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arxiv: 2507.09189 · v2 · submitted 2025-07-12 · ⚛️ physics.flu-dyn

Size Amplification of Jet Drops due to Insoluble Surfactants

Jun Eshima , Tristan Aur\'egan , Palas Kumar Farsoiya , St\'ephane Popinet , Howard A. Stone , Luc Deike This is my paper

Pith reviewed 2026-05-19 04:56 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords bubble burstingjet dropsinsoluble surfactantsMarangoni stressesaerosol generationcavity collapsesurface tension isotherm
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0 comments X

The pith

Insoluble surfactants increase the radius of jet drops from small bursting bubbles by altering cavity collapse.

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

This paper studies how insoluble surfactants change jet drop ejection when bubbles burst at a contaminated surface. For small bubbles that lack precursor capillary waves, the presence of surfactants leads to larger drops rather than the smaller ones seen with larger bubbles. The size increase arises because Marangoni stresses reshape the focusing of the collapsing cavity. Experiments and simulations agree closely once the measured surface-tension isotherm is inserted as the equation of state. The result revises expectations for the sizes of aerosols released from contaminated liquid surfaces.

Core claim

For bubbles without precursor capillary waves, a regime characteristic of small bubbles, insoluble surfactants increase the ejected jet drop radius. This reverses the trend observed for larger bubbles. The reversal occurs because Marangoni stresses induced by surfactant concentration gradients modify the focusing of the collapsing cavity. Quantitative agreement between laboratory experiments and numerical simulations is reached by using the measured equilibrium surface-tension versus concentration relation directly as the equation of state.

What carries the argument

Marangoni stresses generated by surfactant concentration gradients that reshape the focusing dynamics of the collapsing cavity.

If this is right

  • Aerosol size distributions produced by bursting bubbles in contaminated environments will shift toward larger drops in the small-bubble regime.
  • Jet velocity and drop-size predictions require inclusion of surfactant-driven Marangoni stresses to match observations for small bubbles.
  • The size-amplification effect is tied to the absence of precursor capillary waves and does not overturn the radius-reduction trend for larger bubbles.
  • Numerical models of bubble bursting achieve quantitative accuracy when the measured surface-tension isotherm is supplied as the equation of state.

Where Pith is reading between the lines

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

  • The size amplification may increase the atmospheric transport of surface-bound material from surfactant-rich waters such as the ocean.
  • Similar cavity-focusing modifications could appear in other drop-ejection processes that involve surface-active contaminants.
  • Controlled experiments that systematically vary bubble diameter and surfactant concentration would map the transition between the two opposing trends.

Load-bearing premise

The equilibrium surface-tension isotherm measured under static conditions can be used as the equation of state for the rapidly deforming interface without large deviations from non-equilibrium adsorption kinetics or extra interfacial rheology.

What would settle it

Direct measurement of the radii of jet drops ejected by small bubbles (below the precursor-wave size threshold) with and without insoluble surfactant, expecting a clear increase in radius when surfactant is present.

Figures

Figures reproduced from arXiv: 2507.09189 by Howard A. Stone, Jun Eshima, Luc Deike, Palas Kumar Farsoiya, St\'ephane Popinet, Tristan Aur\'egan.

Figure 1
Figure 1. Figure 1: FIG. 1. Surfactant effects on jet drops. (a) Laplace number [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Effect of the surfactant parameter [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Self-similar profile comparison between a clean [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Surface bubbles in the environment or engineering configurations, such as the ocean-atmosphere interface, sparkling wine, or during volcanic eruptions typically live on contaminated surfaces. A particularly common type of contamination is surface active agents (surfactants). We consider the effect of insoluble surfactant on jet drop formation by bubble bursting. Contrary to the observed trend that surfactants decrease the ejected drop radius for bubbles with precursor capillary waves, we find that surfactants increase the ejected drop radius for bubbles without precursor capillary waves - a regime characteristic of small bubbles. Consequently, the results have fundamental implications for understanding aerosol distributions in contaminated conditions. We find that the trend reversal is due to the effect of Marangoni stresses on the focusing of the collapsing cavity. We demonstrate quantitative agreement on the jet velocity and drop size between laboratory experiments and numerical simulations by using the measured surface tension dependence on surfactant concentration as the equation of state for the simulations. *Jun Eshima and Tristan Aur\'egan contributed equally to this work.

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 manuscript claims that insoluble surfactants reverse the usual trend and amplify the ejected jet-drop radius for small bubbles that lack precursor capillary waves (a regime characteristic of small bubbles), due to Marangoni stresses altering cavity focusing during collapse. This is supported by laboratory experiments showing increased drop sizes and by axisymmetric simulations that insert the independently measured equilibrium surface-tension isotherm directly into the boundary condition, yielding quantitative agreement on jet velocity and drop radius.

Significance. If the result holds, the work has implications for aerosol generation and size distributions in surfactant-contaminated settings such as the ocean-atmosphere interface. The assessment is strengthened by the use of an independent surface-tension isotherm (rather than fitting to the jet-drop data) and by the direct, quantitative match between measured and simulated jet velocities and drop sizes.

major comments (2)
  1. [Numerical Methods] Numerical Methods / Equation of state: The simulations adopt the measured static sigma(c) isotherm as the dynamic constitutive relation in the Marangoni-stress boundary condition. Because the central claim of size amplification rests on the resulting alteration of cavity focusing, the manuscript must justify or test the validity of this equilibrium assumption under the high strain rates of cavity collapse (e.g., via a sensitivity study to dilatational viscosity or adsorption kinetics).
  2. [Results] Results: The distinction between the 'with precursor waves' and 'without precursor waves' regimes is load-bearing for the reported trend reversal. The paper should supply explicit quantitative criteria (bubble radius, Bond number, or capillary-wave amplitude threshold) that separate the two regimes and confirm that the small-bubble experiments fall unambiguously in the no-wave regime.
minor comments (2)
  1. [Figures] Figure captions and text should consistently report the number of experimental realizations and the uncertainty (standard deviation or 95 % confidence interval) on measured drop radii and jet velocities.
  2. [Abstract] The equal-contribution statement for the first two authors belongs in the author-contributions section rather than the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each of the major comments below and indicate the revisions made to strengthen the paper.

read point-by-point responses

  1. Referee: [Numerical Methods] Numerical Methods / Equation of state: The simulations adopt the measured static sigma(c) isotherm as the dynamic constitutive relation in the Marangoni-stress boundary condition. Because the central claim of size amplification rests on the resulting alteration of cavity focusing, the manuscript must justify or test the validity of this equilibrium assumption under the high strain rates of cavity collapse (e.g., via a sensitivity study to dilatational viscosity or adsorption kinetics).

    Authors: We thank the referee for highlighting this important consideration. For insoluble surfactants, the surface concentration evolves according to the surface continuity equation with convection and diffusion, and the surface tension is determined instantaneously from the local concentration via the measured isotherm. This approach is standard in the literature for insoluble surfactants. However, to directly address the potential effects of high strain rates, we will include in the revised manuscript a sensitivity analysis varying the surface dilatational viscosity over a range consistent with literature values for similar surfactants. The results show that the jet drop amplification persists, supporting the robustness of our findings under the equilibrium isotherm assumption. revision: yes

  2. Referee: [Results] Results: The distinction between the 'with precursor waves' and 'without precursor waves' regimes is load-bearing for the reported trend reversal. The paper should supply explicit quantitative criteria (bubble radius, Bond number, or capillary-wave amplitude threshold) that separate the two regimes and confirm that the small-bubble experiments fall unambiguously in the no-wave regime.

    Authors: We agree that explicit criteria will improve clarity. In the revised version, we will add quantitative definitions of the regimes, including a critical bubble radius below which precursor waves are absent (based on our experimental observations and prior literature), corresponding Bond numbers, and a threshold for capillary wave amplitude. We will confirm with both experimental images and simulation results that the small bubbles in our study (with radii less than approximately 1 mm) fall clearly in the no-precursor-wave regime, as no waves are visible prior to cavity collapse. revision: yes

Circularity Check

0 steps flagged

No circularity: independent isotherm measurements and separate bursting experiments

full rationale

The paper obtains the surface-tension isotherm sigma(c) from separate equilibrium measurements and inserts it directly into the Marangoni boundary condition of axisymmetric simulations; jet velocity and drop size are then compared to independent laboratory bursting experiments. No parameter is fitted to the jet-drop data, no self-citation supplies a uniqueness theorem that forces the result, and the reported size amplification for small bubbles follows from the simulated cavity-focusing dynamics rather than being imposed by construction. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the applicability of an equilibrium surface-tension isotherm to a fast, unsteady flow and on the fidelity of the numerical discretization of Marangoni stresses.

axioms (1)
  • domain assumption The measured surface tension versus surfactant concentration provides a sufficient equation of state for the dynamic simulation.
    Invoked when the isotherm is inserted into the boundary condition for the Navier-Stokes solver.

pith-pipeline@v0.9.0 · 5720 in / 1178 out tokens · 35502 ms · 2026-05-19T04:56:59.313213+00:00 · methodology

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Reference graph

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