Abstract
A novel primitive model is proposed for the hydrodynamic behaviour of an isolated dissolved polymer molecule in a laminar shear flow. The model, in which inertial effects are neglected, allows for rotation and partial stretching of the molcule, but not for bending. Dilute solutions of flexible long-chain polymers have been experimentally observed to exhibit periodic velocity fluctuations distinct from turbulence over a broad frequency range when flowed in high-shear-rate water-table and pipe configurations. In these experiments, the frequency of the fluctuations does not increase with increasing shear rate; rather, it is lowest in the regions of the flow where the shear is the highest. A manifestation of viscous shear thickening has also been observed in these laminar flows. The proposed polymer representation appears capable of accounting for the salient features of these flows with adjustment of a single dimensionless parameter, a ratio of polymer-spring and solvent-viscosity forces.