arXiv 2001.112332020-01-30physics.flu-dyncond-mat.soft

倾斜表面下悬滴的形状

Shape of pendant droplets under a tilted surface

J. De Coninck, J. C. Fernandez-Toledano, F. Dunlop, T. Huillet, A. Sodji

备注：: 8 pages, 5 figures
DOI：: 10.1016/j.physd.2020.132765

摘要：

对于接触线为半径为$r_0$的圆的悬垂液滴，我们推导出Bond数中一阶的关系式$mg\sinα={π\over2}γr_0\,(\cosθ^{\rm min}-\cosθ^{\rm max})$，其中$θ^{\rm min}$和$θ^{\rm max}$是后面（上坡）和前面（下坡）的接触角，$m$是液滴的质量，$γ$是液体的表面张力。债券（或Eötvös）编号为$Bo=mg/(2r_0γ)$。倾斜角$α$可从$α=0$（固定式下落）增加到$α=π/2$（固定在垂直壁上的下落）再到$α=π$（从天花板垂下）。重点将放在含$α=π/2$和$α=3π/4$的悬滴上。在相同的近似下精确计算液滴轮廓。结果进行了比较，表面进化模拟，显示出良好的协议高达约$Bo=1.2$，对应的半球形水滴的体积高达约$50\,μ$ L。还给出了每个接触角$θ^{\rm min}$和$θ^{\rm max}$的显式公式，并与几乎精确的表面evolver值进行了比较。

英文摘要：

For a pendant drop whose contact line is a circle of radius $r_0$, we derive the relation $mg\sinα={π\over2}γr_0\,(\cosθ^{\rm min}-\cosθ^{\rm max})$ at first order in the Bond number, where $θ^{\rm min}$ and $θ^{\rm max}$ are the contact angles at the back (uphill) and at the front (downhill), $m$ is the mass of the drop and $γ$ the surface tension of the liquid. The Bond (or Eötvös) number is taken as $Bo=mg/(2r_0γ)$. The tilt angle $α$ may increase from $α=0$ (sessile drop) to $α=π/2$ (drop pinned on vertical wall) to $α=π$ (drop pendant from ceiling). The focus will be on pendant drops with $α=π/2$ and $α=3π/4$. The drop profile is computed exactly, in the same approximation. Results are compared with surface evolver simulations, showing good agreement up to about $Bo=1.2$, corresponding for example to hemispherical water droplets of volume up to about $50\,μ$L. An explicit formula for each contact angle $θ^{\rm min}$ and $θ^{\rm max}$ is also given and compared with the almost exact surface evolver values.

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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英文摘要：

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