Courrech du Pont Sylvain, Eggers Jens
Laboratoire Matière et Systèmes Complexes, Université de Paris, CNRS, 75205 Paris cedex 13, France.
School of Mathematics, University of Bristol, Bristol BS8 1UG, United Kingdom
Proc Natl Acad Sci U S A. 2020 Dec 22;117(51):32238-32243. doi: 10.1073/pnas.2019287117. Epub 2020 Dec 7.
When a fluid interface is subjected to a strong viscous flow, it tends to develop near-conical ends with pointed tips so sharp that their radius of curvature is undetectable. In microfluidic applications, tips can be made to eject fine jets, from which micrometer-sized drops can be produced. Here we show theoretically that the opening angle of the conical interface varies on a logarithmic scale as a function of the distance from the tip, owing to nonlocal coupling between the tip and the external flow. Using this insight we are able to show that the tip curvature grows like the exponential of the square of the strength of the external flow and to calculate the universal shape of the interface near the tip. Our experiments confirm the scaling of the tip curvature as well as of the interface's universal shape. Our analytical technique, based on an integral over the surface, may also have far wider applications, for example treating problems with electric fields, such as electrosprays.
当流体界面受到强粘性流作用时，它往往会形成近乎锥形的末端，其尖端非常尖锐，以至于其曲率半径无法检测到。在微流体应用中，可以使尖端喷射出细流，由此可以产生微米级大小的液滴。在此我们从理论上表明，由于尖端与外部流之间的非局部耦合，锥形界面的开口角度随距尖端距离的对数尺度而变化。利用这一见解，我们能够表明尖端曲率像外部流强度平方的指数那样增长，并计算出尖端附近界面的通用形状。我们的实验证实了尖端曲率以及界面通用形状的比例关系。我们基于对表面进行积分的分析技术可能也有更广泛的应用，例如处理电场问题，如电喷雾。
