Fragkopoulos Alexandros A, Pairam Ekapop, Berger Eric, Fernandez-Nieves Alberto
School of Physics, Georgia Institute of Technology , Atlanta, Georgia 30332-0430, United States.
Department of Food Engineering, King Mongkut's Institute of Technology Ladkrabang , Bangkok 10520, Thailand.
Langmuir. 2018 Jan 23;34(3):1218-1224. doi: 10.1021/acs.langmuir.7b02280. Epub 2017 Oct 19.
Toroidal droplets in a viscous liquid are unstable and transform into single or multiple spherical droplets. For thin tori, this can happen via the Rayleigh-Plateau instability causing the breakup of cylindrical jets. In contrast, for thick tori, this can happpen via the shrinking of the "hole". In this work, we use the thin-torus limit to directly measure the growth rate associated with capillary disturbances. In the case of toroidal droplets inside a much more viscous liquid, we even obtain the full dispersion relation, which is in agreement with theoretical results for cylindrical jets. For thick tori, we employ particle image velocimetry to determine the flow field of a sinking toroidal drop inside another viscous liquid. We find that the presence of the "hole" greatly suppresses one of the circulation loops expected for sinking cylinders. Finally, using the flow field of a shrinking toroidal droplet and the time-reversal symmetry of the Stokes equations, we theoretically predict the expected shape deformation of an expanding torus and confirm the result experimentally using charged toroidal droplets.
粘性液体中的环形液滴是不稳定的，会转变为单个或多个球形液滴。对于细环，这可能通过瑞利 - 普拉托不稳定性导致圆柱形射流破裂而发生。相比之下，对于粗环，这可能通过“孔”的收缩而发生。在这项工作中，我们利用细环极限直接测量与毛细扰动相关的增长率。在粘性大得多的液体中的环形液滴情况下，我们甚至得到了完整的色散关系，这与圆柱形射流的理论结果一致。对于粗环，我们采用粒子图像测速技术来确定另一种粘性液体中下沉环形液滴的流场。我们发现“孔”的存在极大地抑制了下沉圆柱体预期的一个环流。最后，利用收缩环形液滴的流场和斯托克斯方程的时间反演对称性，我们从理论上预测了膨胀环预期的形状变形，并使用带电环形液滴通过实验证实了这一结果。
