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

从水龙头流到一系列水滴的破碎是流体动力流动从连通的圆柱体到分离的水滴的拓扑转变的一个常见例子。对这种破裂的研究，包括夹断时的高度非线性动力学，不仅导致了处理新出现的奇点的新的数学方法的发展，而且还允许控制喷墨打印等相关工艺过程中液滴的形成。我们的目标是研究自由表面流动中的这种转变，特别是专注于液体射流被控制地分裂成两个子细丝(而不是衰变成液滴)(参见。无花果。洛杉矶)。虽然第一种描述这一现象的方法在理论上被认为是自由流动的牛顿射流(Paruchuri&Brenner)，但首先试图通过实验证明受控射流分裂的重点是微流体结构，其中聚合物流体射流被另一种同向流动的液体包围。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，并演示受控喷射分裂。喷射分裂不仅是一个有趣的基本流体动力学问题，而且也是一个具有技术意义的问题？S它可能提供一种生产细小纤维的新方法，并可能形成一种新的基于非液滴的、现在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.