Foundations of chaotic mixing
Foundations of chaotic mixing
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DOI：
10.1098/rsta.2003.1356
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发表时间：
2004-05-15
期刊：
影响因子：
--
通讯作者：
Ottino, JM
中科院分区：
文献类型：
--
作者：
Wiggins, S;Ottino, JM
最简单的混合问题对应于流体与其自身的混合;这种情况提供了一个基础上的主题休息。这里的目标是研究混合独立的机制，用于创建运动和审查的理论要素，主要集中在数学基础和最小模型。所考虑的流动有两种类型：二维（2D）“闪烁流”或三维（3D）管道流。考虑到连续3D管道流中的混合关键取决于横截面混合，并且许多微流体应用涉及连续流，我们专注于2D流中混合的基本方面，因为它们提供了一个基础，使我们能够理解更复杂的情况。面包师变换被视为描述动力系统框架的核心。特别是，存在混合特征的层次结构，伯努利-->混合-->各态历经，根据混合的质量排序（最强的先）。最重要的设计过程中，我们展示了如何所谓的链接扭曲映射作为一个最小的混合图片的功能，提供了一个数学结构，用于理解在许多微混合器已经建成的2D流的类型，并给出保证最佳质量的混合条件。这些概念的扩展导致基于第一原理的设计，而无需进行冗长的计算。
The simplest mixing problem corresponds to the mixing of a fluid with itself; this case provides a foundation on which the subject rests. The objective here is to study mixing independently of the mechanisms used to create the motion and review elements of theory focusing mostly on mathematical foundations and minimal models. The flows under consideration will be of two types: two-dimensional (2D) 'blinking flows', or three-dimensional (3D) duct flows. Given that mixing in continuous 3D duct flows depends critically on cross-sectional mixing, and that many microfluidic applications involve continuous flows, we focus on the essential aspects of mixing in 2D flows, as they provide a foundation from which to base our understanding of more complex cases. The baker's transformation is taken as the centrepiece for describing the dynamical systems framework. In particular, a hierarchy of characterizations of mixing exist, Bernoulli --> mixing --> ergodic, ordered according to the quality of mixing (the strongest first). Most importantly for the design process, we show how the so-called linked twist maps function as a minimal picture of mixing, provide a mathematical structure for understanding the type of 2D flows that arise in many micromixers already built, and give conditions guaranteeing the best quality mixing. Extensions of these concepts lead to first-principle-based designs without resorting to lengthy computations.