1. Department of Chemical Engineering and KITP, University of California, Santa Barbara, California 93106-5080, USA
2. Department of Physics and Center for Soft Matter Research, New York University, 2-4 Washington Place, New York, New York 10003, USA
3. Department of Physics, Haverford College, Haverford, Pennsylvania 19041, USA
4. Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
5. Department of Chemical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel

Correspondence to: D. J. Pine^1,2J. F. Brady⁴ Correspondence and requests for materials should be addressed to D.J.P. (Email: pine@nyu.edu); correspondence concerning the simulations should be addressed to J.F.B. (Email: jfb@cheme.caltech.edu).

Abstract

Systems governed by time reversible equations of motion often give rise to irreversible behaviour^{1, 2, 3}. 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 positions⁴. Similarly, slowly sheared suspensions of solid particles, which occur widely in nature and science⁵, 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 walk⁷. 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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