October  2007, 8(3): 707-733. doi: 10.3934/dcdsb.2007.8.707

Anchoring-induced texture & shear banding of nematic polymers in shear cells


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


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


Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510

Received  October 2006 Revised  May 2007 Published  July 2007

We numerically explore texture (resolved by the second-moment of the orientational distribution) and shear banding of nematic polymers in shear cells, allowing for one-dimensional morphology in the gap between par- allel plates. We solve the coupled Navier-Stokes and Doi-Marrucci-Greco orientation tensor model, considering both confined orientation in the plane of shear and full orientation tensor degrees of freedom, and both primary flow and vorticity (in the full tensor model) components. This formulation makes contact with a large literature on analytical and numerical (cf. the review [41]) as well as experimental (cf. the review [45]) studies of nematic polymer texture and flow feedback. Here we focus on remarkable sensitivity of texture & shear band phenomena to plate anchoring conditions on the orientational distribution. We first explore steady in-plane flow-nematic states at low Peclet (Pe) and Ericksen (Er) numbers, where asymptotic analysis provides exact texture scaling properties [18, 6]. We illustrate that in-plane steady states co-exist with, and are unstable to, out-of-plane steady states, yet the structures and their scaling properties are not dramatically different. Non-Newtonian shear bands arise through orientational stresses. They are explored first for steady states, where we show the strength and gap location of shear bands can be tuned with anchoring conditions. Next, unsteady flow-texture transitions associated with the Ericksen number cascade are explored. We show the critical Er of the steady-to-unsteady transition, and qualitative features of the space-time attractor, are again strongly dependent on wall anchoring conditions. Other simulations highlight unsteady flow-nematic structures over 3 decades of the Ericksen number, comparisons of shear banding and texture features for in-plane and out-of-plane models, and vorticity generation in out-of-plane attractors.
Citation: Hong Zhou, M. Gregory Forest, Qi Wang. Anchoring-induced texture & shear banding of nematic polymers in shear cells. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 707-733. doi: 10.3934/dcdsb.2007.8.707

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 and Continuous Dynamical Systems - B, 2006, 6 (2) : 407-425. doi: 10.3934/dcdsb.2006.6.407


Zhenlu Cui, Qi Wang. Permeation flows in cholesteric liquid crystal polymers under oscillatory shear. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 45-60. doi: 10.3934/dcdsb.2011.15.45


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


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


Raphael Stuhlmeier. Effects of shear flow on KdV balance - applications to tsunami. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1549-1561. doi: 10.3934/cpaa.2012.11.1549


Jiakou Wang, Margaret J. Slattery, Meghan Henty Hoskins, Shile Liang, Cheng Dong, Qiang Du. Monte carlo simulation of heterotypic cell aggregation in nonlinear shear flow. Mathematical Biosciences & Engineering, 2006, 3 (4) : 683-696. doi: 10.3934/mbe.2006.3.683


Qiang Tao, Ying Yang. Exponential stability for the compressible nematic liquid crystal flow with large initial data. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1661-1669. doi: 10.3934/cpaa.2016007


Sili Liu, Xinhua Zhao, Yingshan Chen. A new blowup criterion for strong solutions of the compressible nematic liquid crystal flow. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4515-4533. doi: 10.3934/dcdsb.2020110


Patrick Martinez, Jean-Michel Roquejoffre. The rate of attraction of super-critical waves in a Fisher-KPP type model with shear flow. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2445-2472. doi: 10.3934/cpaa.2012.11.2445


Muhammad Mansha Ghalib, Azhar Ali Zafar, Zakia Hammouch, Muhammad Bilal Riaz, Khurram Shabbir. Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 683-693. doi: 10.3934/dcdss.2020037


P. Kaplický, Dalibor Pražák. Lyapunov exponents and the dimension of the attractor for 2d shear-thinning incompressible flow. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 961-974. doi: 10.3934/dcds.2008.20.961


Scott Gordon. Nonuniformity of deformation preceding shear band formation in a two-dimensional model for Granular flow. Communications on Pure and Applied Analysis, 2008, 7 (6) : 1361-1374. doi: 10.3934/cpaa.2008.7.1361


Alessandro Bertuzzi, Alberto d'Onofrio, Antonio Fasano, Alberto Gandolfi. Modelling cell populations with spatial structure: Steady state and treatment-induced evolution. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 161-186. doi: 10.3934/dcdsb.2004.4.161


Matthieu Hillairet, Ayman Moussa, Franck Sueur. On the effect of polydispersity and rotation on the Brinkman force induced by a cloud of particles on a viscous incompressible flow. Kinetic and Related Models, 2019, 12 (4) : 681-701. doi: 10.3934/krm.2019026


Francis C. Motta, Patrick D. Shipman. Informing the structure of complex Hadamard matrix spaces using a flow. Discrete and Continuous Dynamical Systems - S, 2019, 12 (8) : 2349-2364. doi: 10.3934/dcdss.2019147


Matthias Erbar, Max Fathi, Vaios Laschos, André Schlichting. Gradient flow structure for McKean-Vlasov equations on discrete spaces. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 6799-6833. doi: 10.3934/dcds.2016096


Tobias H. Colding and Bruce Kleiner. Singularity structure in mean curvature flow of mean-convex sets. Electronic Research Announcements, 2003, 9: 121-124.


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


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


Oualid Kafi, Nader El Khatib, Jorge Tiago, Adélia Sequeira. Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery. Mathematical Biosciences & Engineering, 2017, 14 (1) : 179-193. doi: 10.3934/mbe.2017012

2021 Impact Factor: 1.497


  • PDF downloads (40)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]