Flow of nematic polymers in eccentric cylinder geometry: influence of closure approximations

The start-up flow of a nematic rod-like polymer in an eccentric cylinder geometry is studied on the basis of the rigid rod model. The simulations neglect the polymer stress contribution in the momentum equation. The nematic configuration is obtained by integrating the diffusion equation for the orientational distribution function with a Galerkin approach. The predictions are compared with results obtained by introducing different closure approximations. Both a quadratic and a Bingham closure are considered. The comparison shows that the approximations have a qualitative impact on the results. (C) 2000 Published by Elsevier Science B.V.

[1]  S. Prager Stress‐Strain Relations in a Suspension of Dumbbells , 1957 .

[2]  Pier Luca Maffettone,et al.  The rigid-rod model for nematic polymers: An analysis of the shear flow problem , 1999 .

[3]  L. G. Leal,et al.  A closure approximation for liquid-crystalline polymer models based on parametric density estimation , 1998 .

[4]  James J. Feng,et al.  Simulating complex flows of liquid-crystalline polymers using the Doi theory , 1997 .

[5]  Wesley Roth Burghardt,et al.  Molecular orientation and rheology in sheared lyotropic liquid crystalline polymers , 1998 .

[6]  Ronald G. Larson,et al.  Effect of molecular elasticity on out-of-plane orientations in shearing flows of liquid-crystalline polymers , 1991 .

[7]  A. Saupe,et al.  Eine einfache molekular-statistische Theorie der nematischen kristallinflüssigen Phase. Teil l1. , 1959 .

[8]  P. Maffettone,et al.  A closure approximation for nematic liquid crystals based on the canonical distribution subspace theory , 2000 .

[9]  Charles L. Tucker,et al.  Orthotropic closure approximations for flow-induced fiber orientation , 1995 .

[10]  R. Keunings,et al.  The Lagrangian particle method for macroscopic and micro-macro viscoelastic flow computations , 1998 .

[11]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[12]  E. J. Hinch,et al.  Constitutive equations in suspension mechanics. Part 1. General formulation , 1975, Journal of Fluid Mechanics.

[13]  R. Larson Arrested Tumbling in Shearing Flows of Liquid Crystal Polymers , 1990 .

[14]  James J. Feng,et al.  Closure approximations for the Doi theory: Which to use in simulating complex flows of liquid-crystalline polymers? , 1998 .

[15]  Masao Doi,et al.  Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and liquid crystalline phases , 1981 .