Numéro
J. Phys. I France
Volume 7, Numéro 12, December 1997
Page(s) 1523 - 1533
DOI https://doi.org/10.1051/jp1:1997153
DOI: 10.1051/jp1:1997153
J. Phys. I France 7 (1997) 1523-1533

On the Validity of the Maxwell Model and Related Constitutive Equations; a Study Based on the First Normal Stress Coefficient

H.-P. Wittmann

Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany



(Received 4 april 1997, revised 21 August 1997, accepted 2 September 1997)

Abstract
In a previous publication (J. Phys. I France 4 (1994) 1791) the semi-microscopical Rouse model was projected onto macroscopic Langevin equations for concentration and stress tensor fluctuations. Adding afterwards appropriate convective terms due to a simple shear flow the resulting equations were shown to be a generalization of the upper convected Maxwell model. Based on the projected equations the first normal stress coefficient $\Psi_{1,0}$ is now calculated in this publication: $\Psi_{1,0}=2\eta^2_0/k_{\rm B} T c_0$ where $\eta_0$ and c0 denote the zero-shear viscosity and the monomer concentration respectively. The resulting steady state compliance $J_{\rm s}$ is found to be $J_{\rm s}=1/k_{\rm B} T c_0$. This turns out to be in desagreement with experimental findings. Based on the derivation of the Lodge equation one can conclude the following: In order to get the right first normal stress coefficient it is necessary to incorporate the shear flow at first into the Rouse model and to project afterwards the modified Rouse model.



© Les Editions de Physique 1997

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