Unifying length-scale-based rheology of dense suspensions

Suspensions, comprising particles and fluid, play a crucial role across diverse domains, including in nature, such as submarine landslides, biological systems such as blood flows, as well as industrial materials like concrete. The rheology of these materials is a combination of both fluid and solid properties. This study introduces a dimensionless number derived from the ratio between characteristic length scales, offering a unified perspective on the rheology of dense suspensions across a spectrum from conditions where fluid-like effects dominate to regimes influenced by inertial forces. The derivation contained herein is strict, offering significant physical insight into these systems.