Oscillatory Shear Flow of Internal Viscosity Dumbbells: a New Analysis Employing an Expansion in Strain
A new formulation is presented for the oscillatory shear flow complex viscosity components η′(ω) and η″(ω) predicted by the dilute-solution internal viscosity model. For IV dumbbells (two beads connected by one submolecule), an expansion of configurational quantities in orders of strain is employed to avoid the pre-averaged angular velocity assumption that has been used in most previous IV model predictions. The new predictions for η′(ω) and η″(ω) retain most of the qualitative features of previous IV model formulations, including a non-zero limiting value for η′(ω) as frequency w becomes infinite. Quantitative features of the complex viscosity components, however, are quite different from those obtained previously. Unlike previous formulations, the model presented here correctly predicts that η′(ω) and η″(ω) for the infinite-IV dumbbell approach the corresponding predictions of the rigid rod model.
KeywordsStrain Amplitude Complex Viscosity Linear Entropy Small Amplitude Oscillatory Shear Dumbbell Model
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