March  2006, 6(2): 407-425. doi: 10.3934/dcdsb.2006.6.407

Anchoring distortions coupled with plane Couette & Poiseuille flows of nematic polymers in viscous solvents: Morphology in molecular orientation, stress & flow

1. 

Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943-5216, United States

2. 

Department of Mathematics & Institute for Advanced Materials, University of North Carolina, Chapel Hill, NC 27599-3250, United States

Received  March 2005 Revised  September 2005 Published  December 2005

The aim of this work is to model and simulate processing-induced heterogeneity in rigid, rod-like nematic polymers in viscous solvents. We employ a mesoscopic orientation tensor model due to Doi, Marrucci and Greco which extends the small molecule, liquid crystal theory of Leslie-Ericksen-Frank to nematic polymers. The morphology has various physical realizations, all coupled through the model equations: the orientational distribution of the ensemble of rods, anisotropic viscoelastic stresses, and flow feedback. Previous studies in plane Couette & Poiseuille flow (with the exception of [7]) have focused on the coupling between hydrodynamics and the orientational distribution of rigid rod polymers with identical anchoring conditions at solid boundaries; without flow, the equilibrium structure is homogeneous. Here we explore steady structures that emerge with mismatch anchoring conditions at the walls, which couple an equilibrium elastic distortion across the channel, short and long range elasticity potentials, and hydrodynamics. In plane Couette (where moving plates drive the flow) and Poiseuille flow (where a pressure gradient drives the flow), in the regime of weak flow and strong distortional elasticity, asymptotic analysis yields closed-form steady solutions and scaling laws with identical wall conditions. We focus simulations in this regime to expose the effects due to wall anchoring conflicts, and illustrate the induced morphology of the orientational distribution, stored viscoelastic stresses, and non-Newtonian flow. A remarkably simple diagnostic emerges in this physical parameter regime, in which salient morphology features are controlled by the amplitude and sign of the difference in plate anchoring angles of the director field at the two plates.
Citation: Hong Zhou, M. Gregory Forest. Anchoring distortions coupled with plane Couette & Poiseuille flows of nematic polymers in viscous solvents: Morphology in molecular orientation, stress & flow. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 407-425. doi: 10.3934/dcdsb.2006.6.407
[1]

Hong Zhou, Hongyun Wang, Qi Wang. Nonparallel solutions of extended nematic polymers under an external field. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 907-929. doi: 10.3934/dcdsb.2007.7.907

[2]

Lingbing He, Claude Le Bris, Tony Lelièvre. Periodic long-time behaviour for an approximate model of nematic polymers. Kinetic & Related Models, 2012, 5 (2) : 357-382. doi: 10.3934/krm.2012.5.357

[3]

Hong Zhou, M. Gregory Forest, Qi Wang. Anchoring-induced texture & shear banding of nematic polymers in shear cells. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 707-733. doi: 10.3934/dcdsb.2007.8.707

[4]

Paolo Antonelli, Pierangelo Marcati. Quantum hydrodynamics with nonlinear interactions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 1-13. doi: 10.3934/dcdss.2016.9.1

[5]

Hiroshi Inoue. Magnetic hydrodynamics equations in movingboundaries. Conference Publications, 2005, 2005 (Special) : 397-402. doi: 10.3934/proc.2005.2005.397

[6]

Boris Kolev. Poisson brackets in Hydrodynamics. Discrete & Continuous Dynamical Systems - A, 2007, 19 (3) : 555-574. doi: 10.3934/dcds.2007.19.555

[7]

Maksym Berezhnyi, Evgen Khruslov. Non-standard dynamics of elastic composites. Networks & Heterogeneous Media, 2011, 6 (1) : 89-109. doi: 10.3934/nhm.2011.6.89

[8]

Tukur Abdulkadir Sulaiman, Hasan Bulut, Haci Mehmet Baskonus. Optical solitons to the fractional perturbed NLSE in nano-fibers. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 925-936. doi: 10.3934/dcdss.2020054

[9]

Pierre Degond, Hailiang Liu. Kinetic models for polymers with inertial effects. Networks & Heterogeneous Media, 2009, 4 (4) : 625-647. doi: 10.3934/nhm.2009.4.625

[10]

Alexander Bobylev, Åsa Windfäll. Boltzmann equation and hydrodynamics at the Burnett level. Kinetic & Related Models, 2012, 5 (2) : 237-260. doi: 10.3934/krm.2012.5.237

[11]

M. Silhavý. Ideally soft nematic elastomers. Networks & Heterogeneous Media, 2007, 2 (2) : 279-311. doi: 10.3934/nhm.2007.2.279

[12]

Guillermo H. Goldsztein. Bound on the yield set of fiber reinforced composites subjected to antiplane shear. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 391-400. doi: 10.3934/dcdsb.2011.15.391

[13]

Luisa Faella, Carmen Perugia. Optimal control for a hyperbolic problem in composites with imperfect interface: A memory effect. Evolution Equations & Control Theory, 2017, 6 (2) : 187-217. doi: 10.3934/eect.2017011

[14]

Daniel Peterseim. Robustness of finite element simulations in densely packed random particle composites. Networks & Heterogeneous Media, 2012, 7 (1) : 113-126. doi: 10.3934/nhm.2012.7.113

[15]

Thierry Colin, Marie-Christine Durrieu, Julie Joie, Yifeng Lei, Youcef Mammeri, Clair Poignard, Olivier Saut. Modeling of the migration of endothelial cells on bioactive micropatterned polymers. Mathematical Biosciences & Engineering, 2013, 10 (4) : 997-1015. doi: 10.3934/mbe.2013.10.997

[16]

Nicola Bellomo, Abdelghani Bellouquid, Juanjo Nieto, Juan Soler. On the multiscale modeling of vehicular traffic: From kinetic to hydrodynamics. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1869-1888. doi: 10.3934/dcdsb.2014.19.1869

[17]

Patricia Bauman, Andrea C. Rubiano. Energy-minimizing nematic elastomers. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 259-282. doi: 10.3934/dcdss.2015.8.259

[18]

Roger E. Khayat, Martin Ostoja-Starzewski. On the objective rate of heat and stress fluxes. Connection with micro/nano-scale heat convection. Discrete & Continuous Dynamical Systems - B, 2011, 15 (4) : 991-998. doi: 10.3934/dcdsb.2011.15.991

[19]

Zhenlu Cui, M. Carme Calderer, Qi Wang. Mesoscale structures in flows of weakly sheared cholesteric liquid crystal polymers. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 291-310. doi: 10.3934/dcdsb.2006.6.291

[20]

Pierre Degond, Silke Henkes, Hui Yu. Self-organized hydrodynamics with density-dependent velocity. Kinetic & Related Models, 2017, 10 (1) : 193-213. doi: 10.3934/krm.2017008

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]