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REVIEW 2 major objections 2 minor 15 references

Side-wall wetting and linear stability of falling films

T0 review · 2 major / 2 minor · reviewed 2026-05-22 · grok-4.3

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Pith's one-line read In weakly-confined channels, decreasing the contact angle at the side walls raises the critical Reynolds number for long-wave instability of falling films.

desk verdict Wetting has opposing effects on falling-film stability depending on confinement strength, shown through biglobal analysis with resolved menisci and some experimental agreement. read the letter →

arxiv 2504.13300 v2 pith:RXVMLTDG submitted 2025-04-17 physics.flu-dyn

Hammam Mohamed , Jörn Sesterhenn This is my paper
classification physics.flu-dyn
keywords fallingliquidfilmsside-wallwettinglinearstabilityanalysiscontactanglemeniscusbiglobalReynoldsnumbercapillaryforces
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 investigates how wetting at the side walls changes the linear stability of liquid films flowing down channels that are confined in the spanwise direction. It builds a biglobal stability analysis that accounts for the curved meniscus and the streamwise velocity overshoot near the walls. In weakly confined geometries, stronger wetting produces a net stabilization of long-wave modes that pushes the onset of instability to higher flow rates. This stabilization grows as the contact angle is reduced and shows trends and magnitudes that line up with existing experiments. The analysis reveals a competition in which capillary anchoring at the walls offsets the usual destabilizing role of inertia.

What carries the argument

A biglobal linear stability analysis of the Navier-Stokes equations performed on a base flow that includes a curved meniscus and streamwise velocity overshoot near the side walls set by the prescribed contact angle.

What would settle it

Measure the critical Reynolds number for the onset of waves in a weakly-confined falling film at several contact angles and check whether it increases as the contact angle decreases.

Watch

Extended reading notes

Core claim

In weakly-confined channels, decreasing the contact angle produces a net long-wave stabilization that significantly increases the critical Reynolds number, with trends and magnitudes consistent with available experimental measurements. In contrast, in confined channels, wetting weakens the stabilization normally provided by side-wall boundary layers and shifts the neutral curves toward the unconfined limit.

Load-bearing premise

The base flow is assumed to be steady and two-dimensional with a fixed contact angle at the side walls.

Editorial extensions

If this is right

  • Lower contact angles in weakly-confined channels raise the Reynolds number at which long-wave instability appears.
  • Perturbation modes become more strongly anchored at the walls, producing interface tensioning that damps growth.
  • In confined channels the same wetting instead reduces viscous damping by creating near-wall vortical structures.
  • The long-wave stabilization effect is strongest when spanwise confinement is weak enough that boundary layers no longer dominate.
  • Quantitative comparison with experiments confirms that the predicted increase in critical Reynolds number lies within measured ranges.

Reading between the lines

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

  • Surface wettability could be tuned deliberately to postpone wave formation in coating or heat-transfer applications that use wide channels.
  • Allowing dynamic contact-line motion or three-dimensional base-flow adjustments would likely change the meniscus shape and therefore the reported stability shift.
  • The same wetting mechanism may interact with other long-wave instabilities, such as those driven by Marangoni effects or bottom topography.
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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

2 major / 2 minor

Summary. The manuscript develops a biglobal linear stability analysis of falling liquid films confined in the spanwise direction, incorporating side-wall wetting through the contact angle. It identifies two regimes: in confined channels, decreasing contact angle weakens side-wall stabilization and shifts neutral curves toward the unconfined limit; in weakly-confined channels, wetting produces net long-wave stabilization (k→0) that raises the critical Reynolds number via capillary forces competing with inertia. The predicted stabilization is shown to be consistent in trend and magnitude with available experimental measurements of critical Re.

Significance. If the results hold, the work is significant for clarifying the competing roles of geometric confinement and wetting in film stability. Strengths include the direct numerical solution of the linearized Navier-Stokes operator (avoiding fitted parameters) and the quantitative comparison to experimental critical-Re trends, which grounds the long-wave stabilization claim in weakly-confined channels.

major comments (2)
  1. [Base-flow section] Base-flow section: the analysis assumes a steady, strictly two-dimensional base flow with a prescribed constant contact angle. This produces the curved meniscus and near-wall velocity overshoot that anchor the reported long-wave stabilization mechanism in weakly-confined channels. Dynamic contact-line motion or spanwise base-flow adjustments (common in experiments) would alter meniscus curvature and overshoot, directly affecting the capillary stabilization and the quantitative match to measured critical Re.
  2. [Numerical implementation and results] Numerical implementation and results: the manuscript does not report mesh-convergence studies or discretization-error estimates for the biglobal stability calculations. Because the central claim rests on quantitative shifts in neutral curves and critical Reynolds numbers, such verification is required to confirm that the long-wave stabilization is resolved accurately rather than being an artifact of discretization.
minor comments (2)
  1. [Abstract] Abstract: the description of the two limiting regimes would be clearer if the specific spanwise aspect ratios or channel widths that separate 'confined' from 'weakly-confined' were stated explicitly.
  2. [Eigenmode discussion] Eigenmode discussion: the qualitative description of near-wall vortical structures and interface anchoring is useful, but adding a quantitative metric (e.g., integrated perturbation energy near the side wall) would strengthen the mechanistic interpretation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions planned for the next version.

read point-by-point responses

  1. Referee: [Base-flow section] Base-flow section: the analysis assumes a steady, strictly two-dimensional base flow with a prescribed constant contact angle. This produces the curved meniscus and near-wall velocity overshoot that anchor the reported long-wave stabilization mechanism in weakly-confined channels. Dynamic contact-line motion or spanwise base-flow adjustments (common in experiments) would alter meniscus curvature and overshoot, directly affecting the capillary stabilization and the quantitative match to measured critical Re.

    Authors: We agree that the assumption of a strictly steady, two-dimensional base flow with a fixed contact angle is an idealization. Dynamic contact-line motion and possible spanwise base-flow adjustments present in experiments could modify the meniscus shape and velocity overshoot, thereby influencing the precise magnitude of the capillary stabilization. Our framework follows the standard approach in linear stability studies of film flows by solving for the steady base state that satisfies the prescribed contact angle. The reported quantitative comparison is framed as consistency in trend and order of magnitude rather than exact numerical agreement. In the revised manuscript we will add a dedicated paragraph in the base-flow section that explicitly discusses these modeling limitations and their potential implications for the long-wave stabilization results. revision: partial

  2. Referee: [Numerical implementation and results] Numerical implementation and results: the manuscript does not report mesh-convergence studies or discretization-error estimates for the biglobal stability calculations. Because the central claim rests on quantitative shifts in neutral curves and critical Reynolds numbers, such verification is required to confirm that the long-wave stabilization is resolved accurately rather than being an artifact of discretization.

    Authors: We acknowledge the importance of documenting numerical verification for the quantitative claims. Although mesh-convergence tests were performed during code development and validation, the details were omitted from the original submission. In the revised manuscript we will include a new subsection (or appendix) that reports the grid resolutions employed, the observed changes in critical Reynolds number and neutral-curve locations under successive refinement, and estimates of discretization error for the long-wave stabilization results. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: results obtained from numerical solution of linearized Navier-Stokes operator

full rationale

The paper constructs a biglobal stability framework and computes linear stability by direct numerical solution of the linearized Navier-Stokes equations on a base flow that incorporates a curved meniscus and near-wall velocity overshoot arising from the prescribed constant contact angle boundary condition. The reported long-wave stabilization in weakly-confined channels and the associated increase in critical Reynolds number emerge from the computed eigenmodes and neutral curves of this operator; they are not imposed by fitting, self-definition, or reduction to prior self-citations. The quantitative comparison with external experiments is presented as validation rather than as an input that forces the result. Under the hard rules, this constitutes a self-contained derivation with no load-bearing circular steps.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The analysis assumes the incompressible Navier-Stokes equations, a constant contact angle, and a steady two-dimensional base flow; no new entities are postulated and the only adjustable parameters are the usual dimensionless groups (Re, We, contact angle).

free parameters (1)
  • contact angle
    Prescribed boundary condition at side walls; varied parametrically to produce the reported stability shifts.
assumptions (2)
  • standard math Incompressible Navier-Stokes equations govern the flow
    Invoked as the starting point for both base-flow and perturbation equations.
  • domain assumption Contact angle is constant and prescribed
    Used to close the meniscus boundary condition; appears in the base-flow computation.

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Cite this review

Pith. "Pith review of Side-wall wetting and linear stability of falling films." pith.science (2026). https://pith.science/paper/RXVMLTDG

@misc{pith2026250413300,
  author       = {Pith},
  title        = {Pith review of: Side-wall wetting and linear stability of falling films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RXVMLTDG}},
  note         = {Machine review of arXiv:2504.13300}
}
abstract

We investigate the influence of side-wall wetting on the linear stability of falling liquid films confined in the spanwise direction. A biglobal stability framework is developed, capturing inertia, viscosity, gravity, capillarity, and geometric confinement. The base flow exhibits a curved meniscus and a streamwise velocity overshoot near the side walls. Linear stability analysis based on the Navier--Stokes equations is performed in two limiting regimes. In \textit{confined} channels, where spanwise confinement stabilizes moderate-wavenumber perturbations via side-wall boundary layers, wetting weakens this stabilization; as the contact angle decreases, the neutral curves shift towards the unconfined one-dimensional limit, thus wetting acts as a relative destabilizing mechanism. In contrast, in \textit{weakly-confined} channels where side-wall boundary layers do not provide confinement-induced stabilization, wetting produces a net long-wave stabilization ($k \rightarrow 0$), significantly increasing the critical Reynolds number. This effect strengthens as the contact angle decreases, indicating a competition between destabilizing inertia and stabilizing wetting-induced capillary forces. The predicted long-wave stabilization effect is compared quantitatively with available experimental measurements, showing consistent trends and comparable magnitudes within the accessible parameter range. Perturbation eigenmode structures show that, in confined channels, the relative destabilization is associated with near-wall vortical structures induced by the meniscus elevation and velocity overshoot, which reduce effective viscous damping. In contrast, in weakly-confined channels, stabilization is consistent with interface tensioning through strong anchoring of the perturbations at the side walls.

Figures

Figures reproduced from arXiv: 2504.13300 by the authors.

Figure 1
Figure 1. Schematic diagram of a liquid film falling down an inclined channel. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Base state solution: Interface profile, and (b) Interface velocity in the vicinity of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Growth rate in the 𝑅𝑒 − 𝑘 plane for different surface tension and contact angle values. The purple line shows the neutral curve at which the flow goes from stable to unstable. 𝑊/𝐻 = 100, 𝛽 = 10 solved using the QZ algorithm, where the solution consists of the eigenvalues (𝜔) which is the perturbation complex angular frequency, and the eigenfunctions (𝒖ˆ, 𝑝,ˆ ℎˆ) which are the perturbation amplitudes. 3. Results The … view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Maximum growth rate for different contact angle values for (a) [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Critical Reynolds number normalized with the classical 1 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Interface perturbation amplitude (ℎˆ) and velocity perturbation amplitude fields (𝑢,ˆ 𝑣,ˆ 𝑤ˆ) for (a) non-wetting case and (b) wetting case with 𝜃 = 60◦ for the parameters 𝑘 = 0.01, 𝑆 = 15000. The fields are normalized with their respective maximum value for clarity. w…

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