Shear banding in time-dependent flows of polymers and wormlike micelles.

摘要

We study theoretically the formation of shear bands in time-dependent flows of polymeric andudwormlike micellar surfactant fluids, focussing on the protocols of step shear stress, step shear strainud(or in practice a rapid strain ramp), and shear startup, which are commonly studied experimentally.udFor each protocol we perform a linear stability analysis to provide a fluid-universal criterion for theudonset of shear banding, following our recent letter [Moorcroft and Fielding, Phys. Rev. Lett. 110,ud086001 (2013)]. In each case this criterion depends only on the shape of the experimentally measuredudrheological response function for that protocol, independent of the constitutive properties of theudmaterial in question (Therefore our criteria in fact concern all complex fluids and not just theudpolymeric ones of interest here.). An important prediction is that pronounced banding can ariseudtransiently in each of these protocols, even in fluids for which the underlying constitutive curve ofudstress as a function of strain-rate is monotonic and a steadily flowing state is accordingly unbanded.udFor each protocol we provide numerical results in the rolie-poly and Giesekus models that support ourudpredictions. We comment on the ability of the rolie-poly model to capture the observed experimentaludphenomenology and on the failure of the Giesekus model.