Granular Matter

, 21:95 | Cite as

Push and pull: attractors and repellors of a dynamical system can localize inertial particles

  • Guy MetcalfeEmail author
Original Paper
Part of the following topical collections:
  1. In Memoriam of Robert P. Behringer, late Editor in Chief of Granular Matter


Recent experiments in a laminar flow stirred tank found that particles, initially moving throughout the fluid domain, undergo an instability and cluster into subdomains of the fluid when the flow Reynolds number exceeds a critical value that depends on particle and fluid inertia. As the dynamical system for inertial particles in fluid flow has both attracting and repelling regions, I show how the interplay of these regions can localize particles and derive an expression for the instability boundary that is suitable for comparison to data. Moreover, I model a master curve for the particle clustering rate in terms of excess inertia past the instability.


Localization Inertia Separation Chaotic advection 



GM had eight happy years in undergraduate and graduate research under Bob Behringer’s guidance and is tremendously grateful for the experience. This updated paper was originally to appear in the 2014 special issue for BobFest, but GM’s employer withdrew it, to file patents. A year later the employer killed off fluids research. GM had worked 20 years with the late CSIRO manufacturing fluids group.

Compliance with ethical standards

Conflict of interest

The author declare that they have no conflict of interest


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Science, Engineering and TechnologySwinburne University of TechnologyHawthornAustralia

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