Push and pull: attractors and repellors of a dynamical system can localize inertial particles
- 7 Downloads
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.
KeywordsLocalization 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
- 3.Metcalfe, G.: Applied fluid chaos: designing advection with periodically reoriented flows for micro to geophysical mixing and transport enhancement. In: Dewar, R.L., Detering, F. (eds.) Complex Physical, Biophysical and Econophysical Systems, pp. 187–239. World Scientific, Singapore (2010)CrossRefGoogle Scholar
- 4.Agricola, G.: De Re Metallica. Dover Publications, vol. 1556. Book 8, image 22 (1950)Google Scholar
- 9.Metcalfe, G., Speetjens, M.F.M., Lester, D.R., Clercx, H.J.H.: Beyond passive: chaotic transport in stirred fluids. Adv. Appl. Mech. 45, 109 (2012). https://doi.org/10.1016/B978-0-12-380876-9.00004-5 CrossRefGoogle Scholar
- 13.Wang, J.K.S.: Mixing of fluids and suspensions in a laminar stirred tank. Ph.D. thesis, Monash University (2014). https://doi.org/10.4225/03/58a5351e77252. Advised by Jie Wu, David Boger, and Guy Metcalfe
- 30.Paul, E.L., Atiemo-Obeng, V., Kresta, S.M. (eds.): Handbook of Industrial Mixing. Wiley, Hoboken (2003)Google Scholar