Torque Reduction in Finite Amplitude Secondary Flows of Dilute Polymer Solutions

When a dilute polymer solution is sheared between concentric cylinders with the inner cylinder rotating and the outer fixed, the onset of cellular secondary flows (Taylor vortices) is usually delayed relative to a Newtonian liquid of the same kinematic viscosity, and the extra torque in the polymer solution following instability is less than that for the Newtonian liquid at the same relative Taylor Number. This torque reduction is explained here by means of a finite amplitude analysis of the secondary motion in a second-order fluid using the energy equilibrium approach of Landau and Stuart. The theoretical calculations are in general agreement with data of Denn and Roisman for a 0.5% solution of polyisobutylene in decalin. Using these calculations and the linearized stability theory it is possible to estimate the three rheological parameters for a second-order fluid from a single set of torque-rotational speed data in a Couette viscometer.