ABSTRACT Understanding spatiotemporal complexity1,2,3 is important to many disciplines, from biology4,5 to finance6. However, because it is seldom possible to achieve complete control over

the parameters that determine the behaviour of real complex systems, it has been difficult to study such behaviour experimentally. Here we demonstrate a simple microfluidic bubble generator

that shows stable oscillatory patterns (both in space and time) of unanticipated complexity and uniquely long repetition periods. At low flow rates, the device produces a regular stream of

bubbles of uniform size. As the flow increases, the system shows intricate dynamic behaviour typified by a stable limit cycle of order 29 bubbles per period, which repeats without change

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UNPREDICTABLE NATURE OF BUBBLE EVOLUTION Article Open access 01 December 2022 GALLOPING BUBBLES Article Open access 12 February 2025 UNIFIED FRAMEWORK FOR LASER-INDUCED TRANSIENT BUBBLE

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(Harvard University) for helpful discussions. P.G. acknowledges a postdoctoral fellowship from the Foundation for Polish Science. We thank the Harvard MRSEC for the use of high-speed cameras

and microfabrication facilities. This work was supported by the US Department of Energy (DE-FG02-00ER45852). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Chemistry and

Chemical Biology, Harvard University, 12 Oxford St., Cambridge, Massachusetts, USA Piotr Garstecki, Michael J. Fuerstman & George M. Whitesides * Institute of Physical Chemistry, Polish

Academy of Sciences, Kasprzaka 44/52, 01-224, Warsaw, Poland Piotr Garstecki Authors * Piotr Garstecki View author publications You can also search for this author inPubMed Google Scholar *

Michael J. Fuerstman View author publications You can also search for this author inPubMed Google Scholar * George M. Whitesides View author publications You can also search for this author

inPubMed Google Scholar CORRESPONDING AUTHORS Correspondence to Piotr Garstecki or George M. Whitesides. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial

interests. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION (PDF 90 KB) RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Garstecki, P., Fuerstman, M.

& Whitesides, G. Oscillations with uniquely long periods in a microfluidic bubble generator. _Nature Phys_ 1, 168–171 (2005). https://doi.org/10.1038/nphys176 Download citation *

Received: 07 July 2005 * Accepted: 14 October 2005 * Published: 04 December 2005 * Issue Date: 01 December 2005 * DOI: https://doi.org/10.1038/nphys176 SHARE THIS ARTICLE Anyone you share

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