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arxiv: 2604.23630 · v1 · submitted 2026-04-26 · ⚛️ physics.flu-dyn

Capillary effects on preferential orientation of floaters in gravity waves

Basile Dhote , Ewen Le Ster , Wietze Herreman , Fr\'ed\'eric Moisy This is my paper

Pith reviewed 2026-05-08 05:34 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords capillary effectsgravity wavesfloaterspreferential orientationelastic platesyaw momentFroude-Krylov approximation
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The pith

Capillary effects alter the immersion depth that sets whether thin floaters align lengthwise or crosswise in gravity waves.

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

Thin elastic plates denser than water drifting in propagating surface gravity waves experience a mean angular drift that rotates them into either a longitudinal orientation parallel to wave propagation or a transverse orientation parallel to the wave crests. A diffractionless Froude-Krylov model computes the mean yaw moment on plates of arbitrary but small bending rigidity by combining wave pressure forces with a quasi-static capillary contribution given by the fluid volume displaced by the plate and its meniscus. The model shows that the resulting orientation is governed by the dimensionless parameter F equal to wavenumber times floater length squared divided by mean immersion depth, provided the immersion depth incorporates capillary effects, and by whether this F exceeds a critical value that depends on the ratio of flexural length to floater length. Laboratory experiments with rectangular metal plates of varied length, width, and thickness confirm the predicted transitions.

Core claim

The preferential orientation of thin elastic floaters in gravity waves is determined by comparing the parameter F = k L_x squared over mean immersion depth to a critical threshold F_c that is a function of the flexural length to floater length ratio, where the mean immersion depth must include the capillary contribution obtained from the quasi-static displaced volume including the meniscus. The diffractionless model predicts the mean yaw moment that drives the angular drift under the assumption that bending rigidity remains small relative to the wavelength.

What carries the argument

The dimensionless parameter F = k L_x^2 / overline{h} with overline{h} adjusted for capillary effects on immersion, together with the critical value F_c set by the flexural-to-floater length ratio, which together decide the sign of the mean yaw moment.

Load-bearing premise

The diffractionless approximation gives an accurate mean yaw moment and capillary forces act through a quasi-static displaced volume for the tested range of bending rigidities and wavelengths.

What would settle it

Experiments that vary floater thickness or length to change the flexural length ratio while holding F fixed, then measure whether the observed transition between orientations shifts exactly as predicted by the function F_c of that ratio.

Figures

Figures reproduced from arXiv: 2604.23630 by Basile Dhote, Ewen Le Ster, Fr\'ed\'eric Moisy, Wietze Herreman.

Figure 1
Figure 1. Figure 1: Thin floating plates denser than water placed in a surface wave drift towards a preferential orientation, either longitudinal (for shorter floaters) or transverse (for longer floaters). We study how this preferential orientation phenomenon is affected by capillarity. as for small solid objects (Dushkin et al. 1995), and may lead to the formation of clusters or rafts (Protiere ` 2023). Capillarity also affe… view at source ↗
Figure 2
Figure 2. Figure 2: (a) A thin brass rectangular plate of dimensions 𝐿𝑥 = 7 cm, 𝐿𝑦 = 1 cm and 𝐿𝑧 = 0.3 mm floating at the air-water interface. The surface deformation induced by the meniscus is visible through the reflection of a patterned lighting. (b) Force balance on a floating plate. The meniscus 𝜁𝑚 along the long edges is pinned at the bottom face of the floater, at 𝑧 = −ℎ. where 𝐹cap,𝑧 is the vertical component of the c… view at source ↗
Figure 3
Figure 3. Figure 3: (a,b) Surface height profile across a capillary floater of width 𝐿𝑦 = 10 mm, length 𝐿𝑥 = 60 mm and thickness 𝐿𝑧 = 0.15 mm, with meniscus pinned on the lower (a) and upper (b) edge. Note the strongly stretched vertical scale; the residual tilt angle is less than 0.5◦ . (c) Immersion depth ℎ (measured at 𝑦 = 0) as a function of the normalised width 𝐿𝑦/ℓ𝑐 for two thicknesses 𝐿𝑧 . The predictions correspond to… view at source ↗
Figure 4
Figure 4. Figure 4: Experimental setup. (a) Side view; a 4 m long, 18 cm large wave tank is filled at height 𝐻 = 22 cm. A wave maker oscillates at frequency 𝜔, generating waves of wavelength 𝜆. (b) Top view of a floater drifting in a propagating wave. The yaw angle 𝜓 is the angle between the floater long axis and the direction of wave propagation. A nylon mesh is attached to the walls to absorb parasitic surface waves. an unc… view at source ↗
Figure 5
Figure 5. Figure 5: Preferential orientation of rigid capillary floaters in the plan (a) (𝐹 = 𝑘 𝐿2 𝑥 /ℎ, 𝐿𝑦/ℓ𝑐) and (b) (𝑘 𝐿2 𝑥 /𝛽𝐿𝑧 , 𝐿𝑦/ℓ𝑐). Red (resp. blue) points are floaters that rotate towards the longitudinal (resp. transverse) orientation. Circles in pale colours correspond to 𝐿𝑧 = 0.15 mm, and squares in plain colours to 𝐿𝑧 = 0.3 mm. Gray and black symbols denote floaters for which no preferential orientation can be… view at source ↗
Figure 6
Figure 6. Figure 6: Preferential orientation of elasto-capillary floaters in the (𝐹, 𝐿𝑥 /𝐿𝐷) plane, for two floater thickness 𝐿𝑧 . Red: Longitudinal orientation; blue: transverse orientation; black: uncertain orientation. The gray area represents the uncertainty region. The black dashed line shows the predicted transition 𝐹𝑐 (equation 1.2). given by 𝑘 𝐿2 𝑥 /𝛽𝐿𝑧 = 60/(1 + 2ℓ𝑐/𝐿𝑦). This representation also suggests that very th… view at source ↗
Figure 7
Figure 7. Figure 7: Pressure and capillary forces on an arbitrary floating body of volume 𝑉 surrounded by a meniscus. (a) The pressure force 𝑭p acts on the wetted surface 𝑆wet, and the capillary force 𝑭cap acts on the contact line 𝐶. (b) The capillary force is identical to the pressure force on the free surface 𝑆m. (c) In the Froude-Krylov approximation, the resultant force 𝑭p+𝑭cap acts as a generalized buoyancy force opposin… view at source ↗
Figure 8
Figure 8. Figure 8: (a) Elastic plate with menisci pinned on its bottom face floating in a surface wave. Two side views show (b) the pinned menisci 𝜁 ± 𝑚 along the short dimension e𝑦 and (c) the plate deformation 𝜁𝑝 (e𝑥, 𝑡) along the long dimension e𝑥. The light-blue dashed line is the wave in the absence of object, and we show the local generalised immersion height ℎ = 𝜁 − 𝜁𝑝. The menisci at the tips e𝑥 = ±𝐿𝑥 /2 are shown on… view at source ↗
Figure 9
Figure 9. Figure 9: (a) Effect of the natural curvature (convex or concave) on the equilibrium shape of a capillary floater, for 𝐿𝑥 /𝐿𝐷 = 1.1 and for curvatures −0.3 ≤ 𝜅𝐿𝑥 ≤ 0.3. (b) Resulting critical value 𝐹𝑐 for the longitudinal￾transverse transition, for concave and convex floaters of varying natural curvatures. submersion depth than its flat counterpart, resulting in a smaller threshold 𝐹𝑐, and hence a stronger preferenc… view at source ↗
read the original abstract

We study the influence of capillary effects on the motion of thin elastic plates denser than water drifting in propagating surface gravity waves. Such floaters experience a mean angular drift that rotates them toward two preferential orientations: parallel to the direction of wave propagation (longitudinal) or parallel to the wave crests (transverse). We develop a diffractionless model (Froude-Krylov approximation) to compute the mean yaw moment acting on floaters with arbitrary bending rigidity, small relative to the wavelength. Capillary forces are incorporated through a quasi-static volume formulation based on the fluid volume displaced by the floater and its meniscus. The model predicts that the preferential orientation is governed by the non-dimensional parameter $F = kL_x^2/\overline{h}$ recently introduced in Herreman et al. (J. Fluid Mech., vol.999, 2024, A92), where $k$ is the wavenumber, $L_x$ the floater length, and $\overline{h}$ the equilibrium immersion depth, provided that $\overline{h}$ accounts for capillary effects. The orientation depends on how $F$ compares to a critical value $F_c$, which is a function of the ratio of the flexural length to the floater length. These predictions are in good agreement with experiments performed with thin metal rectangular plates of various length, width and thickness.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops a diffractionless Froude-Krylov model for the mean yaw moment on thin elastic rectangular floaters in gravity waves, incorporating capillary effects via a quasi-static displaced-volume correction to the equilibrium immersion depth h-bar. It claims that the resulting preferential orientations (longitudinal or transverse) are controlled by the parameter F = k L_x² / h-bar relative to a critical F_c that depends on the ratio of flexural length to floater length, and that these predictions agree with experiments on metal plates of varying dimensions.

Significance. If the central approximation holds, the work supplies a compact, experimentally supported extension of the F parameter from Herreman et al. (2024) that folds capillarity into the immersion depth without introducing new free parameters. The explicit dependence of F_c on the flexural-length ratio and the reported experimental agreement constitute the main advance.

major comments (2)
  1. [§3, Eq. (8)] §3 (model derivation) and the paragraph following Eq. (8): the Froude-Krylov (diffractionless) closure is invoked for the mean yaw moment even though the governing parameter F can reach O(1) or larger for the reported plate lengths; no explicit bound on k L_x is supplied, nor is a comparison presented against a diffractive reference solution or a numerical check that quantifies the error in the time-averaged torque when k L_x is not ≪ 1. Because the quasi-static capillary correction modifies only the mean immersion depth and does not restore the neglected scattering, this assumption is load-bearing for the claimed predictive power of F.
  2. [§4.2] §4.2 (comparison with experiments): the agreement is stated to be good, but the manuscript does not report the range of k L_x realized in the data set or show that the subset of runs with k L_x > 0.3 still collapses onto the predicted F_c curve; without this, it is unclear whether the experimental support is restricted to the regime where the diffractionless assumption is safest.
minor comments (2)
  1. [Notation / Fig. 2] The definition of the flexural length ℓ_f should be restated explicitly in the notation section rather than only in the caption of Fig. 2, to avoid ambiguity when F_c is plotted versus ℓ_f / L_x.
  2. [Abstract, §1] In the abstract and §1 the phrase “small relative to the wavelength” is used for bending rigidity; a quantitative statement (e.g., D / (ρ g λ^4) ≪ 1) would clarify the regime.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The two major comments raise valid points about the range of validity of the diffractionless Froude-Krylov approximation and the need for more detailed experimental diagnostics. We address each below and will revise the manuscript to incorporate the requested information and checks.

read point-by-point responses

  1. Referee: [§3, Eq. (8)] §3 (model derivation) and the paragraph following Eq. (8): the Froude-Krylov (diffractionless) closure is invoked for the mean yaw moment even though the governing parameter F can reach O(1) or larger for the reported plate lengths; no explicit bound on k L_x is supplied, nor is a comparison presented against a diffractive reference solution or a numerical check that quantifies the error in the time-averaged torque when k L_x is not ≪ 1. Because the quasi-static capillary correction modifies only the mean immersion depth and does not restore the neglected scattering, this assumption is load-bearing for the claimed predictive power of F.

    Authors: We acknowledge that the manuscript does not provide an explicit bound on k L_x nor a direct comparison with a diffractive solution. The Froude-Krylov approximation is adopted because the mean yaw moment is obtained by integrating the undisturbed pressure field over the instantaneous wetted surface; for the time-averaged torque this leading-order contribution remains useful even when weak scattering is present. Nevertheless, we agree that quantifying the error when k L_x is not small is important. In the revision we will add the range of k L_x realized in the model calculations and experiments, together with a short discussion (supported by an order-of-magnitude estimate of the scattered potential) showing that the correction to the mean torque remains small for the parameter values considered. The capillary correction affects only the mean immersion depth and does not alter the diffractionless assumption, as noted. revision: yes

  2. Referee: [§4.2] §4.2 (comparison with experiments): the agreement is stated to be good, but the manuscript does not report the range of k L_x realized in the data set or show that the subset of runs with k L_x > 0.3 still collapses onto the predicted F_c curve; without this, it is unclear whether the experimental support is restricted to the regime where the diffractionless assumption is safest.

    Authors: We agree that the range of k L_x in the experimental data set should be reported explicitly and that a subset analysis for k L_x > 0.3 would strengthen the claim. In the revised §4.2 we will include the observed range of k L_x (which reaches values up to approximately 0.6 in the longest-plate runs) and will show the collapse of the k L_x > 0.3 subset onto the predicted F_c curve. Any modest deviations will be discussed in light of the approximation's expected accuracy. revision: yes

Circularity Check

1 steps flagged

Minor self-citation of F parameter; new capillary model and experiments provide independent content

specific steps
  1. self citation load bearing [Abstract]
    "The model predicts that the preferential orientation is governed by the non-dimensional parameter F = kL_x^2/overline{h} recently introduced in Herreman et al. (J. Fluid Mech., vol.999, 2024, A92)"

    The governing role of F is asserted by direct reference to the prior paper rather than re-derived from the new capillary-augmented equations; however the capillary modification itself and the experimental tests supply independent content, keeping the circularity minor.

full rationale

The derivation introduces a diffractionless Froude-Krylov model with a quasi-static capillary volume term that modifies equilibrium immersion depth h-bar. This yields the claim that orientation is governed by the same non-dimensional F as in prior work, now with capillary-adjusted h-bar. The cited source for F has author overlap, but the present model derivation, the explicit incorporation of meniscus volume, and the experimental comparisons are self-contained and do not reduce to the citation by construction. No fitted-input-as-prediction, self-definitional closure, or ansatz smuggling is exhibited in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model introduces no new free parameters or entities but relies on standard fluid dynamics approximations and a new quasi-static capillary model.

axioms (2)
  • domain assumption Froude-Krylov approximation is applicable for computing mean yaw moment on small floaters
    Stated as diffractionless model for arbitrary bending rigidity small relative to wavelength.
  • domain assumption Capillary forces can be incorporated via quasi-static volume formulation based on displaced fluid volume and meniscus
    Used to adjust equilibrium immersion depth h-bar.

pith-pipeline@v0.9.0 · 5556 in / 1395 out tokens · 41239 ms · 2026-05-08T05:34:17.773311+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · 1 internal anchor

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    work page 2025

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    Preferential orientation of slender elastic floaters in gravity waves

    Falkovich, Gregory, Weinberg, A, Denissenko, P & Lukaschuk, Sergey2005 Floater clustering in a standing wave.Nature435(7045), 1045–1046. Harris, Daniel M & Barotta, Jack-William2025 Propulsion and interaction of wave-propelled interfacial particles.Physical Review Fluids10(10), 100503. Herreman, W., Dhote, B., Danion, L. & Moisy, F.2024 Preferential orien...

    work page internal anchor Pith review Pith/arXiv arXiv 2024

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    Landau, L

    Kralchevsky, Peter A & Nagayama, Kuniaki2000 Capillary interactions between particles bound to interfaces, liquid films and biomembranes.Advances in colloid and interface science85(2-3), 145–192. Landau, L. D. & Lifshitz, E. M.1986 Theory of Elasticity, 3rd edn.,Course of Theoretical Physics, vol

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    cheerios effect

    Oxford: Pergamon Press. Mansfield, EH, Sepangi, HR & Eastwood, EA1997 Equilibrium and mutual attraction or repulsion of 0X0-23 B. Dhote et al. objects supported by surface tension.Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences355(1726), 869–919. Monsalve, Eduardo, Maurel, Agn`es, Pagneu...

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