Letter | Published:

Separating stretching from folding in fluid mixing

Nature Physics volume 7, pages 477480 (2011) | Download Citation

Abstract

Fluid mixing controls many natural and industrial processes, including the spread of air pollution1, mass transfer and reactions in microfluidic devices2,3 and the detection of odours or other chemical signals4. Strongly nonlinear flows enhance mixing by chaotic advection5,6, stretching and folding7,8 fluid volumes. Though these processes have been studied in simple models9,10, stretching and folding are difficult to distinguish in real flows with complex spatiotemporal structure. Here we report measurements of these two distinct processes in a two-dimensional laboratory flow. We decouple stretching and folding using tools developed for analysing glassy solids11 and colloids12, breaking fluid deformation into a linear, affine component (primarily stretching) and a nonlinear, non-affine component (primarily folding). Short-time deformation is dominated by stretching, whereas folding occurs only after fluid elements are elongated. The relative strength of the two processes depends strongly on space and time; folding-dominated regions are initially isolated, but later grow to fill space.

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Acknowledgements

This work was supported in part by the facilities and staff of the Yale University Faculty of Arts and Sciences High Performance Computing Center. We acknowledge financial support from the US National Science Foundation under grant No DMR-0906245.

Author information

Affiliations

  1. Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA

    • Douglas H. Kelley
    •  & Nicholas T. Ouellette

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Contributions

N.T.O. conceived the original idea and supervised the project. D.H.K. ran the experiments and analysed the data. Both authors wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Nicholas T. Ouellette.

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DOI

https://doi.org/10.1038/nphys1941

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