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The dynamical states of a prolate spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia

Published online by Cambridge University Press:  17 April 2015

T. Rosén ,
M. Do-Quang ,
C. K. Aidun  and
F. Lundell
T. Rosén
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Wallenberg Wood Science Center, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
M. Do-Quang
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
C. K. Aidun
Affiliation:
George W. Woodruff School of Mechanical Engineering, and Parker H. Petit Institute for Bioengineering and Bioscience, 801 Ferst Drive, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA
F. Lundell*
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Wallenberg Wood Science Center, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: fredrik@mech.kth.se
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Abstract

The rotational motion of a prolate spheroidal particle suspended in shear flow is studied by a lattice Boltzmann method with external boundary forcing (LB-EBF). It has previously been shown that the case of a single neutrally buoyant particle is a surprisingly rich dynamical system that exhibits several bifurcations between rotational states due to inertial effects. It was observed that the rotational states were associated with either fluid inertia effects or particle inertia effects, which are always in competition. The effects of fluid inertia are characterized by the particle Reynolds number $\mathit{Re}_{p}=4Ga^{2}/{\it\nu}$, where $G$ is the shear rate, $a$ is the length of the particle major semi-axis and ${\it\nu}$ is the kinematic viscosity. Particle inertia is associated with the Stokes number $\mathit{St}={\it\alpha}\,\mathit{Re}_{p}$, where ${\it\alpha}$ is the solid-to-fluid density ratio. Previously, the neutrally buoyant case ($\mathit{St}=\mathit{Re}_{p}$) was studied extensively. However, little is known about how these results are affected when $\mathit{St}\neq \mathit{Re}_{p}$, and how the aspect ratio $r_{p}$ (major axis/minor axis) influences the competition between fluid and particle inertia in the absence of gravity. This work gives a full description of how prolate spheroidal particles in the range $2\leqslant r_{p}\leqslant 6$ behave depending on the chosen $\mathit{St}$ and $\mathit{Re}_{p}$. Furthermore, consequences for the rheology of a dilute suspension containing such particles are discussed. Finally, grid resolution close to the particle is shown to affect the quantitative results considerably. It is suggested that this resolution is a major cause of quantitative discrepancies between different studies. Thus, the results of this work and previous direct numerical simulations of this problem should be regarded as qualitative descriptions of the physics involved, and more refined methods must be used to quantitatively pinpoint the transitions between rotational states.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Complex Fluids: Complex Fluids Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 771 , 25 May 2015 , pp. 115 - 158
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Copyright
© 2015 Cambridge University Press 

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Rosén et al. supplementary movie

The movie illustrates the stable rotational states in each of the thirteen different regions in a Re_p/St-plane and the corresponding dynamical transitions and bifurcations between the regions.

Download Rosén et al. supplementary movie(Video)
Video 102.2 MB

Rosén et al. supplementary movie

The movie illustrates the seven different rotational states of a single prolate spheroidal particle in a linear shear flow.

Download Rosén et al. supplementary movie(Video)
Video 78.9 MB