Daniel M. Harris , Alfonso A. Castrejon-Pita This is my paper
classification physics.flu-dyn
keywords dropletimpactmovingpoolejectasheetlamellaCapillarynumbervelocityratiolength-scaleinvarianceoblique
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

The paper shows that when a fast droplet hits a deep pool that is itself moving slowly, the outcome upstream of the impact can change from a separate ejecta sheet to a lamella, even at low Capillary numbers where a static pool would always give a separate sheet. The authors propose that the transition is governed by the Capillary number (viscosity relative to surface tension) and the square root of the pool-to-drop velocity ratio, with a single constant boundary that is independent of droplet size. They derive this parameterization by considering how pool motion constrains the ejecta sheet angle, and support it with experiments across multiple fluids and impact conditions, plus direct numerical simulations showing that oblique impacts on a static pool produce equivalent dynamics. If correct, this provides a practical criterion for predicting impact outcomes on moving pools, which matters for scenarios like rain hitting the ocean or inkjet printing on moving surfaces.

What carries the argument

The key machinery is the ejecta sheet angle theta, the angle between the horizontal and the normal to the ejecta sheet base. The paper builds on the geometric model of Thoroddsen et al. (2011) where the ejection velocity scales as un cos theta, and on the observation that theta increases as sqrt(Re) for static deep pools. For a moving pool, the pool velocity effectively reduces theta upstream, and the authors argue that the relevant dimensionless group is sqrt(Re_t/Re) = sqrt(ut/un). This quantity, together with the Capillary number, collapses all experimental data onto a single sharp transition boundary.

What would settle it

Measure surface velocity directly (e.g., with particle tracking velocimetry) at the impact point across a range of rotation rates and compare with the solid-body value; if ut deviates by more than the experimental uncertainty, the fitted boundary and its length-scale invariance would need re-evaluation.

Watch

Extended reading notes

Core claim

The central claim is that for Ca<0.2 normal droplet impacts on a deep pool, increasing pool speed triggers an upstream transition from a separate ejecta sheet (SES) to a lamella, while downstream the SES persists. The transition is sharply delineated by the two dimensionless groups Ca and sqrt(ut/un), which together separate all upstream impact outcomes. The boundary is length-scale invariant and a linear fit to the transition approximately recovers the known Ca=0.2 static-pool threshold, so a single constant (gradient about -0.4) demarcates the transition. The same dynamics appear in simulations of oblique impacts on a static pool, indicating that the pool boundary layer does not play a dec

Load-bearing premise

The regime map's x-axis rests on inferring the local pool surface velocity ut from the rotating-table angular speed, assuming the fluid is in solid body rotation with the tank and that air drag on the free surface is negligible.

Editorial extensions

If this is right

  • A practical criterion now exists for predicting whether rain impacting a moving ocean surface will produce a lamella or a separate ejecta sheet upstream, based on viscosity, surface tension, and the velocity ratio.
  • The length-scale invariance means the same criterion applies to millimeter droplets and potentially to much smaller or larger droplets, as long as the deep-pool condition holds.
  • The absence of a reverse transition for Ca>0.2 suggests that the separate ejecta sheet outcome is caused by an instability at the ejecta sheet base, not just geometry, which could inform models of vortex shedding and jet formation on static pools too.
  • The equivalence with oblique impacts means results from moving-pool experiments can be transferred to oblique-impact scenarios, and vice versa, for low speed ratios.

Reading between the lines

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

  • The boundary's linearity suggests that a simple force-balance model at the ejecta sheet base might derive the constant -0.4 from first principles, rather than relying on empirical fitting.
  • If the transition is truly length-scale invariant, it should also hold for droplets much smaller than those tested, such as in inkjet printing, where pool or substrate motion is common; this is testable with existing high-speed imaging setups.
  • The claim that the boundary layer is not decisive might break down at higher pool speeds, where the surfing regime occurs; the paper's parameterization likely only applies for ut/un below some threshold not yet sharply defined.
  • The lack of downstream lamella-to-SES transition for Ca>0.2 could imply a hysteresis in the outcome depending on whether the ejecta sheet starts forming before or after the instability time scale, which could be probed with time-resolved forcing.
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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

4 major / 3 minor

Summary. The paper reports experiments and DNS on normal droplet impact onto deep pools that move horizontally at small speeds. For low Capillary numbers (Ca<0.2), a static pool yields a separate ejecta sheet (SES); the paper shows that increasing pool speed eventually produces a lamella on the upstream side while SES persists downstream. The authors propose a dimensionless parameterization of this upstream transition in terms of Ca and sqrt(u_t/u_n), where u_t is the pool speed and u_n the impact speed. They present a regime map (Fig. 4a), fit a linear boundary with slope approximately -0.4, and note that extrapolating to u_t=0 recovers the known Ca=0.2 static-pool threshold. They argue that the transition is length-scale invariant (Fig. 4b) and support this with a mechanistic explanation based on pool movement constraining the ejecta-sheet angle. One DNS comparison with an equivalent oblique impact is used to claim that the pool boundary layer is not decisive at low speed ratios.

Significance. If the proposed parameterization is correct, it significantly extends the classical static-pool impact regime diagram to a natural and industrially relevant configuration, with implications for air-sea exchange and inkjet printing. The study combines a broad experimental campaign (multiple fluids, diameters, and speeds), open data/code availability, and a numerical counterpart. The central claim is falsifiable and would be practically useful. However, the quantitative boundary and the length-scale invariance rest on the unvalidated measurement of u_t and on a fitting protocol that is not fully disclosed.

major comments (4)
  1. [§2.1 (Experimental methods)] The entire regime map (Figs. 4a,b) uses the pool velocity u_t inferred from the rotating table speed under the assumptions of solid-body rotation and negligible air drag. The text states that PTV was used to verify free-surface velocities and that a 5-minute spin-up is sufficient via Ekman-layer scaling, but no PTV data, no spatial variation at the impact point, no residuals, and no uncertainty are reported in the main text; the supplementary material is not part of this submission. A systematic error in u_t would shift every data point horizontally in sqrt(u_t/u_n), changing the fitted slope and the claimed Ca=0.2 recovery. Please report the PTV measurements, quantify the departure from solid-body rotation at the impact location, and provide a sensitivity analysis of the fitted boundary to plausible u_t uncertainties.
  2. [§3.2 (Delineating the upstream transition boundary)] The transition line is a linear least-squares fit to binned midpoints with silicone oils excluded. The manuscript does not state the number of bins, the number of experiments per bin, the bin-width selection criterion, or confidence intervals on the fitted slope and intercept. The statement that the fit 'approximately recovers' Ca=0.2 is an extrapolation from data with Ca<0.15 to the static-pool threshold at Ca=0.2. Since the central claim is that Ca and sqrt(u_t/u_n) 'near perfectly separate' all outcomes, the fitting protocol and its uncertainty need to be reported so that the boundary is reproducible. The exclusion of silicone oils should also be justified; if those data are excluded because they deviate, the universality claim is weakened.
  3. [§3.3 (Length-scale invariance)] Figure 4b tests the length-scale invariance at a single Capillary number (Ca=0.072±0.002) and uses two fluids (21 vol% glycerol-water and 1 cSt silicone oil); the range of r_n is not stated. The comparison line with alpha=0.25 is an arbitrary reference, fixed at one point of the data, and no regression or confidence interval for alpha is given. The conclusion that the transition is 'strongly suggested' to be length-scale invariant is stronger than the evidence shown. Please report the number of experiments, error bars, and a confidence interval for alpha, or soften the claim accordingly.
  4. [§3.6 (Oblique impact)] The DNS evidence for the claim that the pool boundary layer does not play a decisive role is based on a single condition (Ca=0.105, u_t=0.15 m/s, Fig. 2). The agreement between the simulation and experiment is described as 'good qualitative agreement', but no quantitative comparison of the ejecta sheet extent, lamella onset, or timing is provided. Since this claim is used to generalise moving-pool results to oblique static-pool impacts, additional simulations or quantitative comparisons across the transition boundary are needed.
minor comments (3)
  1. [§3.1] The units in the text 'u_n = 3.10 ms' should read 'm s^{-1}'.
  2. [§3.4] The correction for the moving impact point (adding 24 µm per t*_mu unit) is not derived. Please state how this value is obtained and what uncertainty it carries.
  3. [Supplementary Material] Multiple references are made to the supplementary material, but it is not included with the submission. Ensure the supplementary material is available for review, particularly the PTV verification and the regime map coloured by fluid.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the moving-pool regime map is empirical and its dimensionless group is independently motivated.

full rationale

The central claim is an empirical regime map, not a derived prediction. The dimensionless group sqrt(ut/un) is motivated before the outcome data are used, via an independent geometric ejecta-sheet-angle argument (Thoroddsen et al. 2011; Thoraval et al. 2012), so it is not defined by the transition labels. The linear boundary in Fig. 4(a) is explicitly described as a least-squares fit to the observed transition, not as a first-principles prediction; its extrapolated intercept at sqrt(ut/un)=0 is checked against the independent literature threshold Ca=0.2 (Agbaglah et al. 2015), which is an external benchmark rather than an imposed constraint. Length-scale invariance is tested separately with fixed-Ca experiments (Fig. 4b), and the moving-pool/DNS and oblique-impact simulation provide independent numerical verification. Self-citations (Sykes et al. 2023; Harris et al. 2025; Cimpeanu & Papageorgiou 2018) are used for supporting mechanisms or methodology only and are not load-bearing for the central parameterization. The unshown PTV validation of ut is a possible experimental uncertainty, but it affects the independent variable and is not a circularity of the derivation.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

All central empirical content rests on standard measurement assumptions (solid-body rotation, deep pool) and on prior ejecta-sheet scaling from the literature. The only fitted quantity is the slope of the transition boundary; the length-scale exponent is inferred from a narrow dataset. No new physical entities are postulated.

free parameters (1)
  • transition line gradient (slope in Ca vs sqrt(ut/un)) = approximately -0.4
    In Sec. 3.2, a linear least-squares fit to binned midpoints between the first lamella and last SES for Ca<0.15 (silicone oils excluded) sets the boundary; the slope supplies the 'single constant' that delineates the transition. This is fitted to the data, not derived from the ejecta-sheet-angle model.
assumptions (6)
  • ad hoc to paper The transition boundary is linear in Ca vs sqrt(ut/un).
    Sec. 3.2: 'Visually, the Ca<0.2 transition boundary appears linear, so it is tempting to attempt a least-squares linear fit.' The linear form is assumed for parametrising the data, not derived.
  • domain assumption Static-pool ejecta-sheet angle grows as theta ~ sqrt(Re), and pool motion effectively reduces theta upstream by sqrt(ut/un).
    Sec. 3.2: based on Thoraval et al. 2012 and Thoroddsen et al. 2011; the authors concede theta is 'practically unmeasurable from our experiments'.
  • domain assumption Deep-pool condition h/D > 3 is sufficient for early-time ejecta dynamics.
    Sec. 2.1: cited to Thoroddsen et al. 2011 and Sykes et al. 2023; finite-depth effects could otherwise alter the SES/lamella transition.
  • domain assumption The pool surface moves at the tank angular speed, with negligible air drag and sufficient spin-up time.
    Sec. 2.1: the authors assume solid-body rotation and a 5-minute spin-up; PTV checks are mentioned, but the x-axis of the regime map depends on this assumption.
  • domain assumption Basilisk adaptive VOF with a symmetry plane and O(1 micron) resolution captures the ejecta sheet dynamics.
    Sec. 2.2: established in prior work, but no convergence study is reported in this paper.
  • domain assumption For ut << un, the moving-pool boundary layer is not decisive, so normal moving-pool impact is equivalent to oblique static-pool impact.
    Sec. 3.6: tested with one DNS case at beta = 3.5 degrees on the leading side.

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Cite this review

Pith. "Pith review of Fast droplet impact onto slowly moving deep pools." pith.science (2026). https://pith.science/paper/76OI2CS2

@misc{pith2026251103682,
  author       = {Pith},
  title        = {Pith review of: Fast droplet impact onto slowly moving deep pools},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/76OI2CS2}},
  note         = {Machine review of arXiv:2511.03682}
}
read the original abstract

When a fast droplet impacts a pool, the resulting ejecta sheet dynamics determine the final impact outcome. At low Capillary numbers, the ejecta sheet remains separate from a deep static pool, whilst at higher viscosities it develops into a lamella. Here, we show that the common natural scenario of a slowly moving deep pool can change the upstream impact outcome, creating highly three-dimensional dynamics no longer characterised by a single descriptor. By considering how pool movement constrains the evolution of the ejecta sheet angle, we reach a length-scale invariant parameterisation for the upstream transition that holds for a wide range of fluids and impact conditions. Direct numerical simulations show similar dynamics for an equivalent oblique impact, indicating that the pool boundary layer does not play a decisive role for low pool-droplet speed ratios. Our results also provide insight into the physical mechanism that underpins pool impact outcomes more generally.

Figures

Figures reproduced from arXiv: 2511.03682 by the authors.

Figure 1
Figure 1. (a) We versus Re for all experiments reported. The purple line delineates the known vortex shedding boundary (Re = 5We, i.e. Ca = 0.2, Agbaglah et al. 2015). (b) A rendering of the experimental setup. For all experiments, the pool depth ℎ was maintained such that ℎ/𝐷 > 3 (typically with ℎ ∈ [12, 14] mm), which is sufficient that the pool can be considered deep for the early￾time dynamics of interest here (Thoroddsen… view at source ↗
Figure 2
Figure 2. (a) Computational box highlighting adaptive grid refinement. (b) Experimental view of the case described by Ca = 0.105 (32 vol% fluid) and 𝑢𝑡 = 0.15 m s−1 (𝑢𝑛 = 2.45 m s−1 , √︁ 𝑢𝑡 /𝑢𝑛 = 0.25), at 𝑡 ∗ 𝜇 = 2. The upstream outcome is a lamella. The orange arrow indicates the direction of pool movement and the scale bar is 2 mm. (c) The result of a simulation matching the conditions in panel (b), with tracer fields used… view at source ↗
Figure 3
Figure 3. (a)–(c) Ca = 0.132 (We = 345; 𝑢𝑛 = 3.10 ms) impact of a 32 vol% droplet onto a 32 vol% deep pool. (a) The pool is static: separate ejecta sheet, which is expected since Ca < 0.2 (figure 1a). (b) The pool moves with 𝑢𝑡 = 0.17 m s−1 ( √︁ 𝑢𝑡 /𝑢𝑛 = 0.23): separate ejecta sheet, but the ejecta sheet dynamics are not axisymmetric. (c) The pool moves with 𝑢𝑡 = 0.26 m s−1 ( √︁ 𝑢𝑡 /𝑢𝑛 = 0.29): lamella upstream and a separate… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Upstream impact outcomes for normal droplet impact on a moving deep pool. Red circular markers indicate a lamella, while green triangular markers indicate a separate ejecta sheet. (a) This regime map includes all experimental conditions described in section 2.1: We ∈ […
Figure 5
Figure 5. Figure 5: (a)–(c) High resolution (327 pixels mm−1 ) images of the early-time ejecta sheet dynamics of Ca = 0.115 ± 0.002 impact (32 vol% fluid). (a) Static pool. (b)–(c) 𝑢𝑡 = 0.20 ± 0.01 m s−1 ( √︁ 𝑢𝑡 /𝑢𝑛 = 0.27): (b) separate ejecta sheet upstream; (c) lamella upstream. Orange…
Figure 6
Figure 6. Figure 6: Ca = 0.213±0.002 with the 43 vol% fluid. (a) Static pool. (b)–(c) Moving pool with √︁ 𝑢𝑡 /𝑢𝑛 = 0.33. The blue tinge in (a) and (b) is an artifact of repeated inner wall surface treatments and the light source. Orange arrows indicate the direction of pool movement and a…

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