发表机构
Universidad de Sevilla（塞维利亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对有限尺寸自由液滴内的气泡破裂问题，通过求解轴对称Navier–Stokes方程，揭示了受限空间对气泡喷出行为的拓展效应，推导了喷出质量的标度关系，为海浪飞沫源函数研究提供了关键依据。
AI 中文摘要
在平坦液体表面破裂的气泡仅在奥内佐格数（Ohnesorge number）低于临界值Oh$_c\backsimeq0.043$时才会喷出液滴。我们探究当液体浴为有限尺寸液滴时，气泡的喷出量有多少。我们针对内部与半径为$λR_0$的自由液滴相切、半径为$R_0$的气泡（在$t=0$时刻破裂），求解了轴对称Navier–Stokes方程，研究的液气体积比$Λ=V_{\rm liq}/V_{\rm gas}=λ^3-1$范围为1/16至512，Oh数范围为0.005至0.11。喷出行为在Oh$_1=Oh_c(1+2β/λ)$时停止，其中$β\backsimeq0.83$，因此受限空间将喷出行为拓展到了在平坦表面下因黏度过高或气泡过小而无法产生喷出的液体体系。$1/λ$一阶项的两种效应导致了这一偏移：外表面附加的拉普拉斯超压，以及液壳惯性的降低。我们的核心结果关于喷出质量$M_e$，与液滴计数不同，该量在网格细化下收敛。当$Λ\backsimeq0.2$时，其满足$M_e=CδV_{\rm gas}V_{\rm liq}/(V_{\rm gas}+V_{\rm liq})$，其中$δ=1-Oh/Oh_1$，$C\backsimeq0.013$：两种体积以约化体积的形式组合。当液体充足时，该式简化为$M_e=CδV_{\rm gas}$，即气泡体积的固定比例，这与经典的射流液滴测量结果一致；当气体充足时，简化为$M_e=CδV_{\rm liq}$。喷出液体的比例跨越四个数量级，在最薄的液壳中超过三分之一，此时一种独特的双射流机制占据主导。由于空心液滴在破碎波浪中普遍存在，受限空间包含了平坦表面会排除的气泡，并确定了每个气泡的喷出量：这是海浪飞沫源函数的两个关键要素。
英文摘要
A bubble bursting from a drop of finite size (a hollow droplet) is the generic bursting event in a breaking wave, yet it has been studied almost exclusively at unbounded baths. We follow it from the puncture of the film to the spectrum of a spray, in axisymmetric simulations over liquid-to-gas volume ratios $Λ$ from $1/16$ to $512$ and Ohnesorge numbers from $0.005$ to $0.11$. Ejection ceases at $\mathit{Oh}_1=\mathit{Oh}_c(1+2β/λ)$, with $β\simeq0.83$ and $λ=(1+Λ)^{1/3}$: confinement extends ejection to bubbles too small to eject at a flat surface, and the distance $δ=1-\mathit{Oh}/\mathit{Oh}_1$ to that boundary organizes everything that follows. The collapse, driven by capillary waves, is that of a gas thread pinching next to its mouth, whether the liquid shell is punctured once or twice. The ejected volume is $M_e=C\,δ\,V_{\rm red}$, with $C\simeq0.013$ and $V_{\rm red}=V_{\rm gas}V_{\rm liq}/(V_{\rm gas}+V_{\rm liq})$ a reduced volume. Whatever the confinement, the first droplet is smallest at $δ\simeq0.2$ in units of the viscocapillary length $\ell_μ=μ^2/(ρσ)$ and at $δ\simeq0.3$ in units of the bubble radius $R_0$, where the unbounded bath also places its optimum. The largest reaches a tenth of $R_0$. Between them the census is exponential, with a scale set by $R_0$ and no lower cut-off: the smallest droplet a simulation records is set by its resolution, not by $\ell_μ$, which belongs to the pinch singularity rather than to the droplets. Mixed over bubble populations, the census gives spray spectra in closed form, whose shape measures the population. The bursting also produces hollow droplets, each a potential new generator.
Comments31 pages, 17 figures
