Nonlinear dynamics of free liquid surfaces: Controlled splitting of a liquid jet

从水龙头流出的水流破碎成一系列的水滴，这是一个日常的例子，说明水动力流动经历了从连接的圆柱体到分离的水滴的拓扑转变。对这种分裂的研究，包括在针尖处的高度非线性动力学，不仅导致了处理新出现的奇点的新数学方法的发展，而且允许在喷墨打印等相关技术过程中控制液滴的形成。我们的目标是研究自由表面流动中的这种转变，特别关注液体射流的控制分裂成两个亚细丝（而不是它的衰变成液滴）（参见图la）。虽然描述这种现象的第一种方法在理论上被认为是自由流动的牛顿射流（Paruchuri & Brenner），但首先尝试通过实验证明受控射流分裂集中在微流体装置上，其中聚合流体射流被另一种共流动液体包围。在与实验人员的密切合作下，我们计划将Paruchuri和Brenner的理论分析扩展到技术上更相关的两相流情况，并演示受控射流分裂。射流分裂不仅构成了一个有趣的基本流体动力学问题，而且与技术相关äs它可能提供一种生产小纤维的新途径，并可能形成一种新的非液滴的、连续的微流体的基础。

The fragmentation of a water stream from a faucet into a sequence of drops is aneveryday example of a hydrodynamical flow undergoing a topological transition from a connected cylinder to separated drops. Studies of this breakup including the highly nonlinear dynamics at pinch-off did not only lead to the development of new mathematical methods to deal with the emerging singularities but also allowed to control the drop formation in relevant technological processes like inkjet printingWe aim at studying such transitions in free-surface flows specifically focusing on controlled Splitting of a liquid jet into two subfilaments (instead of its decay into droplets) (cf. Fig. la). While a first approach to describe the phenomenon theoretically considered a free-flowing Newtonian jet (Paruchuri & Brenner), first attempts to experimentally demonstrate controlled jet Splitting focus on a microfluidic setup where a polymeric fluid jet is surrounded by another co-flowing liquid. In close cooperation with experimentalists, we plan to extend the theoretical analysis of Paruchuri and Brenner to the technologically more relevant two-phase flow Situation and to demonstrate controlled jet Splitting. Jet Splitting does not only constitute an interesting fundamental fluid dynamical problem but is also of technological relevance äs it may provide a novel route to producing small fibers and may form the basis of a new non-droplet-based, continuous-now microfmidics.