Abstract The oscillation of a levitated drop is a widely used technique for the measurement of the surface tension and viscosity of liquids. Analyses are mainly based on theories developed in the nineteenth century for surface tension driven oscillations of a spherical, force-free, liquid drop. However, a complete analysis with both analytical and numerical approaches to study the damped oscillations of a viscous liquid drop remains challenging. We first propose in this work an extension of the theory that includes the coupled effects of surface tension and viscosity. The analytical solution permits derivation of both properties simultaneously, which is of interest for fluid with unknown viscosity. Then, the robustness of an Eulerian framework to simulate the fluid flow is discussed. Simulations of different oscillations modes for a liquid iron droplet immersed in a low-density gas and comparisons with the derived theory are detailed and presented.

中文翻译：

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零重力振荡下落的解析与数值模拟

摘要 悬浮液滴的振荡是一种广泛用于测量液体表面张力和粘度的技术。分析主要基于 19 世纪针对表面张力驱动的球形、无力液滴的振荡发展的理论。然而，使用解析和数值方法来研究粘性液滴的阻尼振荡的完整分析仍然具有挑战性。我们首先在这项工作中提出了理论的扩展，包括表面张力和粘度的耦合效应。解析解允许同时推导这两种性质，这对于粘度未知的流体很重要。然后，讨论了欧拉框架模拟流体流动的鲁棒性。