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Steady States of Sheared Active Nematics

Published online by Cambridge University Press:  03 June 2015

Zhenlu Cui ,
Xiaoming Zeng  and
Jianbing Su
Zhenlu Cui*
Affiliation:
The Department of Mathematics and Computer Science, The Center for Defense and Homeland Security, Fayetteville State University, Fayetteville, NC 28301, USA
Xiaoming Zeng
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, China
Jianbing Su
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, Jiangsu, China
*
*Corresponding author. Email: [email protected]
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Abstract

A continuum hydrodynamic model has been used to characterize flowing active nematics. The behavior of such a system subjected to a weak steady shear is analyzed. We explore the director structures and flow behaviors of the system in flow-aligning and flow tumbling regimes. Combining asymptotic analysis and numerical simulations, we extend previous studies to give a complete characterization of the steady states for both contractile and extensile particles in flow-aligning and flow-tumbling regimes. Another key prediction of this work is the role of the system size on the steady states of an active nematic system: if the system size is small, the velocity and the director angle files for both flow-tumbling contractile and extensile systems are similar to those of passive nematics; if the system is big, the velocity and the director angle files for flow-aligning contractile systems and tumbling extensile systems are akin to sheared passive cholesterics while they are oscillatory for flow-aligning extensile and tumbling contractile systems.

Keywords

76A1576M45Asymptotic expansionactive liquid crystalshydrodynamics
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 1 , February 2014 , pp. 75 - 86
Copyright
Copyright © Global-Science Press 2014

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References

[1]Beris, A. N. AND Edwards, B. J., Thermodynamics of Flowing Systems, Oxford University Press, Oxford, 1994.Google Scholar
[2]Chakrabarty, B., Das, m., Dasgupta, C., Ramaswamy, S. and Sood, A. K., Spatiotemporal rheochaos in nematic hydrodynamics, Phys. Rev. Lett., 92 (2004), 055501.Google Scholar
[3]Cui, Zhenlu and Zeng, Xiaoming, Rheology of sheared bacterial suspensions, The IMA Volume in Mathematics and Its Applications, 155 (2012), pp. 217–224.Google Scholar
[4]Cui, Zhenlu, Weakly sheared active suspensions: hydrodynamics, stability and rheology, Phys. Rev. E, 83 (2011), 031911.Google Scholar
[5]Cui, Z., Calderer, M. C. and Wang, Q., A kinetic theory for flows of cholesteric liquid crystal polymers, Discrete and Continuous Dynamical Systems-Series B, 6 (2006), pp. 291–310.Google Scholar
[6]Dombrowski, C. et al., Self-concentration and large-scale coherence in bacterial dynamics, Phys. Rev. Lett., 93 (2004), pp. 098103–098106.Google Scholar
[7]Dreyfus, R., Baudry, J., Roper, M. L., Stone, H. A., Fermigier, M. and Bibette, J., Microscopic artificial swimmers, Nature (London), 437 (2005), 862.Google Scholar
[8]Edwards, S. A. and Yeomans, J. M., Spontaneous flow states in active nematics: a unified picture, Europhys. Lett., 85 (2009), 18008CrossRefGoogle Scholar
[9]Giomi, L., Marchetti, M. C. and Liverpool, T. B., Complex spontaneous flows and concentration banding in active polar films, Phys. Rev. Lett., 101 (2008), 198101.Google Scholar
[10]Kaiser, D., Bacterial swarming: a re-examination of cell-movement patterns, Current Biology, 17 (2007), R561.Google Scholar
[11]Kim, M. J. et al., Use of bacterial carpets to enhance mixing in microfluidic systems, J. Fluids Eng., 129 (2007), pp. 319–324.Google Scholar
[12]Kruse, K. et al., Asters, vortices, and rotating spirals in active gels of polar filaments, Phys. Rev. Lett., 92 (2004), pp. 078101–078104.Google Scholar
[13]Liverpool, T. B. and Marchetti, M. C., Rheology of active filament solutions, Phys. Rev. Lett., 97 (2006), 268101.Google Scholar
[14]Marenduzzo, D., Orlandini, E. AND Yeomans, J. M., Hydrodynamics and rheology of active liquid crystals: a numerical investigation, Phys. Rev. Lett., 98 (2007), 118102.Google Scholar
[15]Marenduzzo, D. et al., Steady-state hydrodynamic instabilities of active liquid crystals: hybrid lattice Boltzmann simulations, Phys. Rev. E, 76 (2007), 031921.CrossRefGoogle ScholarPubMed
[16]Olmsted, P. D., Perspectives on shear banding in complex fluids, Rheol. Acta, 47 (2008) 283.Google Scholar
[17]Voituriez, R., Joanny, J. F. and Prost, J., Spontaneous flow transition in active polar gels, Europhys. Lett., 70 (2005), pp. 404–410.Google Scholar