Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL, 60208, USA.
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, 60208, USA.
Nat Commun. 2018 Aug 7;9(1):3122. doi: 10.1038/s41467-018-05508-7.
Mixing of fluids and mixing of solids are both relatively mature fields. In contrast, mixing in systems where flowing and non-flowing regions coexist remains largely unexplored and little understood. Here we report remarkably persistent mixing and non-mixing regions in a three-dimensional dynamical system where randomness is expected. A spherical shell half-filled with dry non-cohesive particles and periodically rotated about two horizontal axes generates complex structures that vary non-trivially with the rotation angles. They result from the interplay between fluid-like mixing by stretching-and-folding, and solids mixing by cutting-and-shuffling. In the experiments, larger non-mixing regions predicted by a cutting-and-shuffling model alone can persist for a range of protocols despite the presence of stretching-and-folding flows and particle-collision-driven diffusion. By uncovering the synergy of simultaneous fluid and solid mixing, we point the way to a more fundamental understanding of advection driven mixing in materials with coexisting flowing and non-flowing regions.
混合液体和混合固体都是相对成熟的领域。相比之下，在存在流动和非流动区域共存的系统中进行混合，这方面的研究仍在很大程度上尚未探索，也知之甚少。在这里，我们在一个三维动力学系统中报告了非常持久的混合和非混合区域，而该系统中预计存在随机性。一个装满干燥非粘性颗粒的半球壳，围绕两个水平轴周期性地旋转，会产生复杂的结构，这些结构随旋转角度发生显著变化。它们是由拉伸和折叠的流体混合以及切割和混合的固体混合相互作用产生的。在实验中，尽管存在拉伸和折叠流动以及颗粒碰撞驱动的扩散，由切割和混合模型单独预测的较大非混合区域可以在一系列方案中持续存在。通过揭示同时进行的流体和固体混合的协同作用，我们为更深入地了解具有共存流动和非流动区域的材料中的对流驱动混合指明了方向。
