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.

稠密悬浮液经收缩段向下游流动时，通常会发生稀释。我们发现，当剪切增稠悬浮液通过窄口模挤出并伴随此类液体迁移时，挤出物的浓度保持稳定，且与时间和初始浓度均无关。在低体积流量Q条件下，该稳定浓度为Q/r³的普适函数（其中r为口模半径，Q/r³即为口模内的特征剪切速率），且与液体迁移起始时的临界入口浓度一致。我们通过耦合用于描述剪切增稠现象的Wyart-Cates模型(Wyart-Cates model)与用于描述溶剂透过颗粒的悬浮液平衡模型(suspension balance model)，推导出了这一函数关系。