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arxiv: 1907.02962 · v1 · pith:YAR6HJCCnew · submitted 2019-07-03 · ⚛️ physics.flu-dyn

Deformation and breakup of droplets in an oblique continuous air stream

Surendra Kumar Soni , Pavan Kumar Kirar , Pankaj Kolhe , Kirti Chandra Sahu This is my paper

Pith reviewed 2026-05-25 09:30 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords droplet breakupoblique air streamcritical Weber numberEotvos numberOhnesorge numberbag breakuphigh-speed imagingfluid dynamics
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0 comments X

The pith

Critical Weber numbers for bag breakup decrease sharply as air stream angle departs from cross-flow toward in-line.

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

The paper experimentally investigates how droplets with initial momentum deform and break up in an oblique continuous air stream at varying inclination angles. It determines the critical Weber numbers for the transition to bag-type breakup as functions of the Eötvös number, the air stream angle, and the Ohnesorge number. The droplet path starts rectilinear then becomes curvilinear once topological changes begin, with apparent acceleration and droplet size also affecting the breakup threshold. A sympathetic reader cares because the results indicate that flow direction strongly modulates the energy needed for breakup in non-perpendicular configurations.

Core claim

The authors establish that the critical Weber numbers for bag-type breakup are obtained as a function of the Eötvös number, angle of inclination of the air stream and the Ohnesorge number. The departure from the cross-flow arrangement shows a sharp decrease in the critical Weber number for the bag breakup which asymptotically reaches a value associated with the in-line flow configuration for the droplet breakup. The droplet follows a rectilinear motion initially that transforms to a curvilinear motion at later times when the droplet undergoes topological changes, and the apparent acceleration of the droplet and its size influence the critical Weber number for the bag breakup mode.

What carries the argument

The critical Weber number We_cr for vibrational-to-bag breakup transition, expressed as a function of Eötvös number Eo, inclination angle α, and Ohnesorge number Oh, extracted from high-speed imaging of droplet trajectories and deformation modes in oblique air streams.

If this is right

  • The apparent acceleration of the droplet influences the critical Weber number for bag breakup.
  • Droplet size affects the threshold for the bag breakup mode.
  • The droplet's motion changes from rectilinear to curvilinear upon onset of topological changes.
  • We_cr values approach those of opposed-flow breakup as the angle departs from the cross-flow arrangement.

Where Pith is reading between the lines

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

  • Models of aerodynamic droplet breakup should incorporate flow angle as an explicit parameter instead of defaulting to perpendicular incidence.
  • The observed asymptotic approach to in-line thresholds could be tested by extending the angle range closer to 180 degrees in controlled setups.
  • Industrial spray or atomization systems using angled air streams may achieve breakup at lower relative velocities than cross-flow predictions suggest.

Load-bearing premise

That breakup mode transitions can be unambiguously identified from high-speed images and that the air stream remains uniform and continuous, allowing direct attribution of We_cr variation to initial momentum and angle rather than imaging artifacts or flow non-uniformity.

What would settle it

Repeated experiments with a demonstrably uniform oblique air stream that show no dependence of We_cr on inclination angle α, or that yield identical We_cr values across all angles.

Figures

Figures reproduced from arXiv: 1907.02962 by Kirti Chandra Sahu, Pankaj Kolhe, Pavan Kumar Kirar, Surendra Kumar Soni.

Figure 1
Figure 1. Figure 1: Schematic diagram showing a liquid droplet freely falling under the action of gravity and subjected to an [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of the experimental set-up. It consists of a high-speed camera, a nozzle, a diffuser sheet, a light [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The breakup dynamics of a water droplet in the cross-flow condition ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The breakup dynamics of a water droplet in an oblique configuration ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Trajectory and the shape of the droplet at different times for [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Pressure distribution on the droplet subjected to air stream. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Trajectories of a water droplet (Oh ≈ 0.0015) exhibiting (a,c,e) the vibrational and (b,d,f) the bag breakup modes for (a,b) α = 0◦ , (c,d) α = 30◦ and (e,f) α = 60◦ . Next we investigate the path followed by the droplet subjected to an oblique air flow for different sets of Eo and W e as it plays important role in combustors designing and optimisation. Figs. 7(a,b), (c,d) and (e,f) correspond to α = 0◦ (c… view at source ↗
Figure 8
Figure 8. Figure 8: Breakup of a water droplet (Oh ≈ 0.0015) for (a) α = 0◦ , (b) α = 30◦ and (c) α = 60◦ . For each angle, the left side images are corresponding to drop shape just before reaching the air stream, and the right images are the same droplet corresponding to τ (written below the images) just before the onset of the bag breakup. Figs. 8(a), (b) and (c) show instantaneous snapshots of the droplet of different size… view at source ↗
Figure 9
Figure 9. Figure 9: Breakup of a water droplet (Oh ≈ 0.0015) at α = 0 (cross-flow configuration). The left side images are corresponding to drop shape just before entering the air stream and the right set of images are for the same droplet t = 23.67 ms. Then we investigate the effect of angle of the air stream, α on the critical Weber number W ecr. In [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Region maps showing the vibrational and the bag breakup modes in [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Variation of the transitional Weber number, [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: (a,c) The critical dimensional air velocity, [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The critical Weber number, W ecr versus Ohnesorge number, Oh for different values of Eo: (a) α = 0◦ , (b) α = 30◦ and (c) α = 60◦ [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Variations of the critical Weber number, [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
read the original abstract

We experimentally investigate the deformation and breakup of droplets interacting with an oblique continuous air stream. A high-speed imaging system is employed to record the trajectories and topological changes of the droplets of different liquids. The droplet size, the orientation of the air nozzle to the horizontal and fluid properties (surface tension and viscosity) are varied to study different breakup modes. We found that droplet possessing initial momentum prior to entering the continuous air stream exhibits a variation in the required Weber number for the vibrational to the bag breakup transition with a change in the angle of the air stream. The critical Weber numbers $(We_{cr})$ for the bag-type breakup are obtained as a function of the E\"{o}tv\"{o}s number $(Eo)$, angle of inclination of the air stream $(\alpha)$ and the Ohnesorge number $(Oh)$. It is found that although the droplet follows a rectilinear motion initially that transforms to a curvilinear motion at later times when the droplet undergoes topological changes. The apparent acceleration of the droplet and its size influence the critical Weber number for the bag breakup mode. The departure from the cross-flow arrangement shows a sharp decrease in the critical Weber number for the bag breakup which asymptotically reaches to a value associated with the in-line (opposed) flow configuration for the droplet breakup.

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 / 0 minor

Summary. The manuscript reports an experimental investigation using high-speed imaging of droplet deformation and breakup in an oblique continuous air stream. Droplet size, air-stream inclination angle α, and fluid properties are varied. The central claim is that the critical Weber number We_cr for the vibrational-to-bag breakup transition is a function of Eötvös number Eo, inclination angle α, and Ohnesorge number Oh, exhibiting a sharp decrease as α departs from cross-flow (90°) toward in-line configurations, with an asymptotic approach to the opposed-flow value.

Significance. If the reported We_cr(Eo, α, Oh) dependence is robust, the work supplies new empirical data on the effect of flow obliqueness on breakup thresholds, which could inform multiphase-flow models in atomization or aerosol applications. The noted transition from rectilinear to curvilinear droplet motion during topological change is a secondary observation. The study is purely experimental and does not include machine-checked proofs, reproducible code, or parameter-free derivations.

major comments (2)
  1. [Abstract] Abstract: the headline result that We_cr decreases sharply with departure from α = 90° rests on unambiguous classification of the vibrational-to-bag transition in high-speed images. No quantitative criteria (aspect-ratio threshold, bag-inflation time relative to aerodynamic time, or rim-feature presence) are stated for mode identification, so the functional dependence on α could partly reflect observer-dependent or imaging-artifact effects rather than the claimed momentum/angle mechanism.
  2. [Abstract] Abstract and implied results: no error bars, sample sizes per (Eo, α, Oh) condition, or data-exclusion criteria are reported. Without these, the statistical significance of the reported sharp decrease and the asymptotic approach to the in-line We_cr value cannot be assessed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and will incorporate revisions to improve clarity and statistical reporting.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline result that We_cr decreases sharply with departure from α = 90° rests on unambiguous classification of the vibrational-to-bag transition in high-speed images. No quantitative criteria (aspect-ratio threshold, bag-inflation time relative to aerodynamic time, or rim-feature presence) are stated for mode identification, so the functional dependence on α could partly reflect observer-dependent or imaging-artifact effects rather than the claimed momentum/angle mechanism.

    Authors: We agree that explicit quantitative criteria for mode classification would strengthen reproducibility. The full manuscript identifies the vibrational-to-bag transition through direct observation of bag inflation and rim formation in high-speed sequences, following conventions in prior droplet breakup literature. However, these criteria are not quantified in the text. In revision we will add a dedicated methods subsection specifying thresholds (e.g., aspect-ratio > 2.5 sustained for at least one aerodynamic time scale together with visible bag rim) and will include representative image sequences with annotations. revision: yes

  2. Referee: [Abstract] Abstract and implied results: no error bars, sample sizes per (Eo, α, Oh) condition, or data-exclusion criteria are reported. Without these, the statistical significance of the reported sharp decrease and the asymptotic approach to the in-line We_cr value cannot be assessed.

    Authors: The referee correctly notes the absence of these details. Each (Eo, α, Oh) condition was repeated at least five times with consistent outcomes, yet sample sizes, standard deviations, and exclusion rules (e.g., discarding runs with nozzle misalignment > 5°) were omitted. In the revised manuscript we will report error bars on all We_cr plots, tabulate the number of valid trials per condition, and state the exclusion criteria explicitly so that the robustness of the observed α dependence can be evaluated. revision: yes

Circularity Check

0 steps flagged

Purely experimental reporting with no derivations or self-referential steps

full rationale

The manuscript is an experimental study that records droplet trajectories and breakup modes via high-speed imaging and directly tabulates critical Weber numbers We_cr as functions of Eo, α, and Oh from observed transitions. No equations, models, or predictions are derived; the reported functional dependence is the measured data itself. No self-citations, ansatzes, or fitted inputs are invoked to support any claim, so the result does not reduce to its inputs by construction and remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

No free parameters or invented entities are introduced. The work rests on two standard domain assumptions about experimental conditions and image interpretation.

axioms (2)
  • domain assumption The air stream is continuous, uniform in velocity, and maintains constant direction throughout the interaction region.
    Invoked to define the oblique flow geometry and to compute Weber number from measured velocities and droplet size.
  • domain assumption Breakup regimes (vibrational versus bag) can be reliably distinguished by visual inspection of high-speed image sequences.
    Required to assign the transition point used to extract We_cr values as functions of Eo, α, and Oh.

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Reference graph

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