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

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 ψ 1,0 is now calculated in this publication: ψ 1,0 = 2η 0 2 /κ B Tc 0 where η 0 and c 0 denote the zero-shear viscosity and the monomer concentration respectively. The resulting steady state compliance J s is found to be J s = 1/κ B Tc 0 . This turns out to be in disagreement 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.