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

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

1. 

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

2. 

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

3. 

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 & Continuous Dynamical Systems - B, 2007, 8 (3) : 707-733. doi: 10.3934/dcdsb.2007.8.707
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