Chaos and threshold for irreversibility in sheared suspensions

D. J. Pine, J. P. Gollub, J. F. Brady, A. M. Leshansky

Research output: Contribution to journalArticle

Abstract

Systems governed by time reversible equations of motion often give rise to irreversible behaviour1-3. 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 positions 4. 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.

Original languageEnglish (US)
Pages (from-to)997-1000
Number of pages4
JournalNature
Volume438
Issue number7070
DOIs
StatePublished - Dec 15 2005

Fingerprint

Suspensions
Physics
Growth

ASJC Scopus subject areas

  • General

Cite this

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

Chaos and threshold for irreversibility in sheared suspensions. / Pine, D. J.; Gollub, J. P.; Brady, J. F.; Leshansky, A. M.

In: Nature, Vol. 438, No. 7070, 15.12.2005, p. 997-1000.

Research output: Contribution to journalArticle

Pine, DJ, Gollub, JP, Brady, JF & Leshansky, AM 2005, 'Chaos and threshold for irreversibility in sheared suspensions', Nature, vol. 438, no. 7070, pp. 997-1000. https://doi.org/10.1038/nature04380
Pine, D. J. ; Gollub, J. P. ; Brady, J. F. ; Leshansky, A. M. / Chaos and threshold for irreversibility in sheared suspensions. In: Nature. 2005 ; Vol. 438, No. 7070. pp. 997-1000.
@article{90e504b4f9a343c5bdda840acab8f1a7,
title = "Chaos and threshold for irreversibility in sheared suspensions",
abstract = "Systems governed by time reversible equations of motion often give rise to irreversible behaviour1-3. 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 positions 4. 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.",
author = "Pine, {D. J.} and Gollub, {J. P.} and Brady, {J. F.} and Leshansky, {A. M.}",
year = "2005",
month = "12",
day = "15",
doi = "10.1038/nature04380",
language = "English (US)",
volume = "438",
pages = "997--1000",
journal = "Nature",
issn = "0028-0836",
publisher = "Nature Publishing Group",
number = "7070",

}

TY - JOUR

T1 - Chaos and threshold for irreversibility in sheared suspensions

AU - Pine, D. J.

AU - Gollub, J. P.

AU - Brady, J. F.

AU - Leshansky, A. M.

PY - 2005/12/15

Y1 - 2005/12/15

N2 - Systems governed by time reversible equations of motion often give rise to irreversible behaviour1-3. 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 positions 4. 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.

AB - Systems governed by time reversible equations of motion often give rise to irreversible behaviour1-3. 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 positions 4. 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.

UR - http://www.scopus.com/inward/record.url?scp=30744478661&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30744478661&partnerID=8YFLogxK

U2 - 10.1038/nature04380

DO - 10.1038/nature04380

M3 - Article

VL - 438

SP - 997

EP - 1000

JO - Nature

JF - Nature

SN - 0028-0836

IS - 7070

ER -