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arxiv: 2604.04559 · v1 · submitted 2026-04-06 · ⚛️ physics.flu-dyn

Cavitation-bubble Interaction with an Initially Perturbed Free Surface

Jingyu Gu , Zirui Liu , A-Man Zhang , Shuai Li This is my paper

Pith reviewed 2026-05-10 20:14 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords cavitation bubblefree surfacemeniscus perturbationcoalescencenon-coalescencestand-off parameterpower-law scalingRayleigh-Taylor instability
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The pith

Cavitation bubble interactions with a perturbed free surface divide into coalescence and non-coalescence regimes separated by a critical stand-off parameter.

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

This paper examines how a spark-generated cavitation bubble interacts with a free surface that begins with a controlled initial meniscus created by a thin rod. The interaction produces a pronounced downward cavity whose behavior depends on the non-dimensional stand-off parameter gamma and the meniscus height. Two regimes appear: coalescence, in which the cavity merges with the bubble and allows air to vent, and non-coalescence, in which the cavity remains separate and reaches a maximum length that scales as gamma to a power near -2.7 when inertia dominates. An analytical model that couples the Rayleigh-Plesset equation for bubble motion with nonlinear Rayleigh-Taylor instability theory reproduces the observed trends and indicates that the meniscus height exerts only secondary influence. These regime distinctions matter for applications that rely on controlling bubble-induced jets, erosion, or pressure waves near liquid surfaces.

Core claim

The coupled cavity-bubble system exhibits two distinct regimes—coalescence and non-coalescence—separated by a critical condition governed by the non-dimensional stand-off parameter γ and the initial meniscus height hm. In the non-coalescence regime, the maximum cavity length hc follows a power-law scaling hc∝γ^α with α=-2.7 (experiments) and α=-2.6 (simulations) for 1.5≲γ≲3. An analytical model based on the Rayleigh-Plesset equation combined with nonlinear Rayleigh-Taylor instability theory captures the trend and confirms that hm plays only a secondary role relative to γ. In the coalescence regime, atmospheric air vents into the bubble through the merged cavity, weakening the collapse.

What carries the argument

The non-dimensional stand-off parameter γ, which sets the boundary between coalescence and non-coalescence regimes and governs the power-law scaling of maximum cavity length hc through coupling of Rayleigh-Plesset bubble dynamics with nonlinear Rayleigh-Taylor instability analysis.

If this is right

  • In the non-coalescence regime the cavity proceeds through inception, expansion, and rebound or jetting phases.
  • Deviations from the power-law scaling occur for gamma below 1.5 due to strong nonlinearity and for gamma above 3 due to surface tension and viscosity.
  • In the coalescence regime air enters the bubble, which reduces collapse intensity and peak pressure.
  • Compressibility and boundary-layer effects increase in importance as gamma decreases.
  • The critical condition that separates the two regimes depends on both gamma and the initial meniscus height hm.

Where Pith is reading between the lines

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

  • The reported power-law scaling could be used to estimate cavity penetration depths in designs involving bubbles near liquid surfaces without needing detailed meniscus measurements.
  • The same regime framework might apply to other controlled initial surface shapes beyond rod-induced menisci, allowing broader prediction of coalescence thresholds.
  • Engineering systems could deliberately select the non-coalescence regime to limit air venting and thereby moderate collapse pressures for noise or erosion control.
  • Numerical or experimental checks at gamma values well below 1 or above 4 would test whether additional regimes emerge when viscosity or tension dominate.

Load-bearing premise

The assumption that the Rayleigh-Plesset equation combined with nonlinear Rayleigh-Taylor instability theory adequately describes cavity evolution and that the initial meniscus height hm exerts only secondary influence relative to the stand-off parameter γ.

What would settle it

Measure or simulate the maximum cavity length hc over a continuous range of gamma values from 1.2 to 3.5 and test whether the data in the interval 1.5 to 3 follow a power law with exponent approximately -2.7 while deviations appear below 1.5 and above 3 as stated.

Figures

Figures reproduced from arXiv: 2604.04559 by A-Man Zhang, Jingyu Gu, Shuai Li, Zirui Liu.

Figure 1
Figure 1. Figure 1: (a) Schematic of experimental setup. The bubble is initiated coaxially with the thin rod covered by super-hydrophilic coating in a 300 × 300 × 300 mm3 water tank. An image of the meniscus is shown in the inset on the top left. (b) Comparison between representative experiments of free-surface–bubble interaction (i) without and (ii) with perturbation. The standoff parameter 𝛾 for both experiments are 1.30. T… view at source ↗
Figure 2
Figure 2. Figure 2: (a) A schematic of the numerical model of free-surface–bubble interaction. The 𝑧 axis is coaxial with the thin rod while the origin 𝑂 is located on the free surface. The bubble is initiated at point 𝑂𝑏 located beneath the free surface at depth 𝐻 with a initial radius of 𝑅0. (b) Configuration of the computational domain. The cavity length ℎ is the distance from the cavity bottom to the initial undisturbed f… view at source ↗
Figure 3
Figure 3. Figure 3: Schematic for the analytical model of the meniscus ( [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Two typical experiments of bubble interaction with a perturbed free surface for large standoff [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Four representative experiments of critical condition for [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Three typical experiments of cavity–bubble coalescence scenario for [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of cavity and bubble evolution between numerical simulation and experiment for the [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison between simulation results and experimental data for the evolution of ( [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of cavity and bubble evolution between numerical simulation and experiment for the [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of cavity and bubble evolution between numerical simulation and experiment for the [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of cavity and bubble evolution between numerical simulation and experiment for [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of the fluid field pressure between the simulations with (red circles) and without [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Dependence of cavity length on governing parameters of [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: (a) Maximum cavity length ℎ𝑐 as a function of the standoff parameter 𝛾. Magenta circles correspond to experimental data with ℎ𝑚 ranging from 0.2 to 0.8 mm, while blue solid lines represent simulation results. ℎ𝑐 decreases monotonically with increasing 𝛾. (b) The same data in (a) are presented in a doubly logarithmic plot. The plot within the range of 1.5 ≲ 𝛾 ≲ 3 reveals a power law of ℎ𝑐 ∝ 𝛾 𝛼, with fitte… view at source ↗
Figure 15
Figure 15. Figure 15: Flow fields in the vicinity of the cavity. Contours of velocity magnitude (left) and pressure (right) [PITH_FULL_IMAGE:figures/full_fig_p027_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Schematic of cavity evolution. (a) A small bowl-shaped depression forms due to the hindrance of the no-slip boundary condition around the thin rod during the rise of the water hump (blue dotted area). (b) The water hump reaches its maximum height ℎ 𝑓 when the bubble reaches its maximum radius. The cavity grows downwards due to the relatively large local pressure gradient (red dotted area) and attains its … view at source ↗
Figure 17
Figure 17. Figure 17: (a) Doubly logarithmic plot for variation of 𝑈0 with 𝛾. Experimental data, numerical results obtained from the FVM and BI method, and theoretical results obtained with (5.7) are brought into comparison. The FVM simulation results are the same as those when ℎ𝑚 = 0.8 mm in figure 14. ℎ 𝑓 obtained from (5.4), FVM simulation, and BI simulation are plotted in the inset. The experimental uncertainties of 𝑈0 and… view at source ↗
Figure 18
Figure 18. Figure 18: Comparisons between (a) numerical results obtained from FVM (blue solid lines) and (b) analytical results obtained from (5.11) (orange solid lines). The dependence between ℎ𝑚 and ℎ𝑐 are plotted in (a) and (b). 𝛾 increases from 1.4 to 3 at a 0.2 interval. Both results are normalized to [0,1] for clearer comparison. The analytical calculations exhibit a similar tendency to the numerical results. The non￾dim… view at source ↗
Figure 19
Figure 19. Figure 19: Comparison of cavity and bubble evolution between numerical simulation and experimental [PITH_FULL_IMAGE:figures/full_fig_p034_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Comparison of cavity evolution across four distinct configurations: (i) free surface without [PITH_FULL_IMAGE:figures/full_fig_p035_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: (a) Comparison of non-dimensional bubble radius evolution in a free field among experimental data, theoretical predictions (derived from the RP equation), and numerical results (obtained from BI (Klaseboer & Khoo 2004) and FVM simulation). All calculations were conducted with identical 𝜀 and 𝑅0 values of 125 and 0.1623, respectively. (b) Computational domain verification of three different scales. We cond… view at source ↗
Figure 22
Figure 22. Figure 22: Convergence analysis of the mesh cell size. Simulations with four different minimum mesh cell [PITH_FULL_IMAGE:figures/full_fig_p038_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: (a) Doubly logarithmic plot for the variation of maximum cavity length ℎ𝑐 versus the standoff parameter 𝛾 for different radii of the thin rod. The radii of the thin rod are 0.2 mm (triangles), 0.35 mm (circles), and 0.5mm (diamonds). The experimental results exhibit the same fitted power-law relationship of −2.7 exponent. (b) Three typical experiments performed with the three thin rod radii. The maximum c… view at source ↗
Figure 24
Figure 24. Figure 24: Comparisons of experiments with different depths of the thin rod. The thin rod is highlighted [PITH_FULL_IMAGE:figures/full_fig_p039_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Comparisons between compressible and incompressible FVM models for the ( [PITH_FULL_IMAGE:figures/full_fig_p040_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Comparisons between experimental observations and numerical predictions obtained using [PITH_FULL_IMAGE:figures/full_fig_p040_26.png] view at source ↗
read the original abstract

The interaction of a spark-generated cavitation bubble with an initially perturbed free surface is investigated experimentally, numerically, and analytically. By exploiting contact-line pinning, we accurately prescribe an initial meniscus with a thin, hydrophilic-coated rod inserted into the liquid. A pronounced surface cavity, driven by the oscillating bubble, forms and penetrates downward to a scale comparable to the bubble itself. The coupled cavity-bubble system exhibits two distinct regimes -- coalescence and non-coalescence -- separated by a critical condition governed by the non-dimensional stand-off parameter $\gamma$ and the initial meniscus height $h_m$. In the non-coalescence regime, the cavity evolves through inception, expansion, and rebound/jetting. The maximum cavity length $h_c$ follows a power-law scaling $h_c\propto\gamma^{\alpha}$ with $\alpha=-2.7$ (experiments) and $\alpha=-2.6$ (simulations) for $1.5\lesssim\gamma\lesssim3$, where inertia dominates. Deviations emerge for $\gamma\lesssim1.5$ (strong nonlinearity) and $\gamma\gtrsim3$ (surface tension and viscosity become noticeable). An analytical model based on the Rayleigh-Plesset equation combined with nonlinear Rayleigh-Taylor instability theory captures the trend and confirms that $h_m$ plays only a secondary role relative to $\gamma$. In the coalescence regime, atmospheric air vents into the bubble through the merged cavity, weakening the collapse intensity and reducing the associated pressure peak. We also examine air/liquid compressibility and boundary layer effects, whose significance grows as $\gamma$ decreases. These findings are relevant to surface-jetting technologies, cavitation-erosion mitigation, and underwater-noise suppression.

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

0 major / 4 minor

Summary. The manuscript investigates the interaction of a spark-generated cavitation bubble with an initially perturbed free surface, using contact-line pinning to control the initial meniscus. It identifies two regimes—coalescence and non-coalescence—separated by a critical condition involving the stand-off parameter γ and initial meniscus height hm. In the non-coalescence regime, the maximum cavity length hc follows a power-law scaling hc ∝ γ^α with α ≈ −2.7 (experiments) and α ≈ −2.6 (simulations) for 1.5 ≲ γ ≲ 3 in the inertia-dominated range; an analytical model combining the Rayleigh-Plesset equation with nonlinear Rayleigh-Taylor instability theory reproduces the observed trend and indicates that hm plays a secondary role. In the coalescence regime, air venting through the merged cavity weakens collapse intensity. The work also discusses compressibility and boundary-layer effects.

Significance. If the reported scaling and regime separation hold, the study is significant for advancing understanding of bubble-free-surface dynamics under controlled perturbations. The multi-method approach (experiment, simulation, and analytical modeling) provides robustness, and the identification of a clear power-law in the inertia-dominated window offers a falsifiable prediction that can be tested in related setups. The findings have direct relevance to applications including surface-jetting technologies, cavitation-erosion mitigation, and underwater-noise suppression. The confirmation that hm is secondary relative to γ is a useful simplification for modeling.

minor comments (4)
  1. [Abstract] The abstract reports scaling exponents without associated uncertainties or error bars; including these (e.g., from fits to the experimental and simulation datasets) would allow readers to assess the precision of α = −2.7 and −2.6.
  2. [Abstract] The deviations from the power-law scaling for γ ≲ 1.5 and γ ≳ 3 are noted qualitatively; a more quantitative discussion of the transition points and the relative importance of nonlinearity, surface tension, and viscosity would improve clarity.
  3. [Abstract] The analytical model is described as capturing the trend, but the abstract does not provide the explicit equations or the manner in which the nonlinear Rayleigh-Taylor growth rate is coupled to the Rayleigh-Plesset solution; adding these details (perhaps as a short derivation) would make the confirmatory role of the model easier to evaluate.
  4. [Abstract] The manuscript mentions examination of air/liquid compressibility and boundary-layer effects, but the abstract does not indicate whether these are quantified (e.g., via additional simulations or scaling arguments) or merely discussed qualitatively.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, the accurate summary of our findings, and the recommendation for minor revision. We appreciate the positive assessment of the work's significance for bubble-free-surface dynamics and its relevance to applications such as surface-jetting and cavitation-erosion mitigation.

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper reports the two regimes, critical condition on γ and hm, and power-law scaling hc ∝ γ^α (with α ≈ -2.7/-2.6) as direct outcomes of experimental observations and numerical simulations in the inertia-dominated window. The analytical model invokes pre-existing Rayleigh-Plesset and nonlinear Rayleigh-Taylor equations only to capture the observed trend and to confirm hm is secondary; it does not derive the exponent or reduce the reported scaling to a fit of the same data by construction. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work appear in the provided material, and the central claims remain independently supported by the data rather than by redefinition or statistical forcing.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard bubble dynamics and fluid instability models plus empirical scaling from data; no new entities are postulated, and the analytical confirmation uses pre-existing equations rather than ad-hoc fitting.

free parameters (1)
  • scaling exponent alpha = -2.7
    The value alpha approximately -2.7 is obtained by fitting the observed maximum cavity length versus standoff parameter in the inertia-dominated range.
axioms (2)
  • domain assumption Rayleigh-Plesset equation governs the radial dynamics of the cavitation bubble
    Invoked as the foundation for the analytical model of bubble oscillation coupled to the surface cavity.
  • domain assumption Nonlinear Rayleigh-Taylor instability describes the evolution of the free-surface cavity
    Combined with the Rayleigh-Plesset equation to derive the trend for cavity length.

pith-pipeline@v0.9.0 · 5615 in / 1651 out tokens · 40280 ms · 2026-05-10T20:14:59.392891+00:00 · methodology

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Reference graph

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