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Dynamic vorticity banding in discontinuously shear thickening suspensions
The phenomenon of discontinuous shear thickening is a step increase of the viscosity with increasing shear rate observed in some dense suspensions of hard particles, the most well-known example of being cornstarch suspensions. It is associated to an underlying shear stress versus shear rate constitutive curve which is S-shaped. While a S-shaped flow curve generically leads to flow instabilities such as banding, it has recently been argued that steady-state bands cannot arise in shear thickening suspensions, because the normal stress imbalance across the interface between the bands will set up particle migrations. In this talk, I will introduce a simple continuum model that couples shear thickening to particle migration. Linear stability analysis shows that homogeneous flow is unstable towards vorticity banding in the regime of negative constitutive slope. In full nonlinear computations, the resulting vorticity bands are unsteady, with spatiotemporal patterns governed by stress-concentration coupling. I will furthermore show that these dynamical bands also arise in direct particle simulations, in good agreement with the continuum model.