American Institute of Mathematical Sciences

Advanced
October  2010, 26(4): 1359-1382. doi: 10.3934/dcds.2010.26.1359

Flow driven dynamics of sheared flowing polymer-particulate nanocomposites

Jun Li 1, and  Qi Wang 2,

1. 

School of Mathematics and Nankai Institute of Scientific Computing, Nankai University, Tianjin, 300071, China
2. 

Department of Mathematics and NanoCenter at USC, University of South Carolina, Columbia, SC 29208, United States

Received  January 2009 Revised  March 2009 Published  December 2009

We study orientational dynamics in sheared polymer-particulate nanocomposites (PNCs) using an approximate tensor model derived from the kinetic theory for flows of PNCs in the weak semiflexible regime. We focus on dynamics induced by shear and enhanced by the interaction between the nanoparticles and the host polymer matrix in a set of selected model parameters, highlighting solution behavior and bifurcations in the semidilute regime of PNCs. We witness the existence of logrolling states, out-of-plane steady states, kayaking and chaotic motions, and flow-aligning steady states of nanoparticle ensembles and corresponding steady states, time-periodic fluttering and chaotic motions in the host polymer matrix in various ranges of shear rates and selected model parameters. A striking feature observed in the polymer matrix is its collective orientational order follows a master curve as the shear rate varies despite that the nanoparticle ensemble experiences a variety of states and motions with widely varying local nematic order.
Keywords: shear flows, nanoparticles, stability., dynamical systems, dynamics, polymer-nanocomposites, Bifurcation, polymer.
Mathematics Subject Classification: Primary: 37A60, 35Q35; Secondary: 34K1.
Citation: Jun Li, Qi Wang. Flow driven dynamics of sheared flowing polymer-particulate nanocomposites. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1359-1382. doi: 10.3934/dcds.2010.26.1359
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