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Chaos and threshold for irreversibility in sheared suspensions

Pine, D. J. and Gollub, J. P. and Brady, J. F. and Leshansky, A. M. (2005) Chaos and threshold for irreversibility in sheared suspensions. Nature, 438 (7070). pp. 997-1000. ISSN 0028-0836. doi:10.1038/nature04380.

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Systems governed by time reversible equations of motion often give rise to irreversible behaviour. The transition from reversible to irreversible behaviour is fundamental to statistical physics, but has not been observed experimentally in many-body systems. The flow of a newtonian fluid at low Reynolds number can be reversible: for example, if the fluid between concentric cylinders is sheared by boundary motion that is subsequently reversed, then all fluid elements return to their starting positions. Similarly, slowly sheared suspensions of solid particles, which occur widely in nature and science, are governed by time reversible equations of motion. Here we report an experiment showing precisely how time reversibility6 fails for slowly sheared suspensions. We find that there is a concentration dependent threshold for the deformation or strain beyond which particles do not return to their starting configurations after one or more cycles. Instead, their displacements follow the statistics of an anisotropic random walk. By comparing the experimental results with numerical simulations, we demonstrate that the threshold strain is associated with a pronounced growth in the Lyapunov exponent (a measure of the strength of chaotic particle interactions). The comparison illuminates the connections between chaos, reversibility and predictability.

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Brady, J. F.0000-0001-5817-9128
Additional Information:© 2005 Nature Publishing Group. Received 8 August; accepted 25 October 2005. We appreciate discussions with L. G. Leal and G. Homsy. K. Knipmeyer and E. Knowlton provided assistance with data acquisition and reduction. This work was supported by the Keck Foundation (D.J.P.), the National Science Foundation (J.P.G.) and the US-Israel Binational Science Foundation (A.M.L.). The work was initiated during a granular physics workshop hosted by the Kavli Institute for Theoretical Physics at UCSB. Author Contributions D.J.P and J.P.G. were responsible for the experiments; J.F.B. and A.M.L. did the numerical simulations.
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W. M. Keck FoundationUNSPECIFIED
Binational Science Foundation (USA-Israel)UNSPECIFIED
Issue or Number:7070
Record Number:CaltechAUTHORS:20150331-092329031
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Official Citation:Pine, D. J., Gollub, J. P., Brady, J. F., & Leshansky, A. M. (2005). Chaos and threshold for irreversibility in sheared suspensions. [10.1038/nature04380]. Nature, 438(7070), 997-1000.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56237
Deposited On:31 Mar 2015 18:15
Last Modified:10 Nov 2021 20:56

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