Liquid migration in shear thickening suspensions flowing through constrictions

Dense particulate 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 $\phi_c$, independent of time or initial concentration. This concentration $\phi_c$ varies with volumetric flow rate $Q$ and die radius $r_{\rm d}$, but at low $Q$ collapses onto a universal function of $Q/r_{\rm d}^3$, a characteristic shear rate in the die. We explain quantitatively the onset of liquid migration in extrusion by coupling a recent model for discontinuous shear thickening and the `suspension balance model' for solvent permeation through particles.