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REVIEW 3 major objections 6 minor 48 references

Non-coalescence and in-plane momentum generation in sessile droplet clusters

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper establishes that non-coalescence is the rule, not the exception, for sessile droplet clusters on water-repellent surfaces: when two droplets coalesce, the merged interface bounces off neighbouring droplets rather than merging…

desk verdict Genuinely new empirical observation of non-coalescence in sessile droplet clusters, but the size claims and the kink-based mechanism need to be reined in before this is publishable. read the letter →

arxiv 2506.13942 v2 pith:P4IV2SUB submitted 2025-06-16 physics.flu-dyn cond-mat.soft

Gopal Chandra Pal , Cheuk Wing Edmond Lam , Chander Shekhar Sharma This is my paper · ORCID
classification physics.flu-dyncond-mat.soft
keywords non-coalescencesessiledropletssuperhydrophobicsurfacesairfilmdrainagedropletself-propulsiondropwisecondensationclusterskinkentrapment
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 reports that sessile water droplets sitting in clusters on water-repellent surfaces can come into apparent contact with each other without merging: when two droplets in a cluster coalesce, the expanding interface of the merged pair reaches a neighbouring droplet and bounces off it instead of triggering further coalescence. The authors show that this non-coalescence happens over a wide size range, from millimetric droplets down to roughly 100 microns, with no surfactants, external fields, or pre-existing droplet velocity. They trace the bounce to a thin entrapped air film whose drainage is blocked by a kink in the film profile, and show that the rejected interface can transfer enough lateral momentum to self-propel the neighbouring droplet along the surface. The finding matters because it offers a passive pathway for droplet removal and surface renewal during dropwise condensation on superhydrophobic surfaces.

What carries the argument

The mechanism that carries the argument is kink-induced entrapment of the interstitial air film. As the interface of two coalescing droplets advances toward a neighbour, it squeezes the air between them, creating a nearly flat film region; at $t/\tau \approx 0.99$ the two interfaces form a kink where the film thickness is locally minimum. This kink suppresses air drainage—radial drainage velocity drops and overpressure rises in the stagnation zone behind the kink—so the film does not thin to the tens-of-nanometres scale at which van der Waals forces would trigger coalescence. During retraction the film drains again and the kink disappears. The paper arrives at this picture through axisymmetric Volume-of-Fluid simulations that resolve the air film with adaptive meshing, validated against high-speed experiments.

What would settle it

Measure the interstitial air film thickness in real time during apparent contact between a coalescing pair and a neighbouring sessile droplet, for example by high-speed interferometry; if the film thins below the roughly 10 nm rupture threshold before the interface retracts in any event the paper classifies as non-coalescence, the kink-entrapment mechanism is falsified. Alternatively, repeat the cluster experiments in a low-pressure chamber: if non-coalescence persists when the interstitial gas density is reduced by an order of magnitude, the air film cannot be the decisive element.

Watch

Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that non-coalescence is a general property of coalescing sessile droplet clusters on water-repellent surfaces, not a special case requiring large droplets, high collision velocities, or surfactants. When two droplets merge, the capillary ripple travelling along the merged interface brings it into apparent contact with a third droplet; whether contact leads to coalescence is decided by the initial geometric arrangement of the cluster. In most configurations the evolving interface forms a flat air film with a kink—a local minimum in film thickness—that acts as a restriction against air drainage, momentarily trapping the interstitial air and preventing film rupture. When the merged interface retracts, the neighbouring droplet, which had been deformed during contact, recoils and can be launched along the surface with a lateral efficiency up to 9% for tightly packed three-droplet clusters, increasing further when more droplets participate. The same bouncing and self-propulsion is observed in micrometric condensate droplets, indicating a new pathway for spontaneous droplet removal.

Load-bearing premise

The load-bearing premise is that a continuum Volume-of-Fluid simulation without disjoining pressure or other molecular-scale forces, but with a finely resolved air film, correctly predicts whether the film ruptures; if molecular-scale rupture would occur before the retraction that the simulation shows, the kink-entrapment mechanism would not explain the observed bouncing.

Editorial extensions

If this is right

  • Non-coalescence is the dominant outcome for most in-line cluster configurations, with coalescence confined to narrow spacing windows.
  • The recoil from a bounced interface can self-propel non-coalescing droplets across superhydrophobic surfaces, with lateral efficiency up to 9% for close-packed three-droplet clusters.
  • Lateral efficiency increases with packing density and with the number of participating droplets beyond three.
  • The same non-coalescence and in-plane propulsion occurs in condensate droplet clusters on nanotextured superhydrophobic surfaces, extending the phenomenon to micrometric droplets.

Reading between the lines

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

  • The kink-entrapment picture predicts that the non-coalescence window should shift if the interstitial gas is replaced by one of different viscosity or pressure; this is a direct, testable consequence not reported in the paper.
  • If confirmed at even smaller scales, cluster non-coalescence could be engineered as a surface-cleaning mechanism for condensation heat transfer, where droplet departure size is a known performance bottleneck.
  • The dependence of lateral efficiency on cluster packing suggests that surface textures that stabilise dense droplet clusters could convert coalescence energy into directed motion more effectively than random droplet arrangements.
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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 / 6 minor

Summary. This manuscript reports an experimental and numerical study of non-coalescence in sessile droplet clusters on nanotextured superhydrophobic surfaces. The authors show that when two droplets in a cluster coalesce, the evolving interface can come into apparent contact with a neighboring droplet and bounce back without merging; in staggered configurations this bounce can transfer lateral momentum and produce in-plane self-propulsion, with an energy conversion efficiency reported as high as 9%. A parameter study maps the third droplet's position (R, θ) and classifies outcomes into full coalescence, coalescence followed by reseparation, and non-coalescence. Axisymmetric Volume-of-Fluid simulations are used to argue that a kink in the interstitial air film suppresses air drainage and entraps the film, thereby preventing coalescence. The phenomenon is also reported for condensed droplets of roughly 0.3–0.4 mm diameter on a cooled superhydrophobic surface, and the authors claim applicability down to 100 µm (abstract) or 200 µm (conclusions). The paper is well organized, with careful substrate fabrication and control of wettability, high-speed imaging, and a systematic geometric survey.

Significance. If substantiated, the central observation is significant: it identifies a previously unreported configuration for droplet non-coalescence, requiring neither relative centroidal velocity, surfactants, high gas pressure, nor millimetric droplet sizes, and it demonstrates a passive pathway for droplet transport on superhydrophobic surfaces during condensation. The manuscript's strengths include the systematic experimental mapping over cluster geometry, high-speed imaging, reproducibility controls (vibration isolation, substrate grounding), dimensionless scaling of the results, and a falsifiable claim that the coalescence/non-coalescence thresholds in the in-line arrangement are independent of droplet size for d0 in 0.6–2 mm. The proposed mechanism, however, rests on a continuum CFD model that, by the authors' own statement in SI Section S3, cannot account for the molecular forces that decide film rupture; the causal claim therefore needs additional support. The claims about droplet size range and about efficiency also need reconciliation with the data shown.

major comments (3)
  1. [Main text (Fig. 4 discussion) and SI Section S3] The central causal claim—that 'kink formation leads to momentary entrapment of the air layer, leading to non-coalescence with the third droplet'—is not established by the simulations. SI Section S3 states that coalescence or non-coalescence after apparent contact depends on molecular forces 'which cannot be directly accounted for in the CFD simulations,' and Eqs. (3.1)–(3.6) indeed contain no disjoining pressure, van der Waals interaction, or rupture criterion. Because a single VOF marker is used for all droplets, numerical coalescence can occur only after the air film becomes unresolved; the finest mesh (1800 cells per radius for d0 ≈ 100 µm) corresponds to a cell size of about 28 nm, and the resolved films in Figs. 3–4 have thickness on the order of 0.01 d0, i.e., about 1 µm, well above the 10–100 nm films in which van der Waals forces decide rupture. The model is also validated only against a non-coalescence event (Fig. S3b), so it does not test the coalescence/non-coalescence boundary. The simulation therefore demonstrates a correlation between kink formation and slow drainage over the resolved part of the film's life, not a mechanism that prevents rupture. A revision should either couple the VOF solution to a thin-film drainage model with a disjoining-pressure rupture criterion, or supply an order-of-magnitude comparison between the film-drainage time and the contact-residence time; unless that is done, the causal wording in the main text and Conclusions overstates the evidence.
  2. [Abstract; Conclusions; Fig. 7a] The droplet-size claim is internally inconsistent and goes beyond the data shown. The abstract claims non-coalescence 'from millimeters to as small as 100 microns,' the Conclusions state 'as small as 200 µm,' and the smallest event actually presented—the condensation event in Fig. 7a—involves droplets of about 0.3–0.4 mm. The cluster experiments use d0 = 0.6–2 mm, and the numerical simulations use d0 ≈ 100 µm, so an experimental observation at 100–200 µm is not demonstrated anywhere in the manuscript. The size-independence of the in-line thresholds has been tested only over 0.6–2 mm in non-dimensional coordinates; extrapolating that trend to 100 µm is not equivalent to observing an event at that scale. The authors should either add experimental non-coalescence data at or below 200 µm or revise the abstract and conclusions to give the size range that the data actually support.
  3. [Main text (efficiency definition) and Fig. 5e–f] The quantitative efficiency claims require more support. The lateral efficiency η_lateral is defined with a denominator that accounts only for the surface energy released by D1+D2, while the numerator includes the kinetic energy of all participating droplets, including the propelled droplet D3; excluding D3's surface energy from the denominator is an accounting choice that directly affects the headline value of 'as high as 9%,' and the paper should justify or discuss it. No error bars, standard deviations, or event counts are reported for η_lateral in Figs. 5e–f, and the sample sizes N in the box plots of Figs. 5a–b are not stated; consequently the regime boundaries (l/d0 ≲ 0.07 and ≳ 0.14 for the in-line arrangement), the trend with packing density, and the claim of size independence rest on unquantified sampling. The statement that the four-droplet configuration is 'higher by ~2 percentage points' appears to be based on a single event in Fig. 6. At minimum, the authors should give event counts per R–θ bin, report the spread of efficiency values across repeats, and indicate how many events define each regime boundary.
minor comments (6)
  1. [Fig. 2 caption vs. main text (p. 4)] The caption of Fig. 2 states that panel (a) triggers coalescence with D3 and panel (b) retracts without coalescence, while the main text says 'Figure 2(a) illustrates a typical non-coalescence event' and 'the coalescence proceeds to completion, as shown in Fig 2(b)'; the labels and the text should be made consistent.
  2. [References] The reference list contains duplicates and one corrupted entry: Ref. 31 is a raw downloaded filename that duplicates Ref. 12; Refs. 3 and 17 (Jayaratne and Mason), Refs. 5 and 18 (Orme), and Refs. 15 and 20 (Tang et al.) are also duplicated. The list should be cleaned.
  3. [Main text (p. 3)] The phrase 'no bulk velocity prior to coming in apparent contact' should be clarified: the interface of the merged droplet approaches D3 with inertial-capillary velocity, and the distinguishing feature is the absence of centroidal droplet motion rather than the absence of approach velocity.
  4. [Fig. 5] The axes, units, and sample sizes should be documented: the text should define the units of S in Fig. 5d and give the values of N for each configuration in Figs. 5a–b, ideally in the caption or methods.
  5. [SI Section S3] The axisymmetry assumption is justified by stating that the interface reaches D3 before the ripple reflects from the substrate; this should be quantified by comparing the relevant travel times, since the symmetry of the computational domain rests on this assumption.
  6. [Throughout] There are typographical inconsistencies, including 'reseperation' for 'reseparation' (S2 heading and main text) and inconsistent spelling of 'water-repellent/repellant'.

Circularity Check

1 steps flagged · score 6.0 of 10

The empirical non-coalescence observation is self-contained, but the CFD-based kink-entrapment mechanism is circular: with a single marker and no molecular rupture model, non-coalescence is the only possible simulated outcome.

  1. self definitional [SI Section S3, Eqs. (3.1)-(3.6); Main text, Fig. 4 discussion]
    "Overall, we conclude that the kink formation leads to momentary entrapment of the air layer, leading to non-coalescence with the third droplet. [SI S3:] In a real scenario, coalescence or non-coalescence of droplets after apparent contact depends on molecular forces, which cannot be directly accounted for in the CFD simulations. ... In our numerical modelling, we have used the latter method, however, with a single marker for all the droplets, and an adaptive meshing strategy to resolve the morphology of air film and flow of air in the film."

    The VOF model solves Eqs. (3.1)-(3.6), which contain pressure, viscosity, surface tension, and gravity, but no disjoining pressure, van der Waals force, or critical film-thickness rupture criterion. The SI explicitly states that molecular forces decide coalescence/non-coalescence and that these forces cannot be accounted for in the CFD simulation. With a single volume-fraction marker for all droplets, the only way the interfaces can merge is if the resolving air film disappears numerically; otherwise non-coalescence is guaranteed by construction. Therefore the simulation's non-coalescence is not an independent prediction of the kink mechanism; it is a built-in consequence of a model that cannot rupture the film. The main-text conclusion that kink formation 'leads to ...

full rationale

The paper's core empirical claim, non-coalescence and in-plane self-propulsion in sessile droplet clusters, is supported by direct high-speed imaging over a size range from roughly 100 micrometers to millimeters, including condensation experiments; no fitted parameter is used to force those outcomes, and the lateral efficiency is measured from image analysis rather than prescribed. The self-citations to the authors' earlier substrate, tip, and condensation methods are not load-bearing for the new observation. The one genuinely circular element is the mechanistic attribution from CFD: the single-marker VOF simulation has no molecular-scale rupture mechanism, so non-coalescence is the default numerical outcome for any resolved film, and the paper's claim that kink formation 'leads to ... non-coalescence' reduces to the model's construction. This is a partial circularity: the empirical phenomenon is independent, but the proposed kink-entrapment explanation is not independently established by the simulation. The score reflects this partial reduction rather than an overall dismissal of the experimental findings.

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

The central observation is experimental and does not depend on fitted constants. The numerical explanation depends on the continuum modeling assumptions listed above; none of them is a parameter fitted to force the reported outcome. No new particles, forces, or material entities are introduced; the kink is a geometric feature of the air film, not an independently postulated entity.

assumptions (6)
  • domain assumption Continuum incompressible laminar two-phase Navier-Stokes with VOF captures interstitial air film dynamics.
    Used throughout SI Section S3; the calculation omits disjoining pressure and molecular forces, so film rupture is not modeled directly.
  • domain assumption The in-line cluster can be modeled as axisymmetric and one-sided with a symmetry boundary condition.
    SI Section S3 invokes the absence of substrate reflection of the capillary ripple and the irrelevance of droplets on the other side to reduce the domain.
  • domain assumption Substrate influence is negligible, so contact angle can be treated as 180 degrees with no hysteresis.
    SI Sections S3 and S4 use this to justify flat-boundary simulations on superhydrophobic surfaces.
  • domain assumption Inertial-capillary scaling makes results transferable from simulated 100 micron droplets to experimental 0.6 to 2 mm droplets.
    SI Section S3 cites Mouterde et al. and Boreyko for this scaling; the paper does not test the scaling across the full claimed size range.
  • domain assumption Triggering coalescence with the superhydrophobic tip imparts negligible kinetic energy, below 5 percent of excess surface energy.
    SI Section S1 states this based on image analysis; it underpins the claim that droplets have no bulk velocity before apparent contact.
  • ad hoc to paper Kink-induced suppression of air drainage is sufficient to prevent coalescence, even without resolving molecular-scale film rupture.
    Main text Fig. 4 discussion concludes non-coalescence from the kink mechanism; this is an interpretation not directly simulated at rupture scales.

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Pith. "Pith review of Non-coalescence and in-plane momentum generation in sessile droplet clusters." pith.science (2026). https://pith.science/paper/P4IV2SUB

@misc{pith2026250613942,
  author       = {Pith},
  title        = {Pith review of: Non-coalescence and in-plane momentum generation in sessile droplet clusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P4IV2SUB}},
  note         = {Machine review of arXiv:2506.13942}
}
abstract

Intuitively, droplets in proximity merge when brought into contact. However, under certain conditions, they may not coalesce due to the entrapment of an interstitial gas film. Non-coalescence between water droplets has so far been observed during collisions of droplets moving with relative centroidal velocity, or in the presence of specific enabling effects such as high intervening gas pressures, surfactants, or large droplet sizes (diameter $\gtrsim 1~\mathrm{mm}$). Here, we report non-coalescence between water droplets over a much wider range of droplet diameters, from millimeters to as small as 100 microns, without the need for any of the above factors. Such non-coalescence occurs in sessile droplet clusters on water-repellent surfaces. When any two droplets in a cluster coalesce, the evolving interface of the coalescing droplets comes in apparent contact with other neighbouring droplets in the cluster, but does not necessarily trigger further coalescence. In fact, such apparent contact can manifest as a bouncing interaction, and depending on the initial geometric arrangement of droplets, it can result in significant lateral momentum generation, consequently leading to spontaneous in-plane self-propulsion of the participating droplets. The energy conversion efficiency of this process reaches as high as 9\% for closely packed clusters of three sessile droplets and increases further with an increase in the number of participating droplets. The resulting self-propulsion of such small droplets reveals a new pathway for passive droplet removal and surface renewal during dropwise condensation on superhydrophobic surfaces, critical in multiple applications.

Figures

Figures reproduced from arXiv: 2506.13942 by the authors.

Figure 6
Figure 6. Non-coalescence of droplets in a cluster with more than 3 droplets. The scale bar in the first frame is 1mm. Here the actual number of participating droplets are 4 (𝐷1, 𝐷2 ,𝐷3 𝑎𝑛𝑑 𝐷4 ). The droplet 𝐷5 does not participate as it is out of reach. The formed interface, as a result of coalescence between 𝐷1 and 𝐷2, deforms the interface of droplets 𝐷3 and 𝐷4 simultaneously, resulting in higher total lateral centroidal k… view at source ↗

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.