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Dynamics and structure of an apolar active suspension in an annulus

Published online by Cambridge University Press:  27 November 2017

Sheng Chen ,
Peng Gao Open the ORCID record for Peng Gao [Opens in a new window]  and
Tong Gao Open the ORCID record for Tong Gao [Opens in a new window]
Sheng Chen
Affiliation:
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA
Peng Gao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Tong Gao*
Affiliation:
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48824, USA
*
†Email address for correspondence: [email protected]
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Abstract

We study the complex dynamics of a two-dimensional suspension comprising non-motile active particles confined in an annulus. A coarse-grained liquid crystal model is employed to describe the nematic structure evolution, and is hydrodynamically coupled with the Stokes equation to solve for the induced active flows in the annulus. For dilute suspensions, coherent structures are captured by varying the particle activity and gap width, including unidirectional circulations, travelling waves and chaotic flows. For concentrated suspensions, the internal collective dynamics features motile disclination defects and flows at finite gap widths. In particular, we observe an intriguing quasi-steady-state at certain gap widths during which $+1/2$-order defects oscillate around equilibrium positions accompanying travelling-wave flows that switch circulating directions periodically. We perform linear stability analyses to reveal the underlying physical mechanisms of pattern formation during a concatenation of instabilities.

JFM classification

Complex Fluids: Complex Fluids Complex Fluids: Liquid crystals Nonlinear Dynamical Systems: Pattern formation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 393 - 405
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Copyright
© 2017 Cambridge University Press 

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Chen et al. supplementary movie 1

Supplementary movie 1: Nematic director/order (left) and flow vector/vorticity (right) for a dense Extensor suspension confined in an annulus when choosing α = -2.0, R1 = 0.75, R2 = 2.0, β = 0.874, ζ = 0.5, dT = dR = 0.025. The black scale bar represents the dimensionless length 1.0.

Download Chen et al. supplementary movie 1(Video)
Video 22.6 MB

Chen et al. supplementary movie 2

Supplementary movie 2: Nematic director/order (left) and flow vector/vorticity (right) for a dense Extensor suspension confined in an annulus when choosing α = -2.0, R1 = 0.5, R2 = 1.6, β = 0.874, ζ = 0.5, dT = dR = 0.025. The black scale bar represents the dimensionless length 1.0.

Download Chen et al. supplementary movie 2(Video)
Video 18.2 MB

Chen et al. supplementary movie 3

Supplementary movie 3: Nematic director/order (left) and flow vector/vorticity (right) for a dense Extensor suspension confined in an annulus when choosing α = -2.0, R1 = 0.75, R2 = 3.0, β = 0.874, ζ = 0.5, dT = dR = 0.025. The black scale bar represents the dimensionless length 1.0.

Download Chen et al. supplementary movie 3(Video)
Video 19.2 MB