Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-19T21:23:22.468Z Has data issue: false hasContentIssue false
  • English
  • Français

An ellipsoidal particle in tube Poiseuille flow

Published online by Cambridge University Press:  07 June 2017

Haibo Huang Open the ORCID record for Haibo Huang [Opens in a new window]  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Haibo Huang*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
*
†Email address for correspondence: huanghb@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

A suspended ellipsoidal particle inside a Poiseuille flow with Reynolds number up to 360 is studied numerically. The effects of tube diameter ($D$), inertia of the particle and the flow, and the particle geometry (both prolate and oblate ellipsoids) are considered. When a prolate particle with $a/b=2$ is inside a wider tube (e.g. $D/A>1.9$), where $A=2a$ is the length of the major axis of the particle, the terminal stable state is tumbling. When the prolate particle is inside a narrower tube ($1.0<D/A<1.9$), log-rolling or kayaking modes may appear. Which mode occurs depends on the competition between fluid and particle inertia. When the fluid inertia is dominant, the log-rolling mode appears, otherwise, the kayaking mode appears. Inclined and spiral modes may appear when $D/A<1$ and $D/A=1$, respectively. For a prolate ellipsoid with $a/b=4$, if $1<D/A<1.9$, there is only the kayaking mode and the log-rolling mode is not observed. When an oblate particle is inside a wider tube (e.g. $D/A>3.5$), it may adopt the log-rolling mode. Inclined and intermediate modes are firstly identified in narrower tubes. The phase diagram of the modes is also provided. The modes in the phase diagrams were not found to be affected by the initial state of the particle based on limited observation.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Sediment transport Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 822 , 10 July 2017 , pp. 664 - 688
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aidun, C. K., Lu, Y. & Ding, E.-J. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287–311.Google Scholar
Byeon, H. J., Seo, K. W. & Lee, S. J. 2015 Precise measurement of three-dimensional positions of transparent ellipsoidal particles using digital holographic microscopy. Appl. Opt. 54 (8), 2106–2112.Google Scholar
Chen, Y., Cai, Q.-D., Xia, Z.-H., Wang, M.-R. & Chen, S.-Y. 2013 Momentum-exchange method in lattice Boltzmann simulations of particle–fluid interactions. Phys. Rev. E 88 (1), 013303.Google Scholar
D’Avino, G., Greco, F. & Maffettone, P. L. 2015 Rheology of a dilute viscoelastic suspension of spheroids in unconfined shear flow. Rheol. Acta 54 (11–12), 915–928.Google Scholar
D’Avino, G. & Maffettone, P. L. 2015 Particle dynamics in viscoelastic liquids. J. Non-Newtonian Fluid Mech. 215, 80–104.Google Scholar
Ding, E. & Aidun, C. K. 2000 The dynamics and scaling law for particles suspended in shear flow with inertia. J. Fluid Mech. 423, 317–344.Google Scholar
Einarsson, J., Candelier, F., Lundell, F., Angilella, J. R. & Mehlig, B. 2015 Rotation of a spheroid in a simple shear at small Reynolds number. Phys. Fluids 27 (6), 063301.Google Scholar
Feng, J., Hu, H. H. & Joseph, D. D. 1994 Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. J. Fluid Mech. 261, 95–134.Google Scholar
Huang, H., Wu, Y. & Lu, X.-Y. 2012a Shear viscosity of dilute suspensions of ellipsoidal particles with a lattice Boltzmann method. Phys. Rev. E 86 (4), 046305.Google Scholar
Huang, H., Yang, X., Krafczyk, M. & Lu, X.-Y. 2012b Rotation of spheroidal particles in Couette flows. J. Fluid Mech. 692, 369–394.Google Scholar
Huang, H., Yang, X. & Lu, X.-Y. 2014 Sedimentation of an ellipsoidal particle in narrow tubes. Phys. Fluids 26 (5), 053302.Google Scholar
d’Humiéres, D., Ginzburg, I., Krafczyk, M., Lallemand, P. & Luo, L.-S. 2002 Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phil. Trans. R. Soc. Lond. A 360, 437–451.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161–179.Google Scholar
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1963 Axial migration of particles in Poiseuille flow. Nature 200, 159–160.Google Scholar
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1966 The flow of suspensions through tubes: V. inertial effects. Can. J. Chem. Engng 44 (4), 181–193.Google Scholar
Ladd, A. J. C. 1994a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285–309.Google Scholar
Lallemand, P. & Luo, L.-S. 2003 Lattice Boltzmann method for moving boundaries. J. Comput. Phys. 184 (2), 406–421.Google Scholar
Mei, R. W., Luo, L.-S. & Shyy, W. 1999 An accurate curved boundary treatment in the lattice Boltzmann method. J. Comput. Phys. 155 (2), 307–330.Google Scholar
Pan, T.-W., Chang, C.-C. & Glowinski, R. 2008 On the motion of a neutrally buoyant ellipsoid in a three-dimensional Poiseuille flow. Comput. Meth. Appl. Mech. Engng 197 (25), 2198–2209.Google Scholar
Qi, D.-W. 1999 Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows. J. Fluid Mech. 385, 41–62.Google Scholar
Qi, D.-W. & Luo, L.-S. 2003 Rotational and orientational behaviour of three-dimensional spheroidal particles in Couette flows. J. Fluid Mech. 477, 201–213.Google Scholar
Qi, D.-W., Luo, L.-S., Aravamuthan, R. & Strieder, W. 2002 Lateral migration and orientation of elliptical particles in Poiseuille flows. J. Stat. Phys. 107 (1–2), 101–120.Google Scholar
Rosén, T., Einarsson, J., Nordmark, A., Aidun, C. K., Lundell, F. & Mehlig, B. 2015 Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers. Phys. Rev. E 92 (6), 063022.Google Scholar
Rosén, T., Lundell, F. & Aidun, C. K. 2014 Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow. J. Fluid Mech. 738, 563–590.Google Scholar
Rosén, T., Nordmark, A., Aidun, C. K., Do-Quang, M. & Lundell, F. 2016 Quantitative analysis of the angular dynamics of a single spheroid in simple shear flow at moderate Reynolds numbers. Phys. Rev. Fluids 1 (4), 044201.Google Scholar
Segre, G. & Silberberg, A. 1961 Radial particle displacements in Poiseuille flow of suspensions. Nature 189, 209–210.Google Scholar
Sugihara-Seki, M. 1996 The motion of an ellipsoid in tube flow at low Reynolds numbers. J. Fluid Mech. 324, 287–308.Google Scholar
Swaminathan, T. N., Mukundakrishnan, K. & Hu, H. H. 2006 Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers. J. Fluid Mech. 551, 357–385.Google Scholar
Villone, M. M., D’Avino, G., Hulsen, M. A. & Maffettone, P. L. 2015 Dynamics of prolate spheroidal elastic particles in confined shear flow. Phys. Rev. E 92 (6), 062303.Google Scholar
Xia, Z., Connington, K. W., Rapaka, S., Yue, P., Feng, J. J. & Chen, S.-Y. 2009 Flow patterns in the sedimentation of an elliptical particle. J. Fluid Mech. 625, 249–272.Google Scholar
Yang, B. H., Wang, J., Joseph, D. D., Hu, H. H., Pan, T.-W. & Glowinski, R. 2005 Migration of a sphere in tube flow. J. Fluid Mech. 540, 109–131.Google Scholar
Yang, X., Huang, H. & Lu, X.-Y. 2015 Sedimentation of an oblate ellipsoid in narrow tubes. Phys. Rev. E 92 (6), 063009.Google Scholar
Yu, Z. S., Phan-Thien, N. & Tanner, R. I. 2004 Dynamic simulation of sphere motion in a vertical tube. J. Fluid Mech. 518, 61–93.Google Scholar
Yu, Z.-S., Phan-Thien, N. & Tanner, R. I. 2007 Rotation of a spheroid in a Couette flow at moderate Reynolds numbers. Phys. Rev. E 76 (2), 026310.Google Scholar
Zhu, M.-Y.2000 Direct numerical simulation of solid-liquid flow of Newtonian and viscoelastic fluids. PhD thesis, University of Pennsylvania.Google Scholar