On the Estimation of Stresses in Steady Shear Flow from the Dynamic Viscoelasticity for Polymeric Liquids

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  • Osaki K.
    Institute for Chemical Research, Kyoto University
  • Watanabe H.
    Institute for Chemical Research, Kyoto University
  • Inoue T.
    Institute for Chemical Research, Kyoto University

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タイトル別名
  • On the Estimation of Stresses in Steady

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First we show that the Cox-Merz rule, that η(γ) is approximated by η*(ω)|γ=ω, exhibits considerable deviations for systems with very strong or weak damping functions for the strain-dependent relaxation modulus; here η*(ω) is the complex viscosity. The deviation can be accounted for in view of the BKZ constitutive model. Secondly we propose an equation to approximate the first normal stress coefficient, ψ1(γ), from the dynamic modulus, G′(ω); ψ1(γ)≅2G′(ω)/ω2|γ=κ′ω. Here κ′ is an adjustable parameter. It is proved that this equation is almost equivalent to a Gleissle formula, ψ1(γ)≅ψ1+(t)|γ=κ/t with κ′=/1.55, where ψ1+(t) is the growth function of the first normal stress coefficient at the start-up of shear flow at the limit of zero rate of shear. The normal stress coefficient is approximated well over a wide range of rate of shear for the data by Laun of IUPAC A polyethylene and those for a solution of polystyrene with a narrow molecular mass distribution. The appropriate values of κ′ for these systems over moderate ranges of γ were 2.0 and 1.4, respectively. These values are related to the damping function through the BKZ model and may be estimated from the damping function, approximated as exp(-αt), with a relation κ′≅0.37/α.

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