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REVIEW 4 major objections 5 minor 58 references

Ambient humidity and internal droplet circulation, not just the vapour film, control Leidenfrost droplet shape and evaporation; large droplets need 3D simulations.

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A unified simulation of Leidenfrost water droplets reveals that ambient humidity and internal circulation control evaporation, and that axisymmetry is invalid for large droplets.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection Strong computational paper with a real humidity/circulation result; the bolder axisymmetry claim is suggestive but not yet proven. the 4 major comments →

arxiv 2608.01828 v1 pith:5PBBM57G submitted 2026-08-03 physics.flu-dyn

Leidenfrost droplets: The roles of ambient humidity and internal droplet circulation

Maxim de Wildt , Andrea Prosperetti , Christian Diddens , Detlef Lohse This is my paper
classification physics.flu-dyn
keywords Leidenfrost effectdroplet evaporationambient humidityinternal circulationazimuthal instabilityaxisymmetric simulationlubrication modeldirect numerical simulation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 argues that the standard picture of a Leidenfrost droplet—a pure-vapour film, an isothermal drop, and an axisymmetric shape—misses the two ingredients that set the drying rate and geometry: ambient humidity and the circulation inside the drop. Using one numerical model across four decades of droplet radius, it connects the puddle and take-off regimes and shows that humidity plus internal flow produces evaporative cooling of the drop's top, thinner vapour layers, faster evaporation, and lifetimes closer to experiment. It then shows that axisymmetric simulations of large droplets predict prolate shapes because they forbid azimuthal symmetry breaking; a stability analysis finds a critical radius near 0.2 mm, and a simplified 3D model recovers puddle shapes. If correct, the work implies pure-vapour and isothermal assumptions are inadequate, and large-Leidenfrost-droplet modelling must be three-dimensional.

Core claim

Within one quasi-stationary model, increasing the realism from pure vapour to a mixed gas-vapour phase and allowing internal circulation changes the evaporation mechanism: strong internal flow creates thin thermal boundary layers, cooling the top of the droplet by about 10 K, reducing evaporation at the base, and increasing the contribution from the outer surface, so that the film no longer dominates evaporation. This raises the global evaporation rate and lowers the droplet toward the plate, matching observed lifetimes better. The same model, when constrained to axisymmetry, produces prolate shapes for large droplets; linear stability analysis shows the axisymmetric base state is unstable t

What carries the argument

The central object is a finite-element direct numerical simulation of an axisymmetric Leidenfrost droplet with full Navier-Stokes flow in liquid and gas, species transport of vapour in a mixed gas-vapour phase, a saturation condition at the interface, and evaporative cooling, run quasi-stationarily over droplet radii from roughly 0.05 mm to 5 mm. Circulation is controlled by artificially raising liquid viscosity to isolate its effect. To test whether the prolate shapes are an artefact of geometry, the authors perform azimuthal eigenmode stability analysis, perturbing the axisymmetric base state with wavenumber m, and then a simplified 3D coupled Navier-Stokes/lubrication model with a plane o

Load-bearing premise

The conclusion that axisymmetry, rather than missing physics, causes the prolate shapes rests on the simplified 3D coupled Navier-Stokes/lubrication model being a faithful representation of the full system, including its patched shear coupling and neglect of humidity in the film.

What would settle it

Run a full 3D DNS of a roughly 1.6 mm radius Leidenfrost water droplet with mixed gas-vapour phase, internal circulation, and no axisymmetry constraint: if it still yields prolate shapes, the axisymmetry attribution is wrong; if it yields puddle shapes with an azimuthal mode cascade comparable to PIV experiments, the claim is supported. A simpler check is to measure the onset of azimuthal perturbations near R≈0.2 mm and compare the critical radius to the predicted bound.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Pure-vapour and isothermal-droplet assumptions under-predict evaporation rates and over-predict lifetimes; both humidity and circulation must be included.
  • In large droplets, evaporation is not dominated by the thin vapour film; the outer surface contributes substantially when circulation is present.
  • Axisymmetric models with internal circulation are unreliable for droplets larger than roughly 0.2 mm in radius, because azimuthal symmetry breaking removes the prolate shapes.
  • The single model stitches together the puddle regime and the take-off regime, recovering known scalings J~R^{9/5}, J~R, and h~R^{-1/2}.

Where Pith is reading between the lines

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

  • This suggests a practical rule of thumb: below roughly 0.2 mm radius, axisymmetric simulations of small and take-off Leidenfrost droplets remain trustworthy; above it, quantitative comparison to experiment needs 3D dynamics.
  • If the simplified 3D model's conclusion holds, the remaining lifetime gap for large droplets may be closed by full 3D simulations that also resolve humidity inside the gas film, rather than by adding only Marangoni effects.
  • A testable extension: droplets whose azimuthal instability is suppressed—for example by contamination or confinement—should show prolate shapes closer to the axisymmetric prediction.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper develops an axisymmetric finite-element model of Leidenfrost water droplets in a mixed gas-vapour environment, with internal droplet flow, evaporation, and a non-isothermal droplet. Simulations are run from droplet radii of about 0.05 mm to several millimetres, spanning the puddle, spherical, and take-off regimes. The authors compare four models: mixed gas-vapour with and without internal circulation, and pure vapour with and without circulation. They report that ambient humidity and internal circulation together change the evaporation flux distribution and droplet height, increase the global evaporation rate, and improve agreement with measured droplet lifetimes. For large droplets, the axisymmetric model with circulation produces prolate, 'wimple'-shaped droplets that disagree with experiments; an azimuthal linear stability analysis shows instability for R ≳ 0.2 mm, and 3D simulations of a simplified coupled Navier-Stokes/lubrication model yield puddle-like shapes. The abstract concludes that the axisymmetric constraint is the cause of the discrepancy.

Significance. If the conclusions hold, the paper makes a useful contribution by coupling ambient humidity, internal circulation, and evaporation in one model and by providing a quantitative bridge between the lubrication-theory regime (Sobac et al. 2014) and the small-droplet take-off regime (Sobac et al. 2025). The paper is not curve-fitted to the target experiments: thermophysical properties are taken from prior literature, and the model recovers the known scalings h~R^{-1/2} and J~R^{9/5}. The azimuthal stability analysis (Section 5) and the systematic viscosity- and humidity-sweep methodology (Table 1) are valuable even if the final attribution to axisymmetry is not yet fully proven. The comparison with experimental evaporation times (Fig. 12d) is a concrete falsifiable prediction. However, the paper's strongest advertised claim, namely that the large-droplet shape discrepancy is due to the axisymmetry constraint, is supported only by a reduced 3D model that omits the very humidity effects that Sections 6-7 show to be important.

major comments (4)
  1. [§8.2, Eqs. (8.2)-(8.3), Fig. 14] The central claim in the abstract, that the large-droplet discrepancy 'is due to the unrealistic constraint of axisymmetry', is not yet supported quantitatively. The only 3D evidence comes from the reduced coupled NS-lubrication model, which (i) uses a patching angle of π/4 and surface-tangent gradients, (ii) omits the mixed gas-vapour phase and ambient humidity, and (iii) in axisymmetric form gives shapes that are even more prolate than the full MGV model (Fig. 14). The 3D result is suggestive, but the axisymmetric reduced model does not reproduce the full model, so the change to puddle-like shapes could be affected by the omitted physics or by the patching approximation rather than solely by relaxing axisymmetry. I recommend either a full 3D MGV simulation at least at one representative large-droplet condition, or an explicit validation of the reduced model against the full MGV axisymm
  2. [§5, Appendix A.1] The azimuthal stability analysis establishes linear instability of the axisymmetric base state, but not that the nonlinear saturated state is the puddle-like shape seen in the reduced 3D model. The growth-rate calculation also uses material properties evaluated at the film temperature and a fourth-order Taylor expansion of the saturation pressure (Appendix A.1), so the reported critical radius of about 0.2 mm is an approximation. The paper should state explicitly that the linear analysis gives only the onset, not the post-critical shape, and should quantify the sensitivity of the critical radius to the film-temperature and Taylor-expansion choices. This is not a fatal flaw, but it is load-bearing for the abstract's attribution claim.
  3. [§5, Fig. 7; §7, Fig. 12(d)] The model overpredicts internal droplet velocities by about an order of magnitude relative to the PIV measurements of Bouillant et al. (2018). The paper acknowledges this, but the overprediction is nevertheless used to explain the prolate shapes and to argue that internal circulation is necessary for accurate drying kinetics. Since the magnitude of the internal circulation is a key ingredient in the proposed mechanism, the conclusions would be more robust if the authors showed that the main results are preserved when the circulation is artificially limited to velocities consistent with experiments (e.g., by a modest viscosity increase or by including surfactant-induced Marangoni stresses). Without such a sensitivity test, the quantitative claim that the MGV-with-circulation model 'best aligns' with experimental lifetimes may be partly fortuitous.
  4. [§6, Fig. 10] The statement that ambient humidity has a 'significant impact' on geometry and drying kinetics is clearly demonstrated in the stable small-to-moderate regime (Fig. 10 and Fig. 6), but for the largest droplets the axisymmetric MGV model becomes unphysical (prolate) and the instability argument takes over. The paper should be careful to distinguish where the humidity effect is a robust model prediction and where it is intertwined with the unresolved axisymmetry issue. This is partly a presentation point, but it affects the interpretation of the abstract's first claim.
minor comments (5)
  1. [Appendix A.2, Table 2 and Eqs. (A1)-(A5)] Units for viscosity are written as 'Pa s−1' in Eqs. (A1) and (A2) and 'mPa s−1' in Table 2; these should be 'Pa s' and 'mPa s', respectively.
  2. [Fig. 9 caption] The caption says 'where 0 is at the drop of the bottom'; this should be 'at the bottom of the drop'.
  3. [§2.1, Eqs. (2.10)-(2.11)] The mixing rules are said to follow Poling et al. (2000), while the data source in Fig. 15 is given as Poling et al. (2008). Both references are listed, but the text should clarify which edition is used for the mixing rules and which for the pure-species data.
  4. [§3.1, Eq. (3.1)] The hydrostatic boundary condition is defined by an integral with a minus sign. If p_hydro(z) is intended to be the local hydrostatic pressure, the sign convention should be stated more explicitly, since it is easy to misread.
  5. [§7, Eq. (7.10)] The evaporation time is obtained by integrating the quasi-stationary evaporation rate. This is valid only if the quasi-stationary assumption holds over the entire integration range; the paper notes this for take-off, but it would be helpful to state it directly at Eq. (7.10) as well.

Circularity Check

0 steps flagged

No significant circularity; the derivation is self-contained, with all qualitative conclusions supported by independent numerical output and external literature rather than by construction.

full rationale

The central claims are not circular by the paper's own equations. The model solves a well-posed set of conservation equations (Section 2.1) with material properties taken from external sources (Poling et al. 2000/2008; Marrero & Mason 1972), and no parameter is fitted to the target Leidenfrost data. The four models (MGV, PV, MGV-NC, PV-NC) are generated by varying ambient vapour mass fraction and liquid viscosity; the viscosity multiplier of 10^4 is explicitly a numerical decoupling device, not a fitted parameter. The recovered scaling laws h ~ R^{-1/2} and J ~ R^{9/5} are presented as independent validations against Pomeau et al. (2012), Celestini et al. (2012), and Sobac et al. (2014, 2025); they are not used as inputs to the simulation. The azimuthal stability analysis uses the authors' own pyoomph/Diddens & Rocha (2024) numerical method, but this is an open-source computational tool, and the stability eigenvalues, critical radius, and mode cascade are new outputs rather than assumed outcomes. The axisymmetry-attribution claim rests on the stability analysis plus the simplified coupled Navier-Stokes/lubrication 3D model in Section 8.2. That model involves acknowledged approximations (patching angle pi/4, surface-tangent gradients, omission of the mixed gas-vapour phase), and the paper explicitly states that full 3D DNS is presently too expensive. This is a legitimate robustness/correctness limitation, not a circular reduction: the simplified 3D simulation is not equivalent by construction to the prolate-shape result it is used to explain, and it does not reproduce the axisymmetric full-model shape exactly (indeed it is even more prolate). The paper also openly discusses remaining discrepancies and missing physics such as Marangoni effects and surfactants, which is inconsistent with a derivation that merely renames its inputs. The only self-citation of note is the numerical-method citation (Diddens & Rocha 2024), which is not load-bearing in a circular sense: the method does not encode the conclusion that axisymmetry is the cause of prolate shapes. Therefore no circular step can be identified, and the appropriate score is 0.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The central claims rest on standard continuum assumptions and on numerical control parameters that are explicitly stated. No new physical entities are introduced. Temperature-dependent material properties are taken from prior experimental data sets, not fitted to the Leidenfrost experiments, so they are not free parameters in the sense used here. The patch angle and stability-analysis film temperature are ad hoc numerical choices that modulate the key results.

free parameters (3)
  • patching angle = π/4
    Chosen by hand in the coupled NS-lubrication 3D model (Section 8.2) for numerical simplicity; introduces an O(|n - e_z|) error. This parameter affects the 3D droplet shapes used to conclude that axisymmetry is the issue.
  • film temperature for stability analysis = (T_w + T_sat)/2
    Used in Appendix A.1 for the azimuthal stability analysis to simplify symbolic computation of material properties. This choice affects the growth rates and thus the reported stability threshold.
  • viscosity multiplier for NC models = 10^4
    Chosen by hand to suppress internal circulation in the control models MGV-NC and PV-NC (Table 1, Section 4). Used to decouple evaporation and flow, not fitted to data.
axioms (5)
  • domain assumption Local thermodynamic equilibrium at the interface (Eq. 2.20): the vapour pressure at the interface is at saturation.
    Standard for evaporation models; invoked in Section 2.2 to close the interface system.
  • domain assumption Quasi-stationary approximation: all time derivatives are zero and the droplet volume is constant (Section 2.3).
    Justified in Appendix A.3 by separation of timescales; used for most simulations.
  • domain assumption Axisymmetric base state for the full DNS models.
    Assumed in Sections 2-7 and tested in Section 5; the paper argues this assumption fails for large droplets.
  • domain assumption Far-field hydrostatic pressure boundary conditions (Eq. 3.1) instead of no-penetration.
    Chosen to avoid artificial streaming; affects the outer gas flow morphology.
  • domain assumption Ideal gas mixture with Fick's law and mixing rules for transport properties (Section 2.1).
    Standard for low-Mach-number gas mixtures; invoked throughout the gas phase model.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Leidenfrost droplets: The roles of ambient humidity and internal droplet circulation." pith.science (2026). https://pith.science/paper/5PBBM57G

@misc{pith2026260801828,
  author       = {Pith},
  title        = {Pith review of: Leidenfrost droplets: The roles of ambient humidity and internal droplet circulation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5PBBM57G}},
  note         = {Machine review of arXiv:2608.01828}
}
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read the original abstract

A volatile droplet gently deposited on a superheated substrate can sit on a thin film of its own vapour, which prevents contact between the drop and surface. This phenomenon is called the Leidenfrost effect. In this paper, through direct numerical simulations, we analyse characteristics of Leidenfrost water droplets with a single computational model over four decades of droplet radius, stitching together previous works in the limit of large and small droplets. Using the model, we show that the ambient humidity, an underappreciated factor in the Leidenfrost system, in combination with the flow in the drop has a significant impact on the geometry and drying kinetics. Our results imply the inadequacies of commonly made assumptions of a pure vapour phase and an isothermal droplet. When modelling large Leidenfrost droplets with an axisymmetric model, large discrepancies between experiments and the computational results occur. Through azimuthal stability analysis, we show that this is due to the unrealistic constraint of axisymmetry. This finding is supported by 3D simulations of a simplified model. Finally, some hypotheses are explored to account for the remaining discrepancies with experimental data.

Figures

Figures reproduced from arXiv: 2608.01828 by Andrea Prosperetti, Christian Diddens, Detlef Lohse, Maxim de Wildt.

Figure 1
Figure 1. Figure 1: Schematic of problem The governing equations in the gaseous phase are derived from the conservation of total mass, species mass (via the vapour mass fraction 𝑤𝑣 = 1 − 𝑤𝑔), momentum and energy (derived from the enthalpy formulation) as in Bird et al. (2006): 𝜌𝑚 𝐷𝒖𝑚 𝐷𝑡 = ∇ · 𝝈𝑚 + 𝜌𝑚 𝒈, 𝝈𝑚 = −𝑝𝑚 𝑰 + 𝜇𝑚  ∇𝒖𝑚 + ∇𝒖 𝑇 𝑚 − 2 3 (∇ · 𝒖𝑚)𝑰  , (2.4) 𝐷 𝜌𝑚 𝐷𝑡 + 𝜌𝑚∇ · 𝒖𝑚 = 0, (2.5) 𝜌𝑚 𝐷𝑤𝑣 𝐷𝑡 = ∇ · 𝜌𝑚𝐷𝑣𝑔∇𝑤𝑣  , (2.6) 𝜌𝑚… view at source ↗
Figure 2
Figure 2. Figure 2: Snapshot from simulation of a quasi-stationary pure water droplet with 𝑅 = 1.59 mm above a plate at 𝑇𝑤 = 370 ◦C. The temperature field in the droplet and gas phase are plotted on the left (Note: for visibility purposes each domain has a different colour bar which share the same minimum temperature, since temperature variations in the drop ∼ 10 K are far smaller than that of the gas ∼ 200 K). The velocity f… view at source ↗
Figure 3
Figure 3. Figure 3: (𝑎) Image of a water drop in the Leidenfrost state with 𝑅 = 1.59 mm adapted with permission from Burton et al. (2012) (Copyrighted by American Physical Society.), with droplet shapes from the numerical models superposed. From top to bottom are the simulations with a pure vapour gaseous phase with drop circulation (PV in red), mixed gas-vapour phase with drop circulation (MGV in blue) and finally, both mode… view at source ↗
Figure 4
Figure 4. Figure 4: Quasi-stationary Leidenfrost water drops shapes from numerical simulations with substrate temperature 𝑇𝑤 = 370 ◦C. (𝑎) Mixed and pure vapour gas phase models (in blue and red respectively) at viscosity 𝜇𝑙 = 𝜇𝑤 with drop sizes varying from 𝑅 ≈ 0.05 mm to 𝑅 ≈ 3 mm. (𝑏) The same models as in (𝑎) but with 𝜇𝑙 = 10000𝜇𝑤 from 𝑅 ≈ 0.05 mm to 𝑅 ≈ 5 mm . (𝑐) Blow-up of the thin vapour film in grey rectangle in (𝑎). … view at source ↗
Figure 5
Figure 5. Figure 5: (𝑎) 𝑅neck and (𝑏) ℎcentre − ℎneck, against 𝑅max calculated from the numerical models with substrate temperature 𝑇𝑤 = 370◦C for water droplets. Also plotted are the experimental results from Burton et al. (2012) and the theoretical results of the model of Sobac et al. (2014). On the right side of figure 6, for large Leidenfrost droplets, as before we observe good agreement of the models neglecting circulati… view at source ↗
Figure 6
Figure 6. Figure 6: ℎcentre and ℎneck against 𝑅max from the numerical models with experimental data for ℎneck from Burton et al. (2012) with 𝑇𝑤 = 370◦C. The grey lines in the part of the figure marked transient indicate quasi-stationary simulations in this region. The data for take-off Leidenfrost droplets from Celestini et al. (2012) are at the slightly higher 𝑇𝑤 = 400◦C, but they are included here anyhow for rough compariso… view at source ↗
Figure 7
Figure 7. Figure 7: Maximum velocity magnitude in the liquid and gaseous phases for large Leidenfrost drop volumes and temperature of the substrate 𝑇𝑤 = 370 ◦C. The maximum drop velocities in the axisymmetric model are considerably higher than those seen in experiments. exhibit axisymmetry breaking flows, which, as the droplet evaporates, transition through successive azimuthal modes. Such non-axisymmetric flows may alter the… view at source ↗
Figure 8
Figure 8. Figure 8: Growth rates of the unstable (or most unstable) eigenmodes for azimuthal wavenumbers 𝑚 = 0, 1, 2, 3 for the most complete model of mixed gaseous phase and internal drop circulation at substrate temperature 𝑇𝑤 = 370 ◦C. These are plotted with maximum drop extent of the axisymmetric base state in the range 0.1 mm ≲ 𝑅max ≲ 1.6 mm. The adjacent plots are the most unstable eigenmodes in each regime visualised i… view at source ↗
Figure 9
Figure 9. Figure 9: (𝑎) Temperature around the surface of the drop for various drop sizes at substrate temperature 𝑇𝑤 = 370 ◦C. The polar angle 𝜃 is depicted in the inset diagram and defined as the angle between the 𝑧 axis and the line through the centre of mass and a point on the droplet surface, where 0 is at the drop of the bottom. (𝑏) Temperature at the bottom and top of the drop at 𝑟 = 0 against volume of the droplet. In… view at source ↗
Figure 10
Figure 10. Figure 10: Evaporation flux 𝑗 against 𝜃 (as defined in figure 9) at the liquid-gas interface for changing ambient humidity for a drop of size 𝑅 = 1.59 mm and substrate temperature 𝑇𝑤 = 370 ◦C. 0 /4 /2 3/4 [rad] −4 −2 0 2 4 [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Evaporation data for the models from figure 6. (𝑎) Log-log plot of the total evaporation rate against the volume of the drop. (𝑏) Contribution to the total evaporation from the thin vapour film, the dashed line indicates the film contribution if the drop is spherical and evaporated uniformly. The film layer is defined to begin from when the normal to the surface of the drop makes angle 𝜋/4 with the negati… view at source ↗
Figure 13
Figure 13. Figure 13: Drop separation from the plate of the models in figure 6 with the new curve including the thermal Marangoni effect into the mixed gas-vapour gaseous model with circulation. The inset shows the shape of the droplet with thermal Marangoni effect activated versus the shape of the mixed vapour model with the same drop volume at the rightmost data point on the thermal Marangoni curve. surfactants in this numer… view at source ↗
Figure 14
Figure 14. Figure 14: Surface contours of a 𝑅 = 2.3 mm Leidenfrost droplet above a plate at 𝑇𝑤 = 370 ◦C in the plane 𝑦 = 0. The models plotted are the mixed gas-vapour gaseous phase model with drop circulation from this work against the coupled Navier-Stokes lubrication models in axisymmetry and 3D (with a plane of symmetry in 𝑦 = 0). Each model was run until a stable droplet shape is reached. Adjacent to the graph are project… view at source ↗
Figure 15
Figure 15. Figure 15: Variation of thermophysical properties with temperature in the gaseous phase of each of dry air and water vapour. The experimental data for thermal conductivity and dynamic viscosity are taken from Poling et al. (2008) and the data for the binary diffusion coefficient comes from Marrero & Mason (1972). A.3. Validity of quasi-stationary assumption In order to neglect the time derivatives and assume a quasi… view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.