Coil-Stretch Transitions in Mixed Shear and Extensional Flows of Dilute Polymer Solutions.

A generalization of Zimm's bead-spring model for dilute solutions of flexible polymers that accounts for the influence of coil distortion on hydrodynamic interaction is used to calculate molecular distortions and coil-stretch transitions in general planar flows. Expressing an arbitrary incompressible planar flow as a superposition of a shearing flow and a planar extension, we find that the shearing flow can reduce the critical extension rate 6 sub c required to produce a coil-stretch transition, whereas the original Zimm theory predicts no influence of shearing on 6 sub c. The scaling theory of de Gennes predicts a much larger influence of shearing on 6 sub c that is obtained in the bead-spring calculations, apparently because the cylindrical shape assumed by de Gennes does not accurately describe the true pre-transition coil shape. The weaker dependence of 6 sub c on shearing found in our calculations is consistent with recent experimental data of Dunlap and Leal.