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首页> 外文期刊>Journal of Fluid Mechanics >Linked twist map formalism in two and three dimensions applied to mixing in tumbled granular flows
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Linked twist map formalism in two and three dimensions applied to mixing in tumbled granular flows

机译：二维和三个维度的链接扭曲图形式主义适用于混合颗粒流

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摘要

We study the mixing properties of two systems: (i) a half-filled quasi-two-dimensional circular drum whose rotation rate is switched between two values and which can be analysed in terms of the existing mathematical formalism of linked twist maps; and (ii) a half-filled three-dimensional spherical tumbler rotated about two orthogonal axes bisecting the equator and with a rotational protocol switching between two rates on each axis, a system which we call a three-dimensional linked twist map, and for which there is no existing mathematical formalism. The mathematics of the three-dimensional case is considerably more involved. Moreover, as opposed to the two-dimensional case where the mathematical foundations are firm, most of the necessary mathematical results for the case of three-dimensional linked twist maps remain to be developed though some analytical results, some expressible as theorems, are possible and are presented in this work. Companion experiments in two-dimensional and three-dimensional systems are presented to demonstrate the validity of the flow used to construct the maps. In the quasi-two-dimensional circular drum, bidisperse (size-varying or density-varying) mixtures segregate to form lobes of small or dense particles that coincide with the locations of islands in computational Poincare sections generated from the flow model. In the 3d spherical tumbler, patterns formed by tracer particles reveal the dynamics predicted by the flow model.
机译：我们研究了两个系统的混合特性：（i）半填充的准二维圆鼓，其转速在两个值之间切换，并且可以根据链接的扭曲图的现有数学形式来分析; （ii）一个半填充的三维球形不倒翁，它绕两等分赤道的正交轴旋转，并且旋转协议在每个轴上的两个速率之间切换，该系统称为三维链接扭曲图，为此，没有现有的数学形式主义。三维案例的数学涉及更多。此外，与二维情况下数学基础牢固的情况相反，对于三维链接扭曲图情况，大多数必要的数学结果仍有待开发，尽管一些分析结果（某些可表达为定理）是可能的，并且在这项工作中介绍。提出了在二维和三维系统中的同伴实验，以证明用于构建地图的流程的有效性。在准二维圆鼓中，双分散（尺寸变化或密度变化）混合物分离形成小颗粒或密颗粒的裂片，与流动模型生成的计算庞加莱截面中的岛位置重合。在3d球形不倒翁中，由示踪剂颗粒形成的图案揭示了流动模型预测的动力学。

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