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arxiv: 2605.19774 · v1 · pith:LPHSGFITnew · submitted 2026-05-19 · ⚛️ physics.flu-dyn

Self-similar breakup of a liquid ligament with a solid particle

Sanjay Shukla , Federico Toschi This is my paper

Pith reviewed 2026-05-20 02:16 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords liquid ligament breakupsolid particleself-similar dynamicsviscous regimeRayleigh-Plateau instabilitypinch-off timestretching ligamentdrop formation
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0 comments X

The pith

A solid particle triggers universal self-similar pinch-off in a stretching liquid ligament once the surface approaches it.

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

The paper examines how a single solid particle alters the breakup of a liquid ligament that is being stretched and thinned. It shows that particle-induced perturbations drive a universal pinch-off process in the viscous regime. After the ligament surface gets close to the particle, the breakup dynamics turn self-similar and lose dependence on the particle size. An analytical expression for the pinch-off time is derived from the balance between the ligament's stretching and the growth of the Rayleigh-Plateau instability. This expression matches the results of numerical simulations.

Core claim

We show that particle-induced perturbations trigger a universal pinch-off dynamics in the viscous regime. Once the ligament surface approaches the particle, the subsequent breakup becomes self-similar and independent of the particle size. We derive an analytical expression for the pinch-off time based on the interplay between ligament stretching and Rayleigh-Plateau instability, which agrees quantitatively with simulations.

What carries the argument

The competition between uniform ligament stretching and Rayleigh-Plateau instability after the surface approaches the particle, producing size-independent self-similar pinch-off.

If this is right

  • Pinch-off time follows a closed-form analytical prediction set by the stretching rate and instability growth.
  • Breakup dynamics become independent of particle diameter once the ligament surface reaches the particle.
  • The same self-similar sequence occurs for any localized perturbation that brings the surface into a similar configuration.
  • Quantitative agreement between the derived expression and direct numerical simulations confirms the controlling balance.

Where Pith is reading between the lines

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

  • The mechanism may set drop sizes in industrial sprays or coatings that contain suspended particles.
  • Similar size-independent self-similar breakup could appear when ligaments interact with bubbles or other fluid inclusions.
  • Extending the balance to include inertial or viscoelastic effects would test the limits of the viscous-regime assumption.
  • The derived pinch-off time formula could be inserted into larger-scale models of atomization processes.

Load-bearing premise

After the ligament surface approaches the particle, breakup is controlled exclusively by uniform stretching competing with the Rayleigh-Plateau instability, without meaningful effects from particle surface properties or three-dimensional flow around the particle.

What would settle it

A simulation or experiment that changes particle surface wettability or introduces significant three-dimensional flow effects around the particle and observes a shift in pinch-off time or loss of self-similarity would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.19774 by Federico Toschi, Sanjay Shukla.

Figure 1
Figure 1. Figure 1: FIG. 1. The setup showing a liquid ligament of density [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Volume renderings of a stretching ligament at five representative times are shown without particle in [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

The breakup of thinning (stretching) liquid ligaments is strongly influenced by localized perturbations arising from impurities or suspended particles. Using numerical simulations and analytical modelling, we investigate the role of a solid particle on the breakup dynamics of a stretching liquid ligament. We show that particle-induced perturbations trigger a universal pinch-off dynamics in the viscous regime. Once the ligament surface approaches the particle, the subsequent breakup becomes self-similar and independent of the particle size. We derive an analytical expression for the pinch-off time based on the interplay between ligament stretching and Rayleigh-Plateau instability, which agrees quantitatively with simulations. Our results reveal a universal mechanism by which localized perturbations control the breakup of ligaments containing solid particles.

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

1 major / 1 minor

Summary. The manuscript uses numerical simulations and analytical modeling to study how a solid particle affects the breakup of a stretching liquid ligament. It claims that in the viscous regime, particle-induced perturbations cause a universal self-similar pinch-off once the ligament surface reaches the particle; this dynamics is independent of particle size. An analytical expression for the pinch-off time is derived from the competition between uniform ligament stretching and Rayleigh-Plateau instability and is reported to agree quantitatively with the simulations.

Significance. If the central claim is substantiated, the work would identify a particle-triggered universal mechanism for ligament breakup in the viscous regime, with implications for atomization processes and multiphase flows. The parameter-free character of the derivation (no free parameters listed in the axiom ledger) and the direct comparison to simulations are positive features that would strengthen the contribution if the underlying 1D reduction is justified.

major comments (1)
  1. [Analytical modeling and derivation of pinch-off time] The derivation of the analytical pinch-off time (described in the abstract and the analytical-modeling section) rests on the assumption that, after the ligament surface approaches the particle, the evolution is controlled exclusively by uniform axial stretching competing with the Rayleigh-Plateau instability. The manuscript does not demonstrate that three-dimensional Stokes flow around the particle, no-slip boundary conditions, or moving-contact-line dynamics remain sub-dominant throughout the self-similar stage. Because this scale separation is required for both the claimed universality and the particle-size independence, the quantitative match with simulations cannot yet be regarded as confirmatory.
minor comments (1)
  1. [Abstract] The abstract states quantitative agreement between the analytical expression and simulations but supplies no error bars, regime-isolation criteria, or details on data selection; adding these would improve clarity without altering the central claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive feedback. We address the major comment below and will incorporate revisions to strengthen the justification of our modeling assumptions.

read point-by-point responses

  1. Referee: The derivation of the analytical pinch-off time (described in the abstract and the analytical-modeling section) rests on the assumption that, after the ligament surface approaches the particle, the evolution is controlled exclusively by uniform axial stretching competing with the Rayleigh-Plateau instability. The manuscript does not demonstrate that three-dimensional Stokes flow around the particle, no-slip boundary conditions, or moving-contact-line dynamics remain sub-dominant throughout the self-similar stage. Because this scale separation is required for both the claimed universality and the particle-size independence, the quantitative match with simulations cannot yet be regarded as confirmatory.

    Authors: We thank the referee for identifying this important point regarding the justification of the 1D reduction. Our fully three-dimensional simulations show that, once the ligament surface reaches the particle, the subsequent dynamics collapses onto a self-similar form that is independent of particle size (as quantified in the results section). This numerical evidence indicates that three-dimensional effects localized near the particle become sub-dominant relative to the global stretching and capillary-driven instability during the late-stage evolution. To make this scale separation explicit, we will revise the analytical-modeling section to include a brief timescale analysis comparing the particle-induced flow relaxation time to the self-similar pinch-off time, together with representative velocity-field snapshots from the simulations that illustrate the transition to axially uniform stretching away from the particle. These additions will directly support the claimed universality and particle-size independence while preserving the parameter-free character of the pinch-off-time derivation. revision: yes

Circularity Check

0 steps flagged

Derivation of pinch-off time from stretching and Rayleigh-Plateau competition is independent of simulation data

full rationale

The paper states that it derives an analytical expression for pinch-off time from the interplay between ligament stretching and Rayleigh-Plateau instability once the surface approaches the particle. This is presented as a first-principles reduction under the stated assumptions of uniform 1D stretching in the viscous regime. The quantitative agreement with simulations is described as validation rather than the origin of the expression or any fitted constants. No load-bearing self-citation, self-definitional step, or fitted-input-renamed-as-prediction is identifiable from the abstract or context; the central claim rests on external knowledge of Rayleigh-Plateau instability and stretching dynamics, making the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the standard viscous-regime assumption of the Rayleigh-Plateau instability and the modeling choice that particle effects become negligible once the surface approaches the particle; no explicit free parameters or new entities are stated.

axioms (1)
  • domain assumption Breakup after the ligament surface approaches the particle is governed by the interplay between ligament stretching and the Rayleigh-Plateau instability.
    This premise is invoked to derive the analytical pinch-off time expression.

pith-pipeline@v0.9.0 · 5637 in / 1391 out tokens · 66735 ms · 2026-05-20T02:16:53.198816+00:00 · methodology

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Reference graph

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