Transient Extension and Relaxation of a Dilute Polymer Solution in a Four-Roll Mill
J. Feng and L. G. Leal
J. Non-Newtonian Fluid Mech. 90, 117-123 (2000)
Abstract - The reaction of polymer solutions to abrupt changes of the strain-rate in an extension-dominated flow is manifest of the behavior of the polymer chains. In our laboratory systematic experiments on sudden changes of flow are being carried out using two-roll and four-roll mills. Because of the coupling between fluid flow and polymer stretching, a sudden change of roller speed generates a rather complex flow history at the stagnation point where flow birefringence is measured. The objective of the numerical simulations to be reported is to complement and elucidate the experimental measurements. We use the Chilcott-Rallison model to represent Boger fluids, and solve the coupled equations for fluid flow and polymer stretching using a finite element method. Results show that when the roller speed is suddenly changed, the strain-rate at the stagnation point undergoes an overshoot and an undershoot before approaching the steady state. The polymer stretching (or birefringence) also has undershoots and overshoots. Away from the stagnation point, the velocity and strain-rate oscillates during the transient. In particular, the polymer solution exhibits considerable recoil after the rollers are suddenly stopped.