Fluid and solute transfer in X-junctions between straight channels is shown to depend critically on the junction angle in the Stokes flow regime. Experimentally, water and a water-dye solution are injected at equal flow rates in two facing channels of the junction: Planar Laser Induced fluorescence (PLIF) measurements show that the largest part of each injected fluid "bounces back" preferentially into the outlet channel at the lowest angle to the injection; this is opposite to the inertial case and requires a high curvature of the corresponding streamlines. The proportion of this fluid in the other channel decreases from 50% at 90\degree to zero at a threshold angle. These counterintuitive features reflect the minimization of energy dissipation for Stokes flows. Finite elements numerical simulations of a 2D Stokes flow of equivalent geometry con rm these results and show that, below the threshold angle 33.8\degree recirculation cells are present in the center part of the junction and separate the two injected flows of the two solutions. Reducing further leads to the appearance of new recirculation cells with lower flow velocities.
Controlled reattachment in separated flows: a variational approach to recirculation length reduction
采用变分法推导了分离流中回流长度对定常强迫的敏感性的解析表达式。本文对雷诺数为$40 \leq Re \leq 120$的二维圆柱定常绕流进行了亚临界和超临界区域的线性灵敏度分析。确定了对体积强迫和壁吹/吸最敏感的区域。控制配置，减少再循环长度的基础上设计的灵敏度信息，特别是小缸用作控制装置在主缸的尾流，在缸壁和流体吸入。对全非线性Navier-Stokes方程计算的验证表明，对于小振幅控制，具有很好的一致性。系统地研究了受控流的线性稳定性。在中等雷诺数下，我们观察到，控制减少回流长度的区域对应于它对与旋涡脱落相关的最不稳定全局模式具有稳定作用的区域，而该属性在较大雷诺数下不再成立。
A variational front-tracking method for multiphase flow with triple junctions
Fakultät für Mathematik, Universität Regensburg（雷根斯堡大学数学学院）；Dipartimento di Mathematica, Università di Trento（特伦托大学数学系）；School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）
