Abstract
The phase-space kinetic theory for polymeric liquid mixtures is used to obtain an expression for the polymer contribution to the thermal conductivity of a nonflowing, dilute solution of polymers, where the polymer molecules are modeled as Fraenkel dumbbells. This theory takes into account three mechanisms for the energy transport: diffusion of kinetic energy (including the Öttinger-Petrillo term), diffusion of intramolecular energy, and the work done against the intramolecular forces. This paper is an extension of previous developments for the Hookean dumbbell model and the finitely-extensible dumbbell model. A comparison among the dumbbell results suggests that the thermal conductivity increases with chain stiffness. In addition, the zero-shear-rate viscosity and first normal-stress coefficient are also given for the Fraenkel dumbbell model.
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Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.
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Byron, R., Curtiss, B.C.F. & Beers, K.J. Polymer contribution to the thermal conductivity and viscosity in a dilute solution (Fraenkel Dumbbell model). Rheola Acta 36, 269–276 (1997). https://doi.org/10.1007/BF00366668
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DOI: https://doi.org/10.1007/BF00366668