Liquid Migration in Shear Thickening Suspensions Flowing through Constrictions

Dense suspensions often become more dilute as they move downstream through a constriction. We find that as a shear-thickening suspension is extruded through a narrow die and undergoes such liquid migration, the extrudate maintains a steady concentration, independent of time or initial concentration. At low volumetric flow rate Q, this concentration is a universal function of Q/r^3, a characteristic shear rate in the die of radius r, and coincides with the critical input concentration for the onset of liquid migration. We predict this function by coupling the Wyart-Cates model for shear thickening and the 'suspension balance model' for solvent permeation through particles.