Shear thinning and polymer deformation in large flow fields

Abstract We theoretically investigate polymer deformation and shear thinning, i.e., a decrease of intrinsic viscosity, in a dilute polymer solution as a function of the applied shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} . We use a bead‐and‐spring model with hydrodynamic interaction in the Rouse‐Zimm framework, approximately accounting also for excluded‐volume effects, and impose a constraint on the average mean‐square spring length to prevent its stretching at large \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} . When suitably normalized, both the intrinsic viscosity [η] and the components of the mean gyration tensor 〈 SS 〉 depend on the single variable \documentclass{article}\pagestyle{empty}\begin{document}$ \xi = {{\dot \gamma \tau _1^{\left( 0 \right)} } \mathord{\left/ {\vphantom {{\dot \gamma \tau _1^{\left( 0 \right)} } {N^{1 - v} }}} \right. \kern-\nulldelimiterspace} {N^{1 - v} }} $\end{document} where τ   (0) 1is the longest relaxation time for \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma = 0 $\end{document} , N is the number of chain springs and v is the Flory exponent. The full shear‐rate dependence is obtained numerically, and compared with analytical results obtained under free‐draining conditions both for low and for very large shear rates. The shortcomings of the theory are also discussed, in particular a substantial stretching under shear of the central springs, where the intramolecular tension is largest, with a corresponding strong contraction of the end springs due to the average character of the constraint.