Europhys. Lett, 46 (4), pp. 542-548 (1999)
Dynamics of a mechanical interface in shear-banded flow
H. H. Wills Physics Laboratory, University of Bristol
Royal Fort, Tyndall Avenue, Bristol BS8 1TL, UK
(received 4 November 1998; accepted in final form 5 March 1999)
PACS. 83.20 - Constitutive relations.
PACS. 68.10Et - Interface elasticity, viscosity, and viscoelasticity.
PACS. 47.50 - Non-Newtonian fluid flows.
Shear banding of wormlike micelle solution has been studied in the context of constitutive instability of the Johnson-Segalman (JS) model plus Newtonian stress. We have incorporated a higher-order gradient term of the deformation-rate tensor into the JS model for investigating the dynamics of a mechanical interface in shear-banded flow. Two-dimensional modelling of the new model has been carried out by a general Lagrangian-Eulerian scheme. Within the unstable region, our results show that the new term plays an important role in selecting steady-state shear stress and the selected stress is independent of the nominal shear rate. The transit period of reaching the steady state can be much longer than the intrinsic relaxation time of the JS fluid. We have verified the experimental evidence on the existence of mechanical metastable regime, over which hysteresis in flow curve might occur. The model captures many features of experimental results on shear banded flow.