Unifying length-scale-based rheology of dense suspensions

We present a length-scale-based rheology for dense sheared particle suspensions as they transition from inertial- to viscous-dominated. We derive a length-scale ratio using straightforward physics-based considerations for a particle subjected to pressure and drag forces. In doing so, we demonstrate that an appropriately chosen length-scale ratio intrinsically provides a consistent relationship between normal stress and system proximity to its "jammed"or solidlike state, even as a system transitions between inertial and viscous states, captured by a variable Stokes number.