This study investigates the unsteady evolution of buoyant oscillating bubbles situated near a rigid boundary via a boundary integral (BI) approach, with a primary objective of identifying universal patterns in axial and annular jetting. We verify the BI simulation against several purposely conducted experiments on electric-discharge bubbles performed inside a depressurized tank. Four collapse patterns of the bubble are identified, namely, (i) downward jet towards the wall, (ii) upward jet, (iii) bubble pinch-off caused by an annular jet, and (iv) quasi-spherical collapse. We categorize them in a phase diagram in the γ-δ parameter space (0 ≼ γ ≼ 2, 0 ≼ δ ≼ 0.6), where γ and δ are the dimensionless standoff parameter and buoyancy parameter, respectively. A new ‘upward jet regime’ is found for a large-buoyancy bubble (γ ≽ 0.3) initially attached to or very close to the wall (γ ≼ 0.5), in which an annular focusing flow causes a complete detachment of the bubble from the wall and further drives an upward liquid jet. In the downward jet regime, the axial jet velocity is found to exhibit a power-law scaling in the maximum curvature of the bubble surface κ, i.e., Vjet = ηκ0.7±0.04, but with a different prefactor η depending on γ. As for the annular jet, the neck radius evolution of the bubble substantially deviates from the classic scaling Rn ∝ τ0.5, where τ represents the time remaining before the pinch-off event. A logarithmic correction, y = Rn(− ln Rn)1/4 (Gordillo et al., [Phys. Rev. Lett. 96, 194501 (2005)]), makes the effective exponent αy closer to 0.5, αy = 0.535 ± 0.004, but cannot account for all the deviations. Importantly, we demonstrate that the annular jet dynamics does not reach a universal regime. Instead, the extracted exponents depend on the specific simulation setup, falling between the theoretical predictions of Gordillo et al. [Phys. Rev. Lett. 96, 194501 (2005)] and Eggers et al. [Phys. Rev. Lett. 98, 094502 (2007)]. This non-universality highlights that the bubble pinch-off dynamics exhibits a weak dependence on the initial dimensionless parameters, a consequence of the slow logarithmic convergence of the governing dynamics.

Axial jet and pinch-off scalings in attached buoyant bubbles

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发表日期：

2026年6月26日

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Lintao Zhou,
Ruinan Cui,
A-Man Zhang,
Zirui Liu,
Shuai Li

摘要

This study investigates the unsteady evolution of buoyant oscillating bubbles situated near a rigid boundary via a boundary integral (BI) approach, with a primary objective of identifying universal patterns in axial and annular jetting. We verify the BI simulation against several purposely conducted experiments on electric-discharge bubbles performed inside a depressurized tank. Four collapse patterns of the bubble are identified, namely, (i) downward jet towards the wall, (ii) upward jet, (iii) bubble pinch-off caused by an annular jet, and (iv) quasi-spherical collapse. We categorize them in a phase diagram in the γ-δ parameter space (0 ≼ γ ≼ 2, 0 ≼ δ ≼ 0.6), where γ and δ are the dimensionless standoff parameter and buoyancy parameter, respectively. A new ‘upward jet regime’ is found for a large-buoyancy bubble (γ ≽ 0.3) initially attached to or very close to the wall (γ ≼ 0.5), in which an annular focusing flow causes a complete detachment of the bubble from the wall and further drives an upward liquid jet. In the downward jet regime, the axial jet velocity is found to exhibit a power-law scaling in the maximum curvature of the bubble surface κ, i.e., V_jet = ηκ^0.7±0.04, but with a different prefactor η depending on γ. As for the annular jet, the neck radius evolution of the bubble substantially deviates from the classic scaling R_n ∝ τ^0.5, where τ represents the time remaining before the pinch-off event. A logarithmic correction, y = R_n(− ln R_n)^1/4 (Gordillo et al., [Phys. Rev. Lett. 96, 194501 (2005)]), makes the effective exponent α_y closer to 0.5, α_y = 0.535 ± 0.004, but cannot account for all the deviations. Importantly, we demonstrate that the annular jet dynamics does not reach a universal regime. Instead, the extracted exponents depend on the specific simulation setup, falling between the theoretical predictions of Gordillo et al. [Phys. Rev. Lett. 96, 194501 (2005)] and Eggers et al. [Phys. Rev. Lett. 98, 094502 (2007)]. This non-universality highlights that the bubble pinch-off dynamics exhibits a weak dependence on the initial dimensionless parameters, a consequence of the slow logarithmic convergence of the governing dynamics.