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arXiv 2304.02460physics.flu-dyn
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自由表面气泡坍塌的动力学:重力与粘度的影响

Dynamics of collapse of free-surface bubbles: effects of gravity and viscosity

Sangeeth Krishnan, Baburaj A. Puthenveettil, Emil J. Hopfinger

AI总结:

本文研究了自由表面气泡腔的轴对称坍塌动力学,基于不同 Bond 数和 Ohnesorge 数的实验提出了标度律,揭示了毛细力驱动下粘度与重力对坍塌过程中扭折切向与法向速度及体积通量的影响。

摘要:

浮在液-气界面上的气泡顶部薄膜破裂导致气泡腔的轴对称坍塌。我们基于气泡半径 $R$ 定义的 Bond 数(${10^{-3}<Bo\leq1}$)和 Ohnesorge 数(${10^{-3}<Oh<10^{-1}}$)范围内的实验,提出了这种腔体坍塌的标度律。腔体坍塌是由毛细力驱动的过程,粘度和重力分别影响腔体边界上的前驱毛细波和静态气泡形状。坍塌特征由扭折的切向和法向速度描述,扭折由顶部薄膜破裂后凹形腔体开口与凸形气泡腔边界的交点形成。切向速度 $U_t$ 在坍塌过程中恒定,表示为 $U_t=4.5~U_c{\mathcal{W}}_R$,其中 $U_c$ 为毛细速度,${\mathcal{W}}_R(Oh,Bo)={(1-\sqrt{Oh {\mathscr{L}}} )^{-1/2}}$ 为前驱毛细波引起的波阻因子,$\mathscr{L}(Bo)$ 为扭折运动的路径修正。扭折法向运动源于薄膜破裂后腔内气压骤降导致的整体腔体内向收缩。该法向速度在赤道平面以 $U_c$ 标度,在腔体底部 $\overline{U}_{nb}=U_c(Z_c/R)({\mathcal{W}_R}/ {\mathscr{L}})$,其中 $Z_c(Bo)$ 为静态腔深。完全由收缩贡献的腔体填充总体积通量标度为 ${Q_T\simeq 2πR Z_c U_c}$,且在整个坍塌过程中保持恒定。

英文摘要:

The rupture of the thin film at the top of a bubble floating at a liquid-gas interface leads to the axisymmetric collapse of the bubble cavity. We present scaling laws for such a cavity collapse, established from experiments conducted with bubbles spanning a wide range of Bond (${10^{-3}<Bo\leq1}$) and Ohnesorge numbers (${10^{-3}<Oh<10^{-1}}$), defined with the bubble radius $R$. The cavity collapse is a capillary-driven process, with a dependency on viscosity and gravity affecting, respectively, precursory capillary waves on the cavity boundary, and the static bubble shape. The collapse is characterised by tangential and normal velocities of the kink, formed by the intersection of the concave cavity opening after the top thin film rupture, with the convex bubble cavity boundary. The tangential velocity $U_t$ is constant during the collapse and is shown to be $U_t=4.5~U_c{\mathcal{W}}_R$, where $U_c$ is the capillary velocity and ${\mathcal{W}}_R(Oh,Bo)={(1-\sqrt{Oh {\mathscr{L}}} )^{-1/2}}$ is the wave resistance factor due to the precursory capillary waves, with $\mathscr{L}(Bo)$ being the path correction of the kink motion. The movement of the kink in the normal direction is part of the inward shrinkage of the whole cavity due to the sudden reduction of gas pressure inside the bubble cavity after the thin film rupture. This normal velocity is shown to scale as $U_c$ in the equatorial plane, while at the bottom of the cavity $\overline{U}_{nb}=U_c(Z_c/R)({\mathcal{W}_R}/ {\mathscr{L}})$, where $Z_c(Bo)$ is the static cavity depth. The total volume flux of cavity-filling, which is entirely contributed by this shrinking, scales as ${Q_T\simeq 2πR Z_c U_c}$; remains a constant throughout the collapse.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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