Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell
Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell
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DOI：
10.1017/jfm.2019.453
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发表时间：
2019-06
影响因子：
3.7
通讯作者：
I. Shukla;N. Kofman;G. Balestra;Lailai Zhu;F. Gallaire
中科院分区：
文献类型：
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作者：
I. Shukla;N. Kofman;G. Balestra;Lailai Zhu;F. Gallaire
我们在这里研究实验，数值计算和使用润滑的方法，形状，速度和润滑膜厚度分布的液滴上升在垂直的Hele-Shaw细胞。液滴被静止的不混溶流体包围，并且纯粹由于浮力而移动。两种介质之间的低密度差异有助于在毛细管数$Ca$介于$0.03$和$0.35$之间的制度中操作，其中$Ca=\unicode[STIX]{x1 D 707}_{o}U_{d}/\unicode[STIX]{x1 D 6 FE}$是根据周围的油粘度$\unicode[STIX]{x1 D 707}_{o}$构建的，液滴速度$U_{d}$和表面张力$\unicode[STIX]{x1 D 6 FE}$。实验数据表明，在该区域内，液滴速度不受薄润滑膜厚度和动态弯月面的影响。在等粘性条件下，实验和三维数值计算得到的油膜厚度分布吻合较好。平均膜厚度由Aussillous & Quéré（Phys. Fluids，第12卷（10），2000，第100页）很好地捕获。2367-2371）模型。液滴还表现出“双体船”形状，这已经在实验上被确定为压力驱动的对应物（Huerre等人，物理修订信函：第115（6）卷，2015，064501）。这种模式已合理化使用二维润滑方程。特别是，我们表明，这种奇特的膜厚分布是内在相关的液滴的运动引起的通量的各向异性。
We study here experimentally, numerically and using a lubrication approach, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two media helps to operate in a regime with capillary number $Ca$ lying between $0.03$ and $0.35$ , where $Ca=\unicode[STIX]{x1D707}_{o}U_{d}/\unicode[STIX]{x1D6FE}$ is built with the surrounding oil viscosity $\unicode[STIX]{x1D707}_{o}$ , the droplet velocity $U_{d}$ and surface tension $\unicode[STIX]{x1D6FE}$ . The experimental data show that in this regime the droplet velocity is not influenced by the thickness of the thin lubricating film and the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional numerical results of the film thickness distribution agree well with each other. The mean film thickness is well captured by the Aussillous & Quéré (Phys. Fluids, vol. 12 (10), 2000, pp. 2367–2371) model with fitting parameters. The droplet also exhibits the ‘catamaran’ shape that has been identified experimentally for a pressure-driven counterpart (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501). This pattern has been rationalized using a two-dimensional lubrication equation. In particular, we show that this peculiar film thickness distribution is intrinsically related to the anisotropy of the fluxes induced by the droplet’s motion.