Static shapes of levitated viscous drops
Static shapes of levitated viscous drops
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悬浮粘性液滴的静态形状
DOI：
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发表时间：
2005
影响因子：
3.7
通讯作者：
U. Lange
中科院分区：
文献类型：
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作者：
L. Duchemin;J. Lister;U. Lange
我们考虑悬浮的一滴熔融玻璃以上的球形多孔模具，通过该模具的空气是以恒定的速度注入。假设玻璃与空气相比具有足够的粘性，使得液滴中的运动可以忽略不计。因此，静态平衡形状由支承气垫中的润滑压力与杨-拉普拉斯方程之间的耦合决定。液滴的上表面处于恒定的大气压力下;液滴的下表面的静态形状使用薄空气膜的润滑理论来计算。匹配的上表面的无座曲率的曲率的模具引起一系列的毛细“边缘”波的边缘附近的下降，其规模与修改后的毛细数的权力。静态解的几个分支被发现，使得对于某些液滴体积有多个解，但是对于其他液滴体积没有物理上合理的解。与实验和完整的Navier-Stokes方程计算的比较表明，该过程的稳定性可以从静态形状的解分支预测，并与边缘波的持久性下降的中心。这一建议仍有待正式的稳定性分析证实。
We consider the levitation of a drop of molten glass above a spherical porous mould, through which air is injected with constant velocity. The glass is assumed to be sufficiently viscous compared to air that motion in the drop is negligible. Thus static equilibrium shapes are determined by the coupling between the lubricating pressure in the supporting air cushion and the Young–Laplace equation. The upper surface of the drop is under constant atmospheric pressure; the static shape of the lower surface of the drop is computed using lubrication theory for the thin air film. Matching of the sessile curvature of the upper surface to the curvature of the mould gives rise to a series of capillary ‘brim’ waves near the edge of the drop which scale with powers of a modified capillary number. Several branches of static solutions are found, such that there are multiple solutions for some drop volumes, but no physically reasonable solutions for other drop volumes. Comparison with experiments and full Navier–Stokes calculations suggests that the stability of the process can be predicted from the solution branches for the static shapes, and related to the persistence of brim waves to the centre of the drop. This suggestion remains to be confirmed by a formal stability analysis.