受限空间中固体盘卷吸气膜的自相似动力学：拓扑转变的一个简单原型
Self-similar dynamics of air film entrained by a solid disk in confined space: a simple prototype of topological transitions
摘要：
在流体动力学拓扑转换中，一个流体质量分裂成两个或两个合并成一个。例如，在蜂蜜滴形成时，蜂蜜从勺子滴下，蜂蜜被扩展成两个，因为连接它们的液体颈变薄到微米级。在拓扑结构由于分裂而改变的那一刻，物理观测量如表面曲率局部发散。这种奇异动力学已经引起了物理学家的广泛关注，揭示了自相似动力学的普遍性，与热力学中的临界现象有许多共同之处。已经发现了许多实验实例，其中包括电喷流和振动诱导射流喷发。然而，只有少数情况下已被物理上理解的基础上的方程，管理奇异动力学，即使在这种情况下，物理上的理解是数学上复杂的，不可避免地涉及微妙的数值计算。在这里，我们研究了在有限空间中，固体圆盘夹带的空气膜破碎成粘性液体，这导致了空气颈部的形成，变薄和破碎。结果，我们意外地发现，由于两个显著的实验特征，颈动力学方程可以解析求解：在奇异点附近只有一个与时间线性相关的长度尺度，描述奇异颈形状和速度场的普适尺度函数都是解析的。本可解的情况下，将是必不可少的，我们更好地理解奇异动力学，并将有助于揭示物理学的未解决的例子密切相关的日常生活中的现象和各种实际应用。
英文摘要：
In hydrodynamic topological transitions, one mass of fluid breaks into two or two merge into one. For example, in the honey-drop formation when honey dripping from a spoon, honey is extended to separate into two as the liquid neck bridging them thins down to micron scales. At the moment when topology changes due to the breakup, physical observables such as surface curvature locally diverges. Such singular dynamics have widely attracted physicists, revealing universality in their self-similar dynamics, which share much in common with critical phenomena in thermodynamics. Many experimental examples have been found, which include electric spout and vibration-induced jet eruption. However, only a few cases have been physically understood on the basis of equations that govern the singular dynamics and even in such a case the physical understanding is mathematically complicated inevitably involving delicate numerical calculations. Here, we study breakup of air film entrained by a solid disk into viscous liquid in a confined space, which leads to formation, thinning and breakup of the neck of air. As a result, we unexpectedly find that equations governing the neck dynamics can be solved analytically by virtue of two remarkable experimental features: only a single length scale linearly dependent on time remains near the singularity and universal scaling functions describing singular neck shape and velocity field are both analytic. The present solvable case would be essential for our better understanding of the singular dynamics and will help unveil the physics of unresolved examples intimately related to daily-life phenomena and diverse practical applications.
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。
