The W-criterion for the onset of shear banding in complex fluids

A stability analysis of planar shear flow shear of a homogeneous, complex fluid predicts that shear banding instabilities can grow in fluids with a shear thinning strength above W _c = 1 and dampen out in fluids with W < 1. The shear thinning strength, \( W\left(\dot{\gamma}\right)=-\kern0.32em \partial \kern0.5em \log \eta /\partial \kern0.5em \log \dot{\gamma} \), arises naturally as the lead material function for the stability analysis of shear thinning fluids. The onset of shear banding is modeled as shear-thinning instability, which is attributed to anomalously strong shear thinning. Not considered here are inertial or elastic instabilities. In lack of suitable viscosity data from experiments, a Carreau powerlaw fluid and a Carreau-Yasuda powerlaw fluid serve as testbeds for the W-criterion. The analysis shows that the limiting high shear viscosity, η _∞, plays an important role in shear banding and that the ratio of the limiting high shear viscosity and zero shear viscosity, η _∞/η ₀, has to be sufficiently small for shear banding to occur. The main purpose of this brief communication is to share this new stability criterion. Extensive testing is still needed and is planned for future study.