Interfacial dynamics of viscoelastic fluid flows

Abstract

The constitutive instability of the Johnson–Segalman (JS) model has been studied in order to understand the shear banding and the spurt effect of viscoelastic fluid flows. We have applied a new model, which incorporates a higher order gradient term of the deformation-rate tensor into the JS model, to investigate the dynamics of the mechanical interface induced by the constitutive instability. Computer modelling of two-dimensional Couette and Poiseuille flows has been carried out by a general Lagrangian–Eulerian scheme. It can track explicitly the evolution of the band structure under flow. Our results show that the new term plays an important role in selecting the steady state shear stress in the unstable region. The period of reaching the steady state can be 20 or more times longer than the intrinsic relaxation time of the JS fluid. We have verified experimental evidences on the existence of a mechanical metastable region, over which hysteresis in the flow curve might occur. The model reproduces many features of the experimental results.