Semiphenomenological model to predict hardening of solid-liquid-liquid systems by liquid bridges

In this study, we developed two semiphenomenological models to quantitatively predict the rheological properties of capillary suspensions. These models can be used to estimate the critical volume fraction of an additional immiscible fluid above which liquid bridges have formed between all neighboring particles, causing gelation. The models can also be used to estimate the numerical value of the yield stress. This model was derived from the mass balance between the net volume of the liquid bridge and the volume fraction of the secondary fluid assuming monodisperse particles and a cylindrical liquid bridge. The yield stress was constructed based on Rumpf's equation. The calculation results demonstrated good agreement with the experimental data. We also used the developed model to investigate the effect of particle size on the yield stress. This model qualitatively described the experimental data and reference data, and revealed the mechanism of the particle size dependence of the yield stress. The model applies to capillary suspensions in the pendular state.