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Published September 7, 2017 | Published + Supplemental Material
Journal Article Open

On the role of initial velocities in pair dispersion in a microfluidic chaotic flow


Chaotic flows drive mixing and efficient transport in fluids, as well as the associated beautiful complex patterns familiar to us from our every day life experience. Generating such flows at small scales where viscosity takes over is highly challenging from both the theoretical and engineering perspectives. This can be overcome by introducing a minuscule amount of long flexible polymers, resulting in a chaotic flow dubbed 'elastic turbulence'. At the basis of the theoretical frameworks for its study lie the assumptions of a spatially smooth and random-in-time velocity field. Previous measurements of elastic turbulence have been limited to two-dimensions. Using a novel three-dimensional particle tracking method, we conduct a microfluidic experiment, allowing us to explore elastic turbulence from the perspective of particles moving with the flow. Our findings show that the smoothness assumption breaks already at scales smaller than a tenth of the system size. Moreover, we provide conclusive experimental evidence that 'ballistic' separation prevails in the dynamics of pairs of tracers over long times and distances, exhibiting a memory of the initial separation velocities. The ballistic dispersion is universal, yet it has been overlooked so far in the context of small scales chaotic flows.

Additional Information

© 2017 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Received: 05 July 2016; Accepted: 25 June 2017; Published online: 07 September 2017. We thank A. Frishman for the helpful and extensive discussions of the theory and O. Hirschberg for useful discussions of the mathematical and statistical analysis; E.A. had fruitful discussions with J. Bec, S. Musacchio, D. Vincenzi, EW Saw and R. Chetrite, kindly organised by the latter; both authors gained from thorough discussions with V. Lebedev, as well as the helpful reading and comments of an earlier version of the manuscript by G. Boffetta, A. Celani and M. Feldman. This work is supported by the Lower Saxony Ministry of Science and Culture Cooperation (Germany; grant #VWZN2729) and the Israel Science Foundation (ISF; grant #882/15). Author Contributions: V.S. proposed the study of pair dispersion in elastic turbulence. E.A. designed the experiment, performed the measurements and analysed the results. Both authors discussed the results, the relevant literature, and wrote the manuscript. Data availability: The data sets generated and analysed during the current study are available in the figshare repository, doi:10.6084/m9.figshare.511299124. All programming and computer aided analysis in this work relies on open-source projects; all based on tools from the SciPy ecosystem41, primarily using IPython42 as an interactive computational environment, Pandas43 for data structures, and Matplotlib44 for plotting. Much of the source code developed in the course of this study is available as open-source at: https://github.com/eldad-a/ridge-directed-ring-detector; https://github.com/eldad-a/particle-tracking; https://github.com/eldad-a/natural-cubic-smoothing-splines The author declares no competing financial interests.

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August 19, 2023
August 19, 2023