The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Foundations of chaotic mixing
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.
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Cites
Chaotic Mixer for Microchannels
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Self-citationErgodic problems of classical mechanics
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CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
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Passive mixing in a three-dimensional serpentine microchannel
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Self-citationChaotic Transport in Dynamical Systems
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Self-citationIntroduction: mixing in microfluidics
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Self-citation
Cited by
Seemann, R., Brinkmann, M., Pfohl, T., & Herminghaus, S. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/1/016601 · Cited by 1,049
Microfluidic systems for chemical kinetics that rely on chaotic mixing in droplets
Bringer, M. R., Gerdts, C. J., Song, H., Tice, J. D., & Ismagilov, R. F. (2004) · Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.2003.1364 · Cited by 416
Imaging and quantifying mixing in a model droplet micromixer
Stone, Z. B., & Stone, H. A. (2005) · Physics of Fluids · doi:10.1063/1.1929547 · Cited by 136
Priye, A., Yu, Y., Hassan, Y. A., & Ugaz, V. M. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1612924114 · Cited by 18
Metadata
- Authors
- Wiggins, S., & Ottino, J. M.
- Venue
- Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 2004-05-15
- Volume
- 362
- Issue
- 1818
- Pages
- 937-970
- ISSN
- 1364-503X (ISSN-L)
- 1471-2962
- OpenAlex
- W2007080427
- Cited by
- 362
- References
- 25
- FWCI
- 18.52
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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