Foundations of chaotic mixing

S Wiggins, JM Ottino

Research output: Contribution to journalArticle (Academic Journal)peer-review

266 Citations (Scopus)

Abstract

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.
Translated title of the contributionFoundations of chaotic mixing
Original languageEnglish
Pages (from-to)937 - 970
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume362 (1818)
Publication statusPublished - 15 May 2004

Bibliographical note

Publisher: Royal Soc London
Other identifier: IDS Number: 818RU

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