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Kinetic and Related Models (KRM)
 

A maximum entropy principle based closure method for macro-micro models of polymeric materials

Pages: 171 - 184, Volume 1, Issue 2, June 2008      doi:10.3934/krm.2008.1.171

 
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Yunkyong Hyon - Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States (email)
José A. Carrillo - ICREA-Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain (email)
Qiang Du - Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States (email)
Chun Liu - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)

Abstract: We consider the finite extensible nonlinear elasticity (FENE) dumbbell model in viscoelastic polymeric fluids. We employ the maximum entropy principle for FENE model to obtain the solution which maximizes the entropy of FENE model in stationary situations. Then we approximate the maximum entropy solution using the second order terms in microscopic configuration field to get an probability density function (PDF). The approximated PDF gives a solution to avoid the difficulties caused by the nonlinearity of FENE model. We perform the moment-closure approximation procedure with the PDF approximated from the maximum entropy solution, and compute the induced macroscopic stresses. We also show that the moment-closure system satisfies the energy dissipation law. Finally, we show some numerical simulations to verify the PDF and moment-closure system.

Keywords:  multiscale modeling, macro-micro dynamics, polymeric fluid, non-newtonian fluid, FENE model, moment closure, Fokker-Planck equation, maximum entropy principle, numerical simulations.
Mathematics Subject Classification:  Primary: 76A05, 76M99 ; Secondary: 65C30.

Received: January 2008;      Revised: January 2008;      Published: May 2008.