Shear fronts in shear-thickening suspensions

We study the fronts that appear when a shear-thickening suspension is submitted to a sudden driving force at a boundary. Using a quasi-one-dimensional experimental geometry, we extract the front shape and the propagation speed from the suspension flow field and map out their dependence on applied shear. We find that the relation between stress and velocity is quadratic, as is generally true for inertial effects in liquids, but with a prefactor that can be much larger than the material density. We show that these experimental findings can be explained by an extension of a phenomenological model originally developed to describe steady-state shear thickening. This is achieved by introducing a sole additional parameter: the characteristic strain scale that controls the crossover from startup response to steady-state behavior. The theoretical framework we obtain points out a linkage between transient and steady-state properties of shear-thickening materials.