标题： 利用共振控制平移和旋转液滴内的混沌混合 显示英文标题

标题： Using Resonances to Control Chaotic Mixing within a Translating and Rotating Droplet

摘要： 增强和控制液滴内的混沌对流或混沌混合对于包括数字微流体装置在内的多种应用至关重要，这些装置使用微观的“离散”流体体积（液滴）作为微反应器。 在本工作中，我们考虑了一个平移的球形液滴的斯托克斯流动，并通过施加时间周期性的刚体旋转对其进行扰动。 利用动力系统工具，我们在以前的工作中已经证明，这种旋转不仅会导致一个或多个三维混沌混合区域，在这些区域中，混合是通过物质线的拉伸和折叠实现的，而且还提供了控制液滴内混沌混合区域大小和位置的可能性。 这种控制是通过适当调整旋转的振幅和频率来实现的，以便利用系统固有频率与外部强迫频率之间的共振。 在本文中，我们研究了旋转轴的方向对混沌混合区域的影响，作为第三个参数，并提出了一个实验装置来实现所讨论的技术。 显示英文摘要

摘要： Enhancing and controlling chaotic advection or chaotic mixing within liquid droplets is crucial for a variety of applications including digital microfluidic devices which use microscopic ``discrete'' fluid volumes (droplets) as microreactors. In this work, we consider the Stokes flow of a translating spherical liquid droplet which we perturb by imposing a time-periodic rigid-body rotation. Using the tools of dynamical systems, we have shown in previous work that the rotation not only leads to one or more three-dimensional chaotic mixing regions, in which mixing occurs through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of chaotic mixing within the drop. Such a control was achieved through appropriate tuning of the amplitude and frequency of the rotation in order to use resonances between the natural frequencies of the system and those of the external forcing. In this paper, we study the influence of the orientation of the rotation axis on the chaotic mixing zones as a third parameter, as well as propose an experimental set up to implement the techniques discussed.